tag:blogger.com,1999:blog-45353678912379193122024-02-20T12:09:46.958-05:00Man OverBoardPaul Owen's boardgaming web logPaul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.comBlogger347125tag:blogger.com,1999:blog-4535367891237919312.post-69344874787507012502018-11-22T10:03:00.000-05:002018-11-22T10:03:22.590-05:00HiatusSince the signing of "Magnificent Marvels" in August, I had resumed posting weekly here about our design progress, about first impressions of various new and upcoming games, and especially about notes on game theory. At this point, more pressing opportunities demand my attention, so rather than continue to assemble an essay every Monday, I intend to shift my focus to other avenues of board game hobby exploration and creativity. I am grateful this Thanksgiving for my readers and their feedback. I will remain active on Twitter at <a href="https://twitter.com/PaulOwenGames">@PaulOwenGames</a>. Until another time when I have more to share, I wish everybody the best. Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-63036192753552282452018-11-19T06:34:00.000-05:002019-01-15T07:24:45.226-05:00Notes on combining sequential and simultaneous movesAs part of a series of discussions on <i>Games of Strategy</i>, I've written here about <a href="https://paulowengames.blogspot.com/2017/04/notes-on-games-with-sequential-moves.html">games with sequential moves</a> - those in which players "take turns" and each decision is made with full knowledge of the opponent's last decision - as well as <a href="https://paulowengames.blogspot.com/2018/09/notes-on-simultaneous-move-games-and.html">games with simultaneous moves</a> - those in which players make decisions not knowing which option an opponent has selected. Continuing our exploration of game theory, Dr. Wictz and I further discussed <a href="https://dr.wictz.com/2017/07/colloquium-on-games-of-strategy-chapter.html">games that combine sequential and simultaneous moves</a>.<br />
<br />
<a name='more'></a><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://kwanghui.com/mecon/value/media%20%20files/static%20graphics/jpegs/Segment%205/5_3_static_bs_game_tree.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://kwanghui.com/mecon/value/media%20%20files/static%20graphics/jpegs/Segment%205/5_3_static_bs_game_tree.jpg" data-original-height="318" data-original-width="500" height="203" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Game tree for "Battle of the Sexes"<br />
Source: "Managerial Economics Online," <br />
kwanghui.com/mecon</td></tr>
</tbody></table>
A simultaneous move pure strategy game can be converted into a sequential move game, which can change the outcome depending on the payoff matrix. When "The Battle of the Sexes" is a simultaneous coordination game (like "Will Harry Meet Sally?"), there are two equilibria, and the outcome is indeterminate. When it is sequential, the player moving first will select the option they prefer, and the player moving second will follow suit because it becomes the only beneficial option. The result is a first-player advantage, meaning that the player moving first maximizes their payoff.<br />
<br />
Suppose the tennis match we looked at in our examination of mixed-strategy games were converted into a sequential move game, perhaps because the defender can react quickly enough to defend either shot regardless of what the shooter decides to do. Then, by rollback analysis, the shooter will be motivated always to choose the shot that the defender is less effective at defending, and then the defender will defend it. The result is a second-player advantage; the first player can never maximize their payoff because the second player can always respond. If, on the other hand, a slower defender has a "tell" and commits to a defense before the shooter decides on their shot, then the shooter can always attack the weak side of the defense and maximize their payoff - again, a second-move advantage.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/s5SyMXpHKpG_C-Lentt3BT7dkT8=/fit-in/900x600/filters:no_upscale()/pic2576459.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="441" height="320" src="https://cf.geekdo-images.com/imagepage/img/s5SyMXpHKpG_C-Lentt3BT7dkT8=/fit-in/900x600/filters:no_upscale()/pic2576459.jpg" width="235" /></a>Recalling that we can model sequential games as a decision-tree network,
we then can represent each node of the sequential game as a
simultaneous game decision matrix whose outcome determines the next
branch of the sequential game. We discussed <a href="http://www.indieboardsandcards.com/index.php/games/the-resistance/"><i>The Resistance</i></a>, a hidden-identity game that consists of a sequence of simultaneous-decision games. The decision tree extends over five rounds in which each team seeks to win three rounds. Each round can itself be thought of as a sequential decision tree of simultaneous decisions - first voting whether to accept a mission team, and second among those on the team, deciding whether to support or sabotage the mission. <br />
<br />
A sequential game can have an equilibrium path that can be determined by roll-back analysis - pruning non-optimal branches of the tree from the end backward to the beginning. I described this processes in my discussion of <a href="https://paulowengames.blogspot.com/2018/09/bidding-and-game-theory.html">bidding and game theory</a>. But a sequential game can also proceed along an "off-equilibrium path" if players make non-optimal decisions - more common in complex games where the decision tree or simultaneous decision matrix defies complete analysis. <br />
<br />
A subgame is defined as part of a multi-move game that begins at a particular decision-tree node of the original game. A "subgame-perfect equilibrium (SPE)" is a set of strategies - one for each player - that defines the optimal decision at each node in the decision tree, whether or not that node is on the equilibrium decision tree path. No matter where the game may start, for every subgame, the SPE defines the optimal strategies for both players.<br />
<br />
Considering our <i>Resistance </i>example, information is incomplete, so players generally will signal intent in attempts to steer one another along a decision path to a subgame that is closer to their own best result. The success of those attempts depends on the credibility of the signal, and therein lies the heart of such social interactive games.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-20573916357612869712018-11-12T06:30:00.000-05:002018-11-19T06:34:29.884-05:00Top ten games with my wife - 2018 editionFour years ago I was inspired to identify <a href="https://paulowengames.blogspot.com/2014/10/top-ten-games-that-i-play-with-my-wife.html">the top ten games that my wife and I liked to play together</a>. We've played a lot of games since then, and added a lot of games to our collection. So I thought I'd revisit this question. We found it very difficult to narrow the list down to ten; there are a dozen not listed here that we could easily have included instead.<br />
<a name='more'></a><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/hm8S0Y-x41Pk-v8w86w1Tfdd-R4=/fit-in/900x600/filters:no_upscale()/pic3503838.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="532" data-original-width="800" height="132" src="https://cf.geekdo-images.com/imagepage/img/hm8S0Y-x41Pk-v8w86w1Tfdd-R4=/fit-in/900x600/filters:no_upscale()/pic3503838.jpg" width="200" /></a>#10. <a href="https://www.dailymagicgames.com/villages-of-valeria"><i>Villages of Valeria</i></a> (Designers <a href="https://boardgamegeek.com/boardgamedesigner/39311/rick-holzgrafe" title="Rick Holzgrafe">Rick Holzgrafe</a> and <a href="https://boardgamegeek.com/boardgamedesigner/48263/isaias-vallejo" title="Isaias Vallejo">Isaias Vallejo</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/70533/mihajlo-dimitrievski" title="Mihajlo Dimitrievski">Mihajlo Dimitrievski</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/28790/daily-magic-games" title="Daily Magic Games">Daily Magic Games</a>): I picked this up in a giveaway at UnPub 8 last March. It turns out to be a clever game of dukedom-building set in the same fantasy world as <i>Valeria Card Kingdoms </i>(below). The game tightly implements multi-use cards and an action-follow mechanic that reminds us of <i>Puerto Rico </i>and <i>Race for the Galaxy </i>in a cleaner format with much more transparent iconography.<br />
<i></i><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/APIeN3gNMNXKsa5-WGl6ccU1TMY=/fit-in/900x600/filters:no_upscale()/pic2919073.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="601" height="199" src="https://cf.geekdo-images.com/imagepage/img/APIeN3gNMNXKsa5-WGl6ccU1TMY=/fit-in/900x600/filters:no_upscale()/pic2919073.jpg" width="200" /></a></div>
#9. <a href="https://www.dailymagicgames.com/valeria-card-kingdoms"><i>Valeria Card Kingdoms</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/48263/isaias-vallejo" title="Isaias Vallejo">Isaias Vallejo</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/70533/mihajlo-dimitrievski" title="Mihajlo Dimitrievski">Mihajlo Dimitrievski</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/28790/daily-magic-games" title="Daily Magic Games">Daily Magic Games</a>): Keith Ferguson introduced me to <i>VCK </i>at Origins 2016, and I subsequently picked up my own copy. Kathy and I have always liked this engine-building dice-driven resource card game in a two-player format, but it turns out to be popular with our sons as a family game as well, which led us to pick up a couple of the expansions (to which the format is particularly well suited).<br />
<br />
#8. <a href="http://en.libellud.com/games/seasons"><i>Seasons</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/1532/regis-bonnessee" title="Régis Bonnessée">Régis Bonnessée</a>, Artists <a href="https://boardgamegeek.com/boardgameartist/36093/xavier-gueniffey-durin" title="Xavier Gueniffey Durin">Xavier Gueniffey Durin</a> and <a href="https://boardgamegeek.com/boardgameartist/12402/stephane-gantiez" title="Stéphane Gantiez">Stéphane Gantiez</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/9051/libellud" title="Libellud">Libellud</a>): I picked this up from the vendor at UnPub 5 on Darrell Louder's recommendation. It took Kathy and me a few plays to get the hang of the Magic-style card drafting and combo-building, but now we are quite taken with the card play in combination with the dice drafting and "seasonal" resource availability. <br />
<br />
<i></i>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/x9Dx4wvuVHM1hTTUAVTXlJPgB-k=/fit-in/900x600/filters:no_upscale()/pic1215969.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="431" height="200" src="https://cf.geekdo-images.com/imagepage/img/x9Dx4wvuVHM1hTTUAVTXlJPgB-k=/fit-in/900x600/filters:no_upscale()/pic1215969.jpg" width="143" /></a></div>
#7. <a href="https://boardgamegeek.com/boardgame/9216/goa"><i>Goa</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/381/rudiger-dorn" title="Rüdiger Dorn">Rüdiger Dorn</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/11901/oliver-freudenreich" title="Oliver Freudenreich">Oliver Freudenreich</a>, Publisher Z-man): We received this neo-classic as a Christmas gift from a very good friend five years ago, and it has evidently disappeared from retail distribution since then. It features a unique bidding process for obtaining resource and scoring tiles, as well as a clever interaction of functions that motivates both diversity and specialization.<br />
<br />
#6. <a href="http://www.7wondersduel.com/7wonders-duel.php?lang=en"><i>7 Wonders: Duel</i></a> (Designers<a href="https://boardgamegeek.com/boardgamedesigner/9714/antoine-bauza" title="Antoine Bauza"> Antoine Bauza</a> and <a href="https://boardgamegeek.com/boardgamedesigner/1727/bruno-cathala" title="Bruno Cathala">Bruno Cathala</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/12016/miguel-coimbra" title="Miguel Coimbra">Miguel Coimbra</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/4384/repos-production" title="Repos Production">Repos Production</a>): This more recent Christmas gift re-formats the excellent multi-player drafting game <i>7W </i>into a much better designed-for-two structure than the original's two-player variant with a dummy third player. We have yet to try out the <i>Pantheon </i>expansion.<br />
<br />
<i></i>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/vpYjo5kF2wGzbxl4hmen6Fwf1AI=/fit-in/900x600/filters:no_upscale()/pic3596681.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="418" height="200" src="https://cf.geekdo-images.com/imagepage/img/vpYjo5kF2wGzbxl4hmen6Fwf1AI=/fit-in/900x600/filters:no_upscale()/pic3596681.jpg" width="138" /></a></div>
#5. <a href="https://czechgames.com/en/codenames-duet/"><i>Codenames: Duet</i></a> (Designers <a href="https://boardgamegeek.com/boardgamedesigner/789/vlaada-chvatil" title="Vlaada Chvátil">Vlaada Chvátil</a> and <a href="https://boardgamegeek.com/boardgamedesigner/68016/scot-eaton" title="Scot Eaton">Scot Eaton</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/28450/tomas-kucerovsky" title="Tomáš Kučerovský">Tomáš Kučerovský</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/7345/czech-games-edition" title="Czech Games Edition">Czech Games Edition</a>): Like <i>7W:D</i>, this recent release is a re-formatted two-player version of a multi-player game, and a brilliantly executed one at that. The only cooperative game on this list, <i>C:D </i>puts us on the same team to give each other clues using the same set of 25 options. <br />
<br />
#4. <a href="https://store.greaterthangames.com/new-bedford.html"><i>New Bedford</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/74432/nathaniel-levan" title="Nathaniel Levan">Nathaniel Levan</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/60615/nolan-nasser" title="Nolan Nasser">Nolan Nasser</a>, Publisher <a href="https://boardgamegeek.com/boardgamepublisher/17424/greater-games-dice-hate-me-games" title="Greater Than Games (Dice Hate Me Games)">Greater Than Games</a>): I fell in love with this game <a href="https://paulowengames.blogspot.com/2013/10/congress-of-gamers-2013-part-3-new.html">when its prototype first appeared at Congress of Gamers</a> five years ago. It remains a favorite combination of worker placement with the <i>Puerto Rico</i> bilateral structure of town building and shipping (or in this case whaling). <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/U8jHB2HvA0zh88uCI0wkXMqEQoo=/fit-in/900x600/filters:no_upscale()/pic714825.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="427" height="200" src="https://cf.geekdo-images.com/imagepage/img/U8jHB2HvA0zh88uCI0wkXMqEQoo=/fit-in/900x600/filters:no_upscale()/pic714825.jpg" width="141" /></a></div>
#3. <a href="http://riograndegames.com/Game/65-Caylus"><i>Caylus</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/5629/william-attia" title="William Attia">William Attia</a>, Artists <a href="https://boardgamegeek.com/boardgameartist/4009/cyril-demaegd" title="Cyril Demaegd">Cyril Demaegd</a>, <a href="https://boardgamegeek.com/boardgameartist/12886/arnaud-demaegd" title="Arnaud Demaegd">Arnaud Demaegd</a>, and <a href="https://boardgamegeek.com/boardgameartist/11858/mike-doyle-i" title="Mike Doyle (I)">Mike Doyle</a>, Publisher Rio Grande): This grandfather of worker placement games deserves a special place among the neo-classic European games of our time. Although stronger at higher player counts, the game holds up well under its two-player variant.<br />
<br />
#2. <a href="http://riograndegames.com/Game/4-Puerto-Rico">Puerto Rico </a>(Designer <a href="https://boardgamegeek.com/boardgamedesigner/117/andreas-seyfarth" title="Andreas Seyfarth">Andreas Seyfarth</a>, Artists <a href="https://boardgamegeek.com/boardgameartist/4959/harald-lieske" title="Harald Lieske">Harald Lieske</a> and <a href="https://boardgamegeek.com/boardgameartist/11883/franz-vohwinkel" title="Franz Vohwinkel">Franz Vohwinkel</a>, Publisher Rio Grande): Another neo-classic European game that belongs in a hall of fame, <i>PR </i>was never intended for two players. As I've mentioned several times in this blog, we did find a <a href="https://boardgamegeek.com/filepage/39937/soloplay-puertorico-v1pdf">variant on bgg</a> that we like.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/sgZLoyg3KKeHvyHel8tZ2TIkXRw=/fit-in/900x600/filters:no_upscale()/pic3536616.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="602" height="198" src="https://cf.geekdo-images.com/imagepage/img/sgZLoyg3KKeHvyHel8tZ2TIkXRw=/fit-in/900x600/filters:no_upscale()/pic3536616.jpg" width="200" /></a></div>
#1. <a href="https://strongholdgames.com/store/terraforming-mars-line/terraforming-mars/"><i>Terraforming Mars</i></a> (Designer <a href="https://boardgamegeek.com/boardgamedesigner/52075/jacob-fryxelius" title="Jacob Fryxelius">Jacob Fryxelius</a>, Artist <a href="https://boardgamegeek.com/boardgameartist/62819/isaac-fryxelius" title="Isaac Fryxelius">Isaac Fryxelius</a>, Publisher <a href="http://strongholdgames.com/">Stronghold Games</a>): I picked this up on sale at our friendly local <a href="https://www.theislandg.com/">Island Games</a> store, and it quickly became a favorite. I actually didn't expect Kathy to like it, but she gave it a try, and before I knew it, she beat me in the first three games we played. So I guess she picked it up pretty well. It's a solid favorite now. <br />
<br />
Only one of these ten games<i> - Puerto Rico</i> - was on this list four years ago. Eight of the other nine games are new acquisitions since then. We still play all the games on the original list, except that <i>7 Wonders:Duel </i>has replaced <i>7W</i> as a two-player game altogether.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com1tag:blogger.com,1999:blog-4535367891237919312.post-10354521848910548082018-11-05T06:30:00.000-05:002018-11-12T15:19:12.136-05:00Highest-rated out-of-print games - 2018 editionFour years ago I identified the <a href="https://paulowengames.blogspot.com/2014/10/most-highly-rated-out-of-print-games.html">top five out-of-print games</a> on boardgamegeek. Since then, a number of games have found new life as reprints, so I thought the topic worth revisiting to see what's "hot but hard to find."<br />
<a name='more'></a><br />
In some cases there are games that the publisher says are unavailable but that retailers still have plenty of copies available, like <a href="https://www.fantasyflightgames.com/en/products/star-wars-rebellion/products/star-wars-rebellion/"><i>Star Wars: Rebellion</i></a>. In that case, the publisher probably has another print run in work, so the game is likely to remain available for the foreseeable future. My focus here is on games that can't generally be found in normal retail channels because the publisher has not maintained it in production or distribution.<br />
<br />
I had expected to include <i><a href="https://na.merch.riotgames.com/en/other/board-games/mechs-v-s-minions-wave-3.html">Mechs vs. Minions</a> </i>on this list as a Kickstarter-only release, but I have come to learn that Riot Games has made it available for direct purchase and in fact is in their third printing.<br />
<br />
A special case is <a href="https://www.fantasyflightgames.com/en/products/android-netrunner-the-card-game/"><i>Android: Netrunner</i></a>, a living card game from 2012 that Fantasy Flight retooled in a "revised edition" last year but which has been <a href="https://icv2.com/articles/news/view/40610/fantasy-flight-license-android-netrunner-ending">discontinued</a> due to a license agreement with Wizards of the Coast that was not renewed. The core set remains available in retail for the time being.<br />
<br />
So here are the top five bgg-ranked games that appear to be unavailable through retail or direct purchase:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/-2wTSEgRqYRs45f7Lgtm9LNZXEw=/fit-in/900x600/filters:no_upscale()/pic2648303.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="434" height="200" src="https://cf.geekdo-images.com/imagepage/img/-2wTSEgRqYRs45f7Lgtm9LNZXEw=/fit-in/900x600/filters:no_upscale()/pic2648303.jpg" width="144" /></a><br />
#14. <i><a href="https://the7thcontinent.seriouspoulp.com/en/">The 7th Continent</a></i> (designers Ludovic Roudy and Bruno Sautter, artist Ludovic Roudy, publisher Serious Poulp): The publisher released it for Kickstarter backers only in 2017, and conducted a second Kickstarter campaign, but never intended it for normal retail distribution.<br />
<br />
#32. <i><a href="http://www.eaglegames.net/product-p/101053.htm">Through the Ages: A Story of Civilization</a> </i>(designer Vlaada Chvatil, artists Richard Cortes and Paul Niemeyer, publishers Czech Board Games and Eagle-Gryphon Games): This 2006 release has been supplanted by <i>Through the Ages: A New Story of Civilization</i>, which is ranked #3 on bgg at this writing. A few copies of the original can still be found on Amazon at what appear to be after-market prices.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/k3PWtaZqHdpPBrAGd5yg4EKACbU=/fit-in/900x600/filters:no_upscale()/pic1974056.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="519" data-original-width="800" height="129" src="https://cf.geekdo-images.com/imagepage/img/k3PWtaZqHdpPBrAGd5yg4EKACbU=/fit-in/900x600/filters:no_upscale()/pic1974056.jpg" width="200" /></a></div>
#36. <i><a href="https://www.lautapelit.fi/Eclipse">Eclipse</a> </i>(designer Touko Tahkokallio, artists Ossi Hiekkala and Sampo Sikiö, publisher Lautopelit.fi): This 2011 game's last English edition was released in 2015 and appears unavailable except on Amazon at a significant premium. Next spring, Lautapelit.fi will release a reimplemention as <i>Eclipse: Second Dawn of the Galaxy</i>. <br />
<br />
#48. <i><a href="https://boardgamegeek.com/boardgame/12493/twilight-imperium-third-edition">Twilight Imperium: Third Edition</a> </i>(designer Christian T. Peterson; Artists Scott Schomburg, Brian Schomburg, and Tyler Walpol; publisher Fantasy Flight): This 2005 game has been supplanted by a Fourth Edition, which is ranked #17 on bgg now.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/Nqc9yJOIhqZYndGPVn8k_syri4Q=/fit-in/900x600/filters:no_upscale()/pic180538.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="578" data-original-width="800" height="144" src="https://cf.geekdo-images.com/imagepage/img/Nqc9yJOIhqZYndGPVn8k_syri4Q=/fit-in/900x600/filters:no_upscale()/pic180538.jpg" width="200" /></a></div>
#56. <i><a href="http://boardgamegeek.com/boardgame/93/el-grande">El Grande</a> </i>(designers
Wolfgang Kramer and Robert Ulrich, artist Doris Matthäus, publisher Rio
Grande): This game was #21 on bgg when it appeared on my list of unavailable games four years ago. The English-language 1996 edition has not been carried by Rio Grande for some time. Rather, Z-man in 2015 released an <i>El Grande Big Box </i>that includes the core game along with six expansions.<br />
<br />
The last time I compiled a list like this, four of the five titles had no prospects for follow-ons. Only one - <i>Command and Colors: Ancients</i> - was a candidate for re-print as part of GMT Games's P500 program, and it did in fact see a 2014 fifth edition release. This time, most of the titles listed had some kind of follow-on that rendered the original obsolete. Even the one Kickstarter-only title had - or will have - a second release in the form of another Kickstarter campaign fulfillment.<br />
<br />
So there has been something of an evolution in the game market that seems to keep the highest-rated titles available in one form or another, which is, I suppose, as it should be.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-62838348669071321622018-10-29T06:30:00.001-04:002021-10-25T06:59:17.861-04:00Notes on simultaneous-move games with continuous strategies<span style="font-family: inherit;">My recent posts on <a href="https://paulowengames.blogspot.com/search/label/Game%20theory">game theory</a> have focused on games with discrete strategies, which is to say that players are faced with a finite number of choices for each decision. Some time ago, in our colloquium on games of strategy, Aaron Honsowetz, Austin Smokowicz, and I discussed <a href="https://dr.wictz.com/2017/05/colloquium-on-games-of-strategy-chapter.html">games with continuous strategies</a> (also on <a href="https://www.youtube.com/watch?v=UN-TJb1rkM8">video</a>) - those games in which players choose a value on a spectrum, such as a price to set on a commodity. </span><br />
<a name='more'></a><span style="font-family: inherit;"><span style="font-family: inherit;"><br />
<span style="font-family: inherit;">Simultaneous games with discrete strategies lend themselves to tabular analysis, which is to say that a decision in the game can be represented by a cross-matrix between one player's decision options and the other's. In a game of continuous strategies, the number of options becomes too large to express as a table in a practical way, so instead such games can be expressed graphically or even algebraically.</span></span></span><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"> </span><br />
</span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><a href="https://images-na.ssl-images-amazon.com/images/I/41SU8PZFiKL._SX355_BO1,204,203,200_.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="357" height="320" src="https://images-na.ssl-images-amazon.com/images/I/41SU8PZFiKL._SX355_BO1,204,203,200_.jpg" width="228" /></a></span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
<span style="font-family: inherit;">The example with which <a href="https://www.amazon.com/Games-Strategy-Fourth-Avinash-Dixit/dp/0393124444/ref=pd_sbs_14_1?_encoding=UTF8&pd_rd_i=0393124444&pd_rd_r=9079eb71-dacd-11e8-8b2a-43f93729c796&pd_rd_w=Z9gA5&pd_rd_wg=VAXKz&pf_rd_i=desktop-dp-sims&pf_rd_m=ATVPDKIKX0DER&pf_rd_p=7d5d9c3c-5e01-44ac-97fd-261afd40b865&pf_rd_r=YCQABY8J71SP12GVH537&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&psc=1&refRID=YCQABY8J71SP12GVH537">Dixit Skeath and Reilly</a> illustrate this concept is a town with two restaurateurs (Xavier and Yvonne), each of whose quantity of customers depends both on their own menu price and on the other's. Xavier attracts more customers the lower his price (<i>P<span style="font-size: xx-small;">X</span></i>) is <u>and</u> the higher Yvonne's price (<i>P<span style="font-size: xx-small;">Y</span></i>) is. Let's suppose market analysts have established the following linear relationship that describes the expected quantity of customers for Xavier (<i>Q<span style="font-size: xx-small;">X</span></i>): </span><br />
</span></span><br />
<div style="text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><i>Q<span style="font-size: xx-small;">X</span></i> = 44 - 2 <i>P<span style="font-size: xx-small;">X</span></i> + <i>P<span style="font-size: xx-small;">Y</span></i></span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
<span style="font-family: inherit;"><br /></span>
<span style="font-family: inherit;">Likewise Yvonne can expect a certain number of customers <i>Q<span style="font-size: xx-small;">Y</span></i> based on the same two prices:</span><br />
</span></span><br />
<div style="text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><i>Q<span style="font-size: xx-small;">Y</span></i> = 44 - 2 <i>P<span style="font-size: xx-small;">Y</span></i> + <i>P<span style="font-size: xx-small;">X </span></i></span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span>
<div style="margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">But customer volume alone does not determine success; it is important to be profitable. Each customer represents a marginal profit equal to the difference between the price charged and the cost of providing the meal. Total profit is the product of that per-customer marginal profit times the number of customers. So Xavier's total profit<i> R</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i> is represented by </span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
<br />
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;"><i>R</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i> = ( <i>P</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i> – 8 ) * <i>Q</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i></span></div>
<div style="margin-bottom: .0001pt; margin: 0in;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;">= ( <i>P</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i> – 8 ) * <span style="mso-bidi-font-style: italic;">( </span>44 - 2 <i>P</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">X</span></sub></i> + <i>P</i><i><sub><span style="mso-bidi-font-size: 7.5pt;">Y</span></sub></i><span style="mso-bidi-font-style: italic;"> )</span></span></div>
<div style="margin-bottom: .0001pt; margin: 0in;">
<br /></div>
<span style="font-family: inherit;">For any given competitor price <i>P<sub>Y</sub></i><sub>
</sub>, Xavier wants to select a price <i>P<sub>X</sub></i> that maximizes his
profit <i>R<sub>X</sub></i>. So we’ll re-write the equation for <i>R<sub>X</sub></i> in a way that we can optimize for <i>P<sub>X</sub></i> as
an independent variable. </span></span></span><br />
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span><span style="font-family: inherit;"><span style="font-family: inherit;"></span></span>
<br />
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><i>R<sub>X</sub></i>
= - 8 * ( 44 +<i> P</i><i><span style="font-size: 7.5pt;">Y</span></i> ) + (44 +
16 + <i>P</i><i><span style="font-size: 7.5pt;">Y</span></i>)<i> P</i><i><span style="font-size: 7.5pt;">X</span></i> - 2<i>P</i><i><span style="font-size: 7.5pt;">X</span></i>
<sup>2</sup></span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span>
<div style="margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><br /></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;">= - 8
* ( 44 +<i> P</i><i><span style="font-size: 7.5pt;">Y</span></i> ) + (60 + <i>P</i><i><span style="font-size: 7.5pt;">Y</span></i>)<i> P</i><i><span style="font-size: 7.5pt;">X</span></i>
- 2<i>P</i><i><span style="font-size: 7.5pt;">X</span></i> <sup>2</sup></span></div>
<br />
<span style="font-family: inherit;">Now for a fixed <i>P<sub>Y</sub></i>
we’ve written <i>R<sub>X</sub></i> as a quadratic in <i>P<sub>X</sub></i>. We can set its
derivative to zero to find the price <i>P<sub>X</sub></i> at which profit <i>R<sub>X</sub></i> is a maximum:</span></span></span><br />
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span>
<br />
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">0 = (60
+ <i>P</i><i><span style="font-size: 7.5pt;">Y</span></i>)<i> </i>- 4<i>P</i><i><span style="font-size: 7.5pt;">X</span></i></span> </span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span><br />
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><i>P</i><i><span style="font-size: 7.5pt;">X</span></i> = (60 + <i>P</i><i><span style="font-size: 7.5pt;">Y</span></i>)<i> </i>/ 4</span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;">= 15
+ <i>P</i><i><span style="font-size: 7.5pt;">Y</span> </i>/ 4</span></div>
<br />
<span style="font-family: inherit;"> This linear equation for <i>P<sub>X</sub></i>
as a function of <i>P<sub>Y</sub></i> is called a <b style="mso-bidi-font-weight: normal;">best response curve</b>. It represents Xavier’s best response to any price
that his competitor Yvonne might set. </span></span></span><span style="font-family: inherit;"><span style="font-family: inherit;"><br />
<span style="font-family: inherit;"> </span></span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieRKNpi9O0cLJzspfmTIOiMauzdcSbUAPNGdG72NoD80gBW95rkJeVXMJoIpdXZ3M3haGNLUHlwHFK_8M2_ls49RVtlAC_2sAqtws5mr6foKhb-pndAYI9v508tJFYEQgGeqx96Pe_dbyx/s1600/Price+best+response+curves.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="530" data-original-width="549" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieRKNpi9O0cLJzspfmTIOiMauzdcSbUAPNGdG72NoD80gBW95rkJeVXMJoIpdXZ3M3haGNLUHlwHFK_8M2_ls49RVtlAC_2sAqtws5mr6foKhb-pndAYI9v508tJFYEQgGeqx96Pe_dbyx/s320/Price+best+response+curves.png" width="320" /></a></span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;">Yvonne can likewise calculate her
best response curve, and by virtue of the symmetric nature of this particular
situation, we find that it is represented by a similar equation: </span></span></span><span style="font-family: inherit;"><span style="font-family: inherit;"></span></span><br />
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="font-family: inherit;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: inherit;"><i>P</i><i><span style="font-size: 7.5pt;">Y</span></i> = 15 + <i>P</i><i><span style="font-size: 7.5pt;">X</span> </i>/ 4</span></span></span></div>
<span style="font-family: inherit;"><span style="font-family: inherit;">
</span></span><span style="font-family: inherit;"><span style="font-family: inherit;">
<br />
<span style="font-family: inherit;">Dixit Skeath and Reilly assert that
the Nash equilibrium resides at the intersection of these two curves (what
mathematicians would call the solution of the system of two linear equations). </span>That solution resides at <i>P<sub>X</sub></i>
= <i>P<sub>Y</sub></i> = $20. At that point, each restaurateur makes a profit
of
$20 - $8 = $12 per customer and
attracts </span></span>44 – 2*20 + 20 = 24 customers for a total profit of
$12 * 24 = $288.<br />
<br />
Why should we believe that this
point represents the Nash equilibrium? We can evaluate what happens if one
restaurateur unilaterally changes their price. Say for example that Xavier attempts
to attract more customers by dropping his price to $19. He now attracts 44 – 2*19
+ 20 = 26 customers but reduces his profit margin to $11 for a total profit of
$281, which is seven dollars less than if he’d stayed at $20. Similarly, if he
increases his price to $21 to raise his profit margin to $13, he only attracts
22 customers, for a total profit of $286 – again, less than if he’d stayed at
$20. Yvonne faces the same math and likewise maximizes profit by adhering to
the $20 price. Thus, that price point represents a Nash equilibrium.<br />
<br />
Note that if Xavier and Yvonne could
trust one another to fix the price at a higher point, say $25, then they both
would make a greater profit: $17 per customer and 19 customers for a total of
$323. But then each would be motivated to secretly undercut the other to attract
more business and increase their own total profit. This situation represents a “continuous
strategy” version of a prisoner’s dilemma in which both could do better if they
cooperated, but the possibility of betrayal yields an equilibrium with lower
pay-off for both.<br />
<br />
So we can extend game theory
analysis to games with continuous strategies, <i style="mso-bidi-font-style: normal;">i.e.</i> a range of options that does not lend itself to tabular
explication. And my <a href="https://paulowengames.blogspot.com/2018/10/notes-on-games-with-mixed-strategies.html">post
two weeks ago on mixed strategies</a> extends to such continuous strategy games
if they introduce best response curves that don’t yield a pure Nash
equilibrium.<input id="idg-io-safe-browsing-enabled" oninit="true" type="hidden" />Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-39854707550074964102018-10-22T06:30:00.000-04:002019-01-04T20:58:13.839-05:00European board games before Catan<br />
Game designer Rob Newton <a href="https://twitter.com/CoinFlipGames/status/1044402921734107136">asked on Twitter</a> what people would consider "classic literature of the board game world." Fellow designer Jonathan Weaver <a href="https://twitter.com/j_weaves/status/1044567350727651329">responded</a> in three categories - citing Chess and Go as "ancient literature," <i>Monopoly </i>as "classic American literature," and then added, "whatever the predecessor of <i>Catan </i>is would be classic European literature." Some time ago, I was inspired to go back and look at <a href="https://paulowengames.blogspot.com/2012/09/boardgame-landscape-76-years-ago.html">what board games Americans had available to them when <i>Monopoly </i>arrived</a>. Now I was faced with a similar question for Europe before <i>Catan</i>. I already knew that <i>Clue </i>was originally English and <i>Risk </i>came from a French design, but Weaver's response made me realize that I really couldn't identify other European games released prior to 1995. Surely <i>Catan</i> couldn't have been the first popular European board game, so I felt that some self-education was in order.<br />
<a name='more'></a><br />
First I turned to boardgamegeek to identify games originally published in Europe that are highly rated by today's audiences. I identified the 11 currently most highly rated games originally published or otherwise originated in Europe prior to 1995. These are all in the top 600 on boardgamegeek: <br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/Gfi8ft4lV1hUrTQOc_mkEf9xuk0=/fit-in/900x600/filters:no_upscale()/pic169494.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="439" height="200" src="https://cf.geekdo-images.com/imagepage/img/Gfi8ft4lV1hUrTQOc_mkEf9xuk0=/fit-in/900x600/filters:no_upscale()/pic169494.jpg" width="146" /></a></div>
<ol>
<li><i>Tichu</i> - German publisher Fata Morgana Spiele, 1991</li>
<li><i>Die Macher </i>- German publisher Hans im Glück, 1986</li>
<li><span style="font-style: italic;">Modern Art</span><i> </i>- German publisher Hans im Glück, 1992</li>
<li><i>Blood Bowl</i> - British publisher Games Workshop, 1994</li>
<li><i>Space Hulk</i> - British publisher Games Workshop, 1989</li>
<li>Contract Bridge - originated in the Russian community in Istanbul, documented in 1886</li>
<li><i>HeroQuest </i>- British publisher Milton Bradley UK, 1989</li>
<li> <i>Britannia</i> - British publisher Gibsons Games, German publisher Welt der Spiele, 1986</li>
<li><i>Cribbage</i> - British, early 1600s</li>
<li><i>6 Nimmt!</i> - German publisher Amigo, 1994</li>
<li><i>Formula Dé</i> - French publisher Ludodélire, 1991 </li>
</ol>
I identified some others that are familiar to many people based on the number of ratings they received. All of these have over 8000 ratings:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/-Q8tuo_T8R7k5fx5UF17EtFThHU=/fit-in/900x600/filters:no_upscale()/pic361348.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="714" height="167" src="https://cf.geekdo-images.com/imagepage/img/-Q8tuo_T8R7k5fx5UF17EtFThHU=/fit-in/900x600/filters:no_upscale()/pic361348.jpg" width="200" /></a></div>
<ul>
<li><i>Risk</i>, a re-implementation of <i>La Conquete du Monde</i> - French publisher Miro Company, 1957</li>
<li><i>Clue</i>, originally <i>Cluedo </i>- British publisher Waddingtons, 1949</li>
<li><i>Scotland Yard</i> - German publisher Ravensburger, 1983</li>
<li><i>Stratego</i>, originally <i>L'Attaque</i> - French publisher Au Jeu Retrouvé, 1910</li>
<li><i>Labyrinth</i> - German publisher Ravensburger, 1986
</li>
</ul>
But then I extended the investigation to consider what the award-winning games were prior to 1995, thinking that such awards might better reflect the board game culture of the time - or at least the most highly thought-of by some. Here are the winners of the <i>Spiel des Jahres</i>, the German Game of the Year, prior to 1995:<br />
<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="false"
DefSemiHidden="false" DefQFormat="false" DefPriority="99"
LatentStyleCount="375">
<w:LsdException Locked="false" Priority="0" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 9"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="header"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footer"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index heading"/>
<w:LsdException Locked="false" Priority="35" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="table of figures"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="envelope address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="envelope return"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="line number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="page number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="table of authorities"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="macro"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="toa heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 5"/>
<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Closing"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Signature"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="true"
UnhideWhenUsed="true" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Message Header"/>
<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Smart Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hashtag"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Unresolved Mention"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:8.0pt;
mso-para-margin-left:0in;
line-height:107%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<blockquote class="tr_bq">
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/GHlRUSE1xcQql8uOMmiGOvz382U=/fit-in/900x600/filters:no_upscale()/pic1431211.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="596" height="200" src="https://cf.geekdo-images.com/imagepage/img/GHlRUSE1xcQql8uOMmiGOvz382U=/fit-in/900x600/filters:no_upscale()/pic1431211.jpg" width="198" /></a></div>
<span style="color: black;">1979</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><a href="https://boardgamegeek.com/boardgame/361/hare-tortoise"><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;">Hare & Tortoise</span></u></a><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><span style="color: black;"> </span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1980</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/811/rummikub">Rummikub</a></span></u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><span style="color: black;"> </span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1981</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/789/focus">Focus</a></span></u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><span style="color: black;"> </span></span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1982</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/938/enchanted-forest">Enchanted
Forest </a></span></u></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1983</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/438/scotland-yard">Scotland Yard</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1984</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/539/dampfross">Dampfross</a></span></u></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1985</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/2511/sherlock-holmes-consulting-detective-thames-murder">Sherlock
Holmes Consulting Detective: The Thames Murders & Other Cases</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1986</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/382/heimlich-co">Heimlich & Co.</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1987</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/110/auf-achse">Auf Achse</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1988</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/550/barbarossa">Barbarossa</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1989</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/214/cafe-international">Café
International</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1990</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/120/hoity-toity">Hoity Toity</a></span></u> </div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1991</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/19/wacky-wacky-west">Wacky Wacky West</a></span></u><i> </i></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1992</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/442/um-reifenbreite">Um Reifenbreite</a></span></u></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1993</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/45/liars-dice">Liar's Dice</a></span></u><i> </i></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<span style="color: black;">1994</span><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><span style="mso-tab-count: 1;"> </span></span><u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"><a href="https://boardgamegeek.com/boardgame/199/manhattan">Manhattan</a></span></u><i> </i></div>
</blockquote>
All have European origins but three. <i>Rummikub </i>was designed by Ephraim Hertzano, who published it under Hertzano Ltd in Israel in 1977. <i>Focus </i>is a Sid Sackson design originally published in America by Whitman Publishing in 1965. <i>Liar's Dice </i>is a public domain game believed to have originated in South America in the early 19th century. (I couldn't ascertain whether <i>Sherlock Holmes</i>, originally released by Sleuth Publications, was European or not; I'm assuming that it was originally British.) Those three exceptions aside, most are German, as one might expect; a few are British, and one (<i>Um Reifenbreite</i>, a re-implementation of <i>Homas Tour</i>) was originally Dutch.<br />
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 5.75pt; margin-right: 0in; margin-top: 0in;">
<u><span style="color: #0563c1; mso-ascii-font-family: Calibri; mso-bidi-font-family: Calibri; mso-hansi-font-family: Calibri;"></span></u><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"></span></div>
<br />
The <i>SdJ </i>list provides some insight in the pre-<i>Catan </i>European board game landscape. It's helpful to go back and see how long some familiar titles have been around, or to consider games that perhaps have faded somewhat in their recognizability.<br />
<br />
So to answer Rob Newton's original question, which of these would we consider "classic European literature in the board game world"? For my part, I might nominate the following (in no particular order) from the above lists for their familiarity, staying power, and influence on subsequent game design:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/BzGB8ZyGGdvUkvoiIuPEMLuV4FA=/fit-in/900x600/filters:no_upscale()/pic2602138.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="461" height="200" src="https://cf.geekdo-images.com/imagepage/img/BzGB8ZyGGdvUkvoiIuPEMLuV4FA=/fit-in/900x600/filters:no_upscale()/pic2602138.jpg" width="153" /></a></div>
<ul type="disc">
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">6 Nimmt!</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
</span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Clue /</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
<i>Cluedo</i></span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Contract Bridge </span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Cribbage</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
</span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Modern Art </span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"></span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Risk /</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
<i>La Conquete du Monde</i> </span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Scotland Yard</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
</span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Sherlock Holmes Consulting Detective</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"></span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Stratego</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
/ <i>L'Attaque</i> </span></li>
<li class="MsoNormal" style="line-height: normal; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; tab-stops: list .5in;"><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Tichu</span></i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;">
</span></li>
</ul>
<div class="MsoNormal">
Others might come up with different lists (and are welcome to do so). For my part, these are the titles that seem to come up in conversation most today in one form or another. The bottom line, of course, is that I've become more aware of the pre-<i>Catan </i>European board game world now, and I hope others have, too.</div>
<ol>
</ol>
Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-83411982269267294862018-10-15T06:30:00.000-04:002018-10-29T23:05:09.881-04:00Notes on games with mixed strategies<!--[if gte mso 9]><xml>
<o:OfficeDocumentSettings>
<o:AllowPNG/>
</o:OfficeDocumentSettings>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:DoNotShowPropertyChanges/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:EnableOpenTypeKerning/>
<w:DontFlipMirrorIndents/>
<w:OverrideTableStyleHps/>
</w:Compatibility>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="false"
DefSemiHidden="false" DefQFormat="false" DefPriority="99"
LatentStyleCount="375">
<w:LsdException Locked="false" Priority="0" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index 9"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 9"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="header"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footer"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="index heading"/>
<w:LsdException Locked="false" Priority="35" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="table of figures"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="envelope address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="envelope return"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="footnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="line number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="page number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote reference"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="endnote text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="table of authorities"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="macro"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="toa heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 5"/>
<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Closing"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Signature"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="true"
UnhideWhenUsed="true" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Message Header"/>
<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="List Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="List Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Mention"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Smart Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hashtag"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Unresolved Mention"/>
</w:LatentStyles>
</xml><![endif]--><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-priority:99;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin-top:0in;
mso-para-margin-right:0in;
mso-para-margin-bottom:8.0pt;
mso-para-margin-left:0in;
line-height:107%;
mso-pagination:widow-orphan;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;
mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin;
mso-bidi-font-family:"Times New Roman";
mso-bidi-theme-font:minor-bidi;}
</style>
<![endif]-->
<br />
<div class="MsoNormal">
In an earlier post regarding <a href="https://paulowengames.blogspot.com/2018/09/notes-on-simultaneous-move-games-and.html">theory of simultaneous move games</a>, I concluded with an example of a game between two tennis players that did not demonstrate a Nash equilibrium between its two pure strategies. Sam Hillier: Consulting Philosopher more recently elaborated on the topic with an excellent post on <a href="https://philosocopter.com/news/2018/10/11/mixin-it-up">mixed strategies</a>. Whereas I had
approached the question of an equilibrium for a <u>single</u> tennis shot and
concluded that none existed, a tennis match of course includes <u>many</u>
shots, so players have an opportunity to invoke a weighted mix of shots and
defenses between the two options.<br />
<a name='more'></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQEdzy5coq_muzQ_gErHPUqdUgEcEIX9CyUF1mFd9yBHQMZilHgETf9kizy56WWCXRQLeqDkyvo_0H9aQ6Jb6AYqpfX5IJHbJGNS0sdDAVO0nLsCM71gcy4FqUgCs5POLuZL4DtJgvmg4p/s1600/Tennis.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="402" data-original-width="451" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQEdzy5coq_muzQ_gErHPUqdUgEcEIX9CyUF1mFd9yBHQMZilHgETf9kizy56WWCXRQLeqDkyvo_0H9aQ6Jb6AYqpfX5IJHbJGNS0sdDAVO0nLsCM71gcy4FqUgCs5POLuZL4DtJgvmg4p/s200/Tennis.JPG" width="200" /></a></div>
<div class="MsoNormal">
To recap, the two-player zero-sum simultaneous-move game represents a tennis volley in which one player - the defender - decides whether to defend a
shot down the line (D) or cross court (C) at the same time the opponent - the shooter - decides which type of shot to attempt. The payoff is depicted as the
probability of the shot scoring a point in a 2x2 matrix cross-referencing each player's decision with the other's. The shooter seeks to maximize that result; the defender wants to minimize it.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Sam stipulated that in a game of mixed strategies between C and D, “the server will shoot C 30% of the time … while the defender will defend against
C 40% of the time,” but didn't explain where those mixed strategy results came from. There’s a little arithmetic in figuring that out that arises
from approaching the problem by trying to “minimize the maximum loss.” </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Suppose <i style="mso-bidi-font-style: normal;">p</i>
represents the frequency with which the shooter will select C. The shooter
wants to maximize the worse case score regardless of the defender’s choice. If
the defender chooses C, then the shooter’s expected value of the result will be</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">E<sub>C</sub></i> = 0.2<i style="mso-bidi-font-style: normal;">p</i> +
0.8(1-<i style="mso-bidi-font-style: normal;">p</i>)</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
If the defender chooses D, the shooter’s expected result is</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">E<sub>D</sub></i> = 0.9<i style="mso-bidi-font-style: normal;">p</i> +
0.5(1-<i style="mso-bidi-font-style: normal;">p</i>)</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
To avoid the defender exploiting one better result over
another, the shooter will find the frequency <i style="mso-bidi-font-style: normal;">p</i> that gives the same result regardless of the chosen defense by
setting the expected values equal to each other:</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">E<sub>C</sub></i> = <i style="mso-bidi-font-style: normal;">E<sub>D</sub></i></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
0.2<i style="mso-bidi-font-style: normal;">p</i> + 0.8(1-<i style="mso-bidi-font-style: normal;">p</i>) = 0.9<i style="mso-bidi-font-style: normal;">p</i> + 0.5(1-<i style="mso-bidi-font-style: normal;">p</i>)</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">p</i> = (0.8 – 0.5) / (0.9 – 0.5 – 0.2 + 0.8) </div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
= 0.3/1.0 </div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
= 30%</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
This result means that if the shooter chooses C 30% of the
time, their expected score will be </div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">E<sub>C</sub></i> = 0.2(0.3) + 0.8(1-0.3) = 0.62 </div>
<div align="center" class="MsoNormal" style="text-align: center;">
or</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">E<sub>D</sub></i> = 0.9(0.3) + 0.5(1-0.3) = 0.62</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
regardless of the defender’s choice. If the shooter chooses
C less frequently (<i style="mso-bidi-font-style: normal;">i.e. p</i> < 30%),
the defender can always choose D and cause a lower shooter score. Similarly, if
the shooter chooses C more frequently, the defender can always choose C and again
cause a lower shooter score. So, the shooter’s best mixed strategy is to choose C 30% of
the time.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Similar analysis – whereby the defender attempts to minimize
the maximum possible shooter score – results in the defender choosing C</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<i style="mso-bidi-font-style: normal;">q</i> = (0.9 – 0.5) / (0.8 – 0.5 – 0.2 + 0.9) </div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
= 0.4/1.0 </div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
= 40%</div>
<div class="MsoNormal">
of the time.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Sam also discusses the idea of Evolutionary Game Theory, which interests me
from the standpoint that superior strategies can emerge in a population of game
players without necessarily invoking explicit analysis. In fact, most games are
sufficiently complex that exhaustive analysis is not possible, and the
evolutionary strategies that emerge may demonstrate consistent success without
a complete understanding of why they succeed. I expect Dr. Wictz and I will discuss that topic at some point in the future as well.</div>
Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-86963548500697961492018-10-08T06:30:00.000-04:002018-10-15T06:32:17.425-04:00Spies vs spies: First impression of Cold Warrior<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjwSgMbax-dQwwm2Z-LqqgouT6kszPjeB65Og1OS1J5-hb6m89Fb_X83rOmporFx-P7tHIWTnF1G9I7I2IwVIvB_rPkbIbAJq14aOKkC-cdmkdfFFBKWpTKuJd40x_JVNMG_2RPlnzSgrD/s1600/Cold+Warrior.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="1600" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjwSgMbax-dQwwm2Z-LqqgouT6kszPjeB65Og1OS1J5-hb6m89Fb_X83rOmporFx-P7tHIWTnF1G9I7I2IwVIvB_rPkbIbAJq14aOKkC-cdmkdfFFBKWpTKuJd40x_JVNMG_2RPlnzSgrD/s320/Cold+Warrior.jpg" width="320" /></a></div>
I have long felt that the Cold War represents a rich thematic opportunity for board games. Yet I can identify only a handful of games set in that NATO-Soviet contest of diplomacy, espionage, and brinkmanship that rank in the top 1000 of boardgamegeek.* Into this cloak-and-dagger arena the new designer Wes Crawford introduces <a href="https://www.thegamecrafter.com/games/cold-warrior?dept_uri=games&dept_name=All%20Games"><i>Cold Warrior</i></a> (artist Jimmy Malone, published on Game Crafter).<br />
<a name='more'></a><br />
This head-to-head card game pits two thinly-veiled fictional nations - the "United Provinces" and the "People's Socialist Union" - in a spy-counterspy conflict. Each player has a team of Agents numbered 001-016. Right away, this three-digit Agent numbering evokes the iconic Ian Fleming novels of 007, and it is this kind of thematic flavor that permeates <i>Cold Warrior</i>. Manila envelope graphic design and heavy use of the <span style="font-family: "courier new" , "courier" , monospace;">Courier typeface </span>further evoke the 20th century era of typewriters and hardcopy files. Agent names are a mix of plays on actual historical figures (my favorite is Olivia North) and silly puns (like the muscleman Gargan Chuen).<br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMe0XWgnuhM2rxH10Pm0dOZM9xRFcg_UEZlSahCbHUENmBFRNrRpGYFkBYBXi3uRtJZnpcSLw6ibkxB_iCitrKMQiA24EDiH78Z4gKV1OhhlTVu0wZ2COQuih60AwUp8glMkIWI16TokZO/s1600/Cold+Warrior+-+Leonid+Rasputin+%25282%2529.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="642" data-original-width="401" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMe0XWgnuhM2rxH10Pm0dOZM9xRFcg_UEZlSahCbHUENmBFRNrRpGYFkBYBXi3uRtJZnpcSLw6ibkxB_iCitrKMQiA24EDiH78Z4gKV1OhhlTVu0wZ2COQuih60AwUp8glMkIWI16TokZO/s320/Cold+Warrior+-+Leonid+Rasputin+%25282%2529.jpg" width="198" /></a>Each Agent has a Value for conducting espionage missions, a Counter Intelligence rating for defending against the opponent's missions, a specialized ability associated with certain types of missions, and ratings in strength, intelligence, martial arts, language, and computer skills. Oddly, these last five stats occupy over a third of the real estate on each Agent card but only weigh in on the outcome of a few specific events - assassination attempts, a few mission requirements, certain mission "adventures" (random modifiers to missions), and a very few others.<br />
<br />
Particularly clever is the presence of a "Mole" in the opponent's intelligence agency. At the start of the game, each player randomly chooses and sets out of play one of his own Agents. The only purpose that card serves is to identify the "Mole" among the opponent's Agents as the one with the matching ID number. So for example, the People's Socialist Union player randomly selects his Agent 008 "I. Kant Singh" and sets him aside, out of play. The PSU player now secretly knows that United Provinces Agent with the same number, Agent 008 "Robert Bedlam," is actually a Mole working for the PSU. Likewise, the UP player will secretly identify which of the PSU Agents is secretly a Mole working for the UP. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicg1NP1OJLuPGf5_ggyZpr5gdO8svdVU87oz2ose6QBgOSnH06hUTuibTUWnOxYYHH7kzQrg5ZMnx8ARK97nPXvre1SFzIEqwWPTaz_DPhvFDAouNh11zqoctia_JCRWmwhd6fGUTZDIec/s1600/Cold+Warrior+-+Crisis+Mission+1.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="657" data-original-width="404" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicg1NP1OJLuPGf5_ggyZpr5gdO8svdVU87oz2ose6QBgOSnH06hUTuibTUWnOxYYHH7kzQrg5ZMnx8ARK97nPXvre1SFzIEqwWPTaz_DPhvFDAouNh11zqoctia_JCRWmwhd6fGUTZDIec/s320/Cold+Warrior+-+Crisis+Mission+1.jpg" width="195" /></a></div>
A Mission deck provides opportunities to progress toward winning the game. Each mission includes some flavor description, such as "recruit valuable military defector" or "break opponent's codes." Four types of missions - political, intelligence, military-industrial, and crisis - can be executed in one of four different geographic regions - Major Powers, Third World East, Third World West, and the opponent's home country. Crisis Missions uniquely require the player to complete them within two turns of drawing them or else lose significant points. Unfortunately the game provides no means of tracking how long a player has held a Crisis Mission and therefore whether they have exceeded the turn limit for completion.<br />
<br />
Beyond Missions, players can also score bonus points by completing a secretly selected National Strategic Objective, which typically requires completing several missions of a specific type or in a specific geographic area. It should be noted that since the NSOs depend on the type of missions completed, their success depends in part on drawing the right kinds of missions from the draw deck. <br />
<br />
Crucially, players must track not only which missions they successfully accomplish, but with which Agents. This requirement represents something of a record-keeping burden on the players. Missions completed with the Mole or with a Double Agent - and any National Strategic Objective those missions support - do <u>not</u> contribute to the player's score. Although the rules provide a helpful example of the information that players need to track with each completed mission, the game would benefit from a score pad with the required fields rather than depend on players to bring their own paper and keep the scoring straight themselves.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgntg9BlIYBeefOJvDc__KDFkz8PQuNvfZoKiMgcWt9MV4crlgUMuqu-lUxf-dJXK3bdOx_4UnZ2rZ8M4gLyT14ajEhyphenhyphenSS1lKzZNEderHRLSYI3NsKOnsOZKJ7_3907fuLuN079-koids30/s1600/Cold+Warrior+-+Mission+Aid+-+Code+Descrambler.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="668" data-original-width="437" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgntg9BlIYBeefOJvDc__KDFkz8PQuNvfZoKiMgcWt9MV4crlgUMuqu-lUxf-dJXK3bdOx_4UnZ2rZ8M4gLyT14ajEhyphenhyphenSS1lKzZNEderHRLSYI3NsKOnsOZKJ7_3907fuLuN079-koids30/s320/Cold+Warrior+-+Mission+Aid+-+Code+Descrambler.jpg" width="208" /></a></div>
Much of the game hinges on card play from a Cold Warrior deck of various thematically rich cards that affect mission success and other game factors. Assassins can take Agents out of action. Mission Aids can contribute to a mission success. Decoys allow players to feint a mission in one location to dilute the opponent's response in another. Players can mark enemy Agents with Tails or Suspicion to reduce their effectiveness - and in the worst case turn one into a Double Agent. Counter Intelligence Units contribute to defense against an opponent's mission and can shake Tails or remove Suspicion.<br />
<br />
The Tail and Suspicion cards - collectively called "mark cards" - represent some of the strongest thematic elements of the game. A player can reduce an enemy Agent's effectiveness by playing a "mark card" face down and sideways on an opponent's face-down card suspected of being an Agent. Face down "mark cards" reduce the target Agent's Value in completing a mission by one. The Tail can be turned face-up to reduce the target Agent's Value by two - suggesting that the "tail" is not trying to hide the fact that they are following the Agent in the open. Otherwise, "mark cards" remain face down until exposed by a sufficiently strong Counter Intelligence Unit or Agent. A Suspicion card - representing doubts being raised as to the loyalty of the Agent - can be either a False Suspicion (having no effect once exposed) or a Double Agent (rendering that Agent ineffective and negating any completed Mission scores in which that Agent participated).<br />
<br />
All of this leads me to an important point: The game cries out for a player aid. Available actions, effects of cards, the Mission Resolution process, the mechanics of "mark cards" - all beg for some kind of one-sheet aid to remind players how the game works and to answer frequently asked questions. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx8NHUtF5GLCaUop0SzVlhMt7WKYZ6sefT207oU_WA6nKp4SQlbbf6hYoW_F-j3hhYxLPi7xDT3D6uzS6RVQb01UXRvOvtrz8O1k9I51XMPtlOhwO_YRt5d-DhyphenhyphenJAzSBr7IkDZCZw6oiTc/s1600/Cold+Warrior+-+card+back.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="684" data-original-width="444" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx8NHUtF5GLCaUop0SzVlhMt7WKYZ6sefT207oU_WA6nKp4SQlbbf6hYoW_F-j3hhYxLPi7xDT3D6uzS6RVQb01UXRvOvtrz8O1k9I51XMPtlOhwO_YRt5d-DhyphenhyphenJAzSBr7IkDZCZw6oiTc/s320/Cold+Warrior+-+card+back.jpg" width="206" /></a></div>
Missions, Agents, and Cold Warrior cards all have the same backs so that they can be held in hand and played face down in a mission without revealing information to the opponent. This common back confuses the initial set-up, however, since cards must be separated into their separate stacks, and the Mission and Cold Warrior decks do not have designated locations on any play mat; the players must keep track of which deck is which.<br />
<br />
The overlap of rules and card effects, in which several different considerations can be in play at the same time, complicate the rules structure, with the result that many key rules end up surfacing late in the rulebook that answer questions and gaps in explanation early in the rules. In particular, "mark cards" are explained very late in the rulebook. The reader would benefit from an earlier explanation, when their effects and counters are discussed as part of the action descriptions. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVkLJvtgvaP-Dwax4KkUFX0L6GDpjwqEZk3dur_-bKtirLIjLo32VYAVhZeSav9eo8PzXgooixpKaBttGg0ylTsKFFe9q3-BlzaV_iBPJrse203iYO-tEgyyLPxf3fzqa5QsYUgrrl2Cr5/s1600/Cold+Warrior+-+Decoy.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="655" data-original-width="419" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVkLJvtgvaP-Dwax4KkUFX0L6GDpjwqEZk3dur_-bKtirLIjLo32VYAVhZeSav9eo8PzXgooixpKaBttGg0ylTsKFFe9q3-BlzaV_iBPJrse203iYO-tEgyyLPxf3fzqa5QsYUgrrl2Cr5/s320/Cold+Warrior+-+Decoy.jpg" width="203" /></a></div>
The rules have a few minor sources of confusion, such as when during Mission Resolution to turn cards face up and whether players can "Initiate a Mission" action with a Decoy instead of a Mission card.<br />
<br />
Perhaps the most problematic aspect of the game is the game end and scoring. A player can attempt to declare victory with 60 points - with 40 points if they have at least twice as many as their opponent. By way of perspective, a high-scoring mission might garner 15 points, and an NSO might add 25. We found that missions can fail as easily as they can succeed, and failed missions can yield negative points. So there is a risk that a game could perpetuate indefinitely without any kind of countdown mechanism. Fortunately the rules allow for two variants to cap the play-time - a literal time-limit mutually agreed to by players, and a six-turn "short game."<br />
<br />
In short, <i>Cold Warrior </i>strongly conveys its theme of espionage, secret agents, and international intrigue in every play of a card. Clearly the Cold War setting informed the rules and cards at every step of design. The game would have benefited from further development, however, to give players some means to mitigate card luck in the direction of strategy, as well as player aids, rulebook organization, and graphic design to more clearly depict game-relevant information.<br />
<br />
<i>The designer provided a review copy of </i>Cold Warrior.<br />
<br />
==<br />
<br />
* The five Cold War games that I found in the top 1000 on boardgamegeek are<br />
<ul>
<li><i>Twilight Struggle</i></li>
<li><i>1989: Dawn of Freedom</i></li>
<li><i>13 Days: The Cuban Missile Crisis</i></li>
<li><i>Wir sind das Volk</i> </li>
<li><i>Kremlin</i></li>
</ul>
I'm happy to hear from readers who can identify other top-1000 Cold War board games.<i> </i>Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com3tag:blogger.com,1999:blog-4535367891237919312.post-19094955723419338462018-10-01T06:30:00.001-04:002021-10-18T07:24:19.155-04:00Quick draw: First impression of Death Pit Duels<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/HyLHRRET71mqtRLwmubak5qwLgA=/fit-in/900x600/filters:no_upscale()/pic2943829.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="526" data-original-width="800" height="131" src="https://cf.geekdo-images.com/imagepage/img/HyLHRRET71mqtRLwmubak5qwLgA=/fit-in/900x600/filters:no_upscale()/pic2943829.jpg" width="200" /></a></div>
In the world of head-to-head two-player battle card games, I'd be hard pressed to name a more distilled, purified entry than <a href="https://www.thegamecrafter.com/games/death-pit-duels?dept_uri=games&dept_name=All%20Games"><i>Death Pit Duels</i></a> (designer Bryan Johnson, publisher Frost Forge on Game Crafter).<br />
<br />
<a name='more'></a>
Let's start with the draft. The game features a single deck of combatants in four races, each with a combat value from two to eight. From six quick rounds of I-split-you-choose, each player ends up with a stable of 12 combatants ready to go. Each player then shuffles their respective combatant deck. That's all there is to the first half of the game.<br />
<br />
The second half is 12 combat rounds, each for a prize of a coin (that is, a card with a coin printed on it) valued between three and seven points. Each player randomly deals out one combatant, then simultaneously plays one card from a hand of "Duel" cards numbered from one to 12 to augment the combatant's strength. The strength of each combatant, plus any special power modifications, plus the player's revealed Duel card determines which player wins the prize. A tie leaves the prize on the table, plus a one-value coin, which move on to the next duel. Each combatant and each Duel card is used exactly once, so while the combatants emerge in random order, the challenge to players is deciding when to toss the cheap Duel cards and when to go big.<br />
<br />
There's a deftness to the I-split-you-choose draft. The player who is "splitting" the draftees has five random combatants from which to form two pairs; the opponent will choose one pair and leave the "splitter" with the other. If players ignore the special powers, there's very little decision-making in balancing the two pairs evenly. But some combatants have bonuses against certain other races, so there's value in paying attention to what the opponent has drafted - and splitting or choosing accordingly. Other combatants gain randomized bonuses from a die or from a "prisoner" deck, so it's important to pay attention to their expected values as well.<br />
<br />
In combat, there is a temptation to throw away cheap cards at three-coin battles and play the big ones for the seven-coin battles, but here again, paying attention to the difference between the combatants and which cards an opponent has already played can yield opportunities for stealing a battle with a cheap card. There is also an opportunity for bluffing an opponent into spending a high-value Duel card while tossing a low-value card, leaving oneself with a stronger hand for the later game.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/8jNUHGV0G5IessnwlG6RdKcnNNA=/fit-in/900x600/filters:no_upscale()/pic3122988.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="309" data-original-width="800" height="153" src="https://cf.geekdo-images.com/imagepage/img/8jNUHGV0G5IessnwlG6RdKcnNNA=/fit-in/900x600/filters:no_upscale()/pic3122988.jpg" width="400" /></a></div>
<br />
The illustrations by <a href="http://alishadoesart.com/index.html">Alisha Volkman</a> are cartoonish and the physical quality is basic, which is in keeping with the light nature of the gameplay. For those concerned about representation, all of the human-race combatants and all the prisoners are white males, although there's no player-identification associated with those characters. <br />
<br />
All in all, <i>Death Pit Duel </i>is at its heart a light quick two-player filler. If you like something short and sweet that you can knock out in 20 minutes but still put a little thought and second-guessing into, this game will fill that niche.<br />
<br />
<i>The designer Bryan Johnson provided a complimentary copy of the game without condition. </i><input id="idg-io-safe-browsing-enabled" oninit="true" type="hidden" />Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-22203388307910672722018-09-24T06:30:00.001-04:002021-10-13T08:26:20.397-04:00Notes on simultaneous-move games, and an exploration of the Stag Hunt<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzFG0WnWc1fXgjGt8OzJ6l7ib5-yOTfzWoC3qoqhPnFk5xpnuTgiuc4ARd3bwYMPNQdY-6IMmzKHXWC58MjggUfu0QNbCvtsjTa1-FsmsBCheJPoceqkqI_L7ZyMiXjsnpYZiQ34DVkRKV/s1600/Games+of+Strategy+223+%25282%2529.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="359" data-original-width="264" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzFG0WnWc1fXgjGt8OzJ6l7ib5-yOTfzWoC3qoqhPnFk5xpnuTgiuc4ARd3bwYMPNQdY-6IMmzKHXWC58MjggUfu0QNbCvtsjTa1-FsmsBCheJPoceqkqI_L7ZyMiXjsnpYZiQ34DVkRKV/s200/Games+of+Strategy+223+%25282%2529.jpg" width="146" /></a></div>
Some time ago, the design team of Dr. Wictz and I started discussing the book <i>Games of Strategy</i> by Dixit, Skeath, and Riley. I wrote on a couple of topics:<br />
<ul>
<li><a href="http://paulowengames.blogspot.ca/2017/02/notes-on-games-of-strategy.html">Games of Strategy</a> (an overview of terminology) and</li>
<li><a href="http://paulowengames.blogspot.ca/2017/04/notes-on-games-with-sequential-moves.html">Games with Sequential Moves</a></li>
</ul><p>
In this post, I'd like to address simultaneous-move games with a specific focus on pure discrete strategies. (We <a href="https://dr.wictz.com/2017/04/colloquium-on-games-of-strategy-chapter.html">recorded</a> our discussion on this topic in April of last year.) I recall such games represented in my earliest readings on game theory in the form of a decision-payoff matrix. In a two-player game in which each player makes a single decision from among a finite number of choices, without knowledge of the other player's decision, the decision-payoff matrix labels the rows with one player's options and the columns with the other player's options. The corresponding cell for a given combination of decisions yields the payoff to both players. </p><p></p><a name='more'></a>
These are the purest simultaneous-move discrete-strategy games - each player faces a single decision based on known payoff results of all possible decisions but without knowing the decision of the other player beforehand. A payoff matrix cross-indexing each player's decision options to yield their payoffs can represent the game in an abstract, analyzable way. For example, suppose the two players are hunters, and each has the option to cooperate to pursue a stag, or to go off independently to hunt a hare. This Stag Hunt game is discussed nicely by Sam Hillier on his <a href="https://philosocopter.com/news/2018/9/14/the-stag-hunt">Consulting Philosopher blog</a>, which inspired me to explore it a little more closely in the context of our game theory book study. In the matrix below, I represent the decision options of each player as 'S' for "Stag" or 'H' for "Hare." Let's assume that if both players hunt for the stag, each is rewarded with enough meat for three days, but if one hunts for the stag alone, he receives nothing. A player who hunts for a hare is rewarded with enough meat for himself alone for one day. <br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgENFIEDY_bPXJDv8Rx5Uy-hwJ56M4mH8TtS9lrIf4hiFCgchb_4gsUSGvQgdV5spe8wUgF_lsxbMxzaZRSNhvPvwETAQGfKyVlcwT7ARzoy0eZlH8dpiPI_fXG7ACjvCmiUtANIkCvxvkO/s1600/Stag+Hunt.JPG" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="474" data-original-width="543" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgENFIEDY_bPXJDv8Rx5Uy-hwJ56M4mH8TtS9lrIf4hiFCgchb_4gsUSGvQgdV5spe8wUgF_lsxbMxzaZRSNhvPvwETAQGfKyVlcwT7ARzoy0eZlH8dpiPI_fXG7ACjvCmiUtANIkCvxvkO/s200/Stag+Hunt.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Stag Hunt payoff matrix</td></tr>
</tbody></table>
In each cell of the payoff matrix, the upper right value is Player B's payoff, and the lower left is Player A's. (I've color-coded them for clarity.) Both players are better off if they decide to hunt the stag, but if one fears that the other will hunt for a hare, he is better off abandoning the stag and hunting for a hare himself. Thus the 'S' strategy is not stable, and in the absence of any communication, the rational outcome is that the two players hunt for hares rather than risk going hungry.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimJI-MOAdSv356IRM9UIWFrL9l0gs5k2V8JUQ-WhdCTSND2f2dLhcm6WJE7uh4e8ao1cncxuhWcUu70l9oUgo0AUQGXvd-0saeOINJkcCeQW9rhfiTqf2gtOyCDteQO-caLPgA_JEwBwLk/s1600/Prisoners+Dilemma.JPG" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="474" data-original-width="666" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimJI-MOAdSv356IRM9UIWFrL9l0gs5k2V8JUQ-WhdCTSND2f2dLhcm6WJE7uh4e8ao1cncxuhWcUu70l9oUgo0AUQGXvd-0saeOINJkcCeQW9rhfiTqf2gtOyCDteQO-caLPgA_JEwBwLk/s200/Prisoners+Dilemma.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Prisoners' Dilemma payoff matrix</td></tr>
</tbody></table>
People are generally more familiar with the Prisoners' Dilemma, which is similar - but not the same. Two prisoners kept in isolation each face charges of conspiracy to murder (carrying a sentence of 25 years) and kidnapping (3 years). The police have sufficient evidence to convict both of kidnapping but need testimony from one to convict the other of murder. The police offer each prisoner to drop the murder charge and reduce the kidnapping sentence to one year to testify against the other - but if both prisoners testify, the police will only reduce the charge to ten years for each. Here sentences are represented by negative numbers, and each player seeks to minimize their sentence.<br />
<br />
In the interest of comparison, let's normalize the Prisoners' Dilemma to payoffs comparable to the Stag Hunt. I'll map values as follows:<br />
<ul>
<li>-25 => 0</li>
<li>-10 => 1</li>
<li>-3 => 2</li>
<li>-1 => 3</li>
</ul>
Now let's look at the normalized Prisoners' Dilemma in comparison to the Stag Hunt:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikE7C9NyPmvlJSCjfy894wv9BiE_Lx8dxbbBZVSWhYs5hMHvjpmGlrQWyTK_Vb1yB9fQLd95kIjMJKl7NUx0UloKiUrP9pyJ7YSIdolkx3WuqCi02DXd8QTZ_bxFQX6seauANprk4sh4xR/s1600/Comparison.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="549" data-original-width="1194" height="147" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikE7C9NyPmvlJSCjfy894wv9BiE_Lx8dxbbBZVSWhYs5hMHvjpmGlrQWyTK_Vb1yB9fQLd95kIjMJKl7NUx0UloKiUrP9pyJ7YSIdolkx3WuqCi02DXd8QTZ_bxFQX6seauANprk4sh4xR/s320/Comparison.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Normalized comparison of Stag Hunt and Prisoners' Dilemma</td></tr>
</tbody></table>
The important difference here is that each player in the Stag Hunt is motivated to cooperate in hunting for the stag if they believe their counterpart will do the same, whereas in the Prisoners' Dilemma, each player is better off defecting and testifying against their counterpart even if they believe their counterpart would cooperate in an agreement not to do so. Ironically, both players' payoffs would be better if they both cooperated, <i>i.e.</i> if neither testified against the other, but the payoff matrix renders that equilibrium point unstable.<br />
<br />
In a later post I hope to explore the significance of communication, or signaling, among players in a game. Clearly players are motivated to communicate and foster trust in the Stag Hunt, whereas the Prisoners' Dilemma fosters suspicion and is ripe for betrayal.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCuzb3F5ixuVCotsVA9t64zYY2FiAETG_T8ZOUgTnsysqSeIjM5WsjdMkKkQpcr2KeydR3Sj02pnGQVF8jnQfb8X4WSTQClbt9d-rvlifHFPkDOapkIMFHAk0y0cfv16-8eNRRZTQyl17I/s1600/Stag+Hunt+winner-take-all.JPG" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="554" data-original-width="636" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCuzb3F5ixuVCotsVA9t64zYY2FiAETG_T8ZOUgTnsysqSeIjM5WsjdMkKkQpcr2KeydR3Sj02pnGQVF8jnQfb8X4WSTQClbt9d-rvlifHFPkDOapkIMFHAk0y0cfv16-8eNRRZTQyl17I/s200/Stag+Hunt+winner-take-all.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Stag Hunt in a winner-take-all format</td></tr>
</tbody></table>
There was some discussion of the Stag Hunt on the <a href="http://dicehateme.com/2018/09/the-state-of-games-ep-156-the-one-about-mutually-assured-destruction/">State of Games podcast</a> as well, but they described the game in a winner-take-all format: The payoff for catching the stag went only to the player that delivered the killing blow, in some reward or recognition from the reigning noble. Now the payoff matrix must be tempered by each player's evaluation of their probability of winning the contest. If Player A evaluates their probability of killing the stag at less than 33%, then the expected value of their payoff in participating in the stag hunt falls to less than 1, and their decision matrix looks more like a Prisoners' Dilemma. Player A is better off hunting for a hare, and Player B is left to realize the same result, since he can't catch the stag alone.<br />
<br />
In general, when a given strategy is better for a player regardless of what action the opponent takes, that strategy is said to be <b>dominant</b>. Any strategy that is objectively worse than some other strategy, regardless of the opponent's action, is a <b>dominated </b>strategy. In the case of the winner-take-all Stag Hunt where one player's expected reward for the stag hunt is less than the hare, the hare (for that player) becomes the dominant strategy. The opponent's best strategy under that dominant strategy - to give up the stag and hunt for a hare as well - defines the <b>Nash equilibrium </b>for the game - the outcome that neither player can improve for themselves unilaterally.<br />
<br />
More complex simultaneous move games (those with more than two choices for each player) can be simplified by the elimination of dominated strategies from consideration. Best-response analysis consists of each player identifying their best response to each of the opponent's strategies. If any strategy combination between players is a best response for both, that combination is a Nash equilibrium (even if neither strategy is dominant).<br />
<br />
Some time ago, I tried a <a href="https://paulowengames.blogspot.com/2013/09/game-theory-simple-multi-player-case.html">game theory approach to a three-player game</a>, which involved multiple decision matrices among the players. The same general principles apply - best-response analysis identifies strategy combinations that result in a Nash equilibrium, as I found in my analysis of the three-player case.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE8h18rFCsSlWq1tBM2-_q8AA1FEre8at_M7bn8wgrTR05xjElNnd1SE83MuU2Yhyphenhypheni-rhSiHzMoErf_mEZa06MM06rgcz4x_cbJYl9n-YLuxcr3dcVNk3ZpgNrG5btTmW9hI57yAipNJmS/s1600/Will+Harry+Meet+Sally.JPG" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="559" data-original-width="559" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE8h18rFCsSlWq1tBM2-_q8AA1FEre8at_M7bn8wgrTR05xjElNnd1SE83MuU2Yhyphenhypheni-rhSiHzMoErf_mEZa06MM06rgcz4x_cbJYl9n-YLuxcr3dcVNk3ZpgNrG5btTmW9hI57yAipNJmS/s200/Will+Harry+Meet+Sally.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Coffee Shop 'C' Preferred By Both</td></tr>
</tbody></table>
Some games can have multiple equilibria. "Will Harry Meet Sally" supposes that two people agree to meet at a coffee shop, but they were not specific as to which of two favorite coffee shops to meet. If they are unable to communicate, each will have to decide where to show up and hope that the other is there. This situation is called a pure coordination game, and if there is a mutually agreeable reason to prefer one coffee shop over the other - and both players know that the other knows it is preferred - that preference or criterion is a focal point that facilitates the coordination even in the absence of communication between the players.<br />
<br />
I happened to notice that this payoff matrix looks like that of the Prisoners' Dilemma (or even the Stag Hunt) except that neither player is rewarded for defecting unilaterally. Both are purely motivated to coordinate their decisions.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpqSvEpPYiwOSeMK2DWuy185YjbCDMP6FZQhiLvaNRhoVzmj29VrHUrwxMaL59Mr9Pd02OrQ3JJ8x7e1D7gH9ZXNd5L9362_utReEBgSm9eu3fHdT3A60YILARr5BBQ8WDsEYRRM7qC7Y6/s1600/Battle+of+the+Sexes+-+simultaneous.JPG" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="555" data-original-width="549" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpqSvEpPYiwOSeMK2DWuy185YjbCDMP6FZQhiLvaNRhoVzmj29VrHUrwxMaL59Mr9Pd02OrQ3JJ8x7e1D7gH9ZXNd5L9362_utReEBgSm9eu3fHdT3A60YILARr5BBQ8WDsEYRRM7qC7Y6/s200/Battle+of+the+Sexes+-+simultaneous.JPG" width="197" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Sally likes 'C' better; Harry prefers 'D'</td></tr>
</tbody></table>
A variation on "Will Harry Meet Sally" is called the "Battle of the Sexes," where each prefers a different coffee shop but both prefer to be together than to be alone at either. I <a href="http://paulowengames.blogspot.com/2017/04/notes-on-games-with-sequential-moves.html">wrote about a sequential version </a>of "Battle of the Sexes"; this simultaneous version involves the two parties finding a focal point so that they can independently arrive at the same coffee shop.<br />
<br />
"Chicken" is a different kind of coordination game in which players drive cars straight toward each other with the payoff going to the player who stays the course if the other swerves to avoid the collision. The penalty for both staying the course, however, is significant. Coordination games like these typically motivate communication, or signaling, to influence an opponent's decision. I expect to discuss signaling and screening in later posts.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaYKhHJvK9eBPZBrU8QwjSA82Wlmm-r1zslMQ6J7izzT_i4nRWaye_KLk39zGoDQzaFdQJqKE-e-gq_yqjkMnieBpZG_wIWJwyXx4lfcQt6m-wEH-hil1Y0bLYtTuC-XyHaGlX1EDOCbXL/s1600/Tennis.JPG" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="402" data-original-width="451" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaYKhHJvK9eBPZBrU8QwjSA82Wlmm-r1zslMQ6J7izzT_i4nRWaye_KLk39zGoDQzaFdQJqKE-e-gq_yqjkMnieBpZG_wIWJwyXx4lfcQt6m-wEH-hil1Y0bLYtTuC-XyHaGlX1EDOCbXL/s200/Tennis.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">No equilibrium</td></tr>
</tbody></table>
Finally, a game can have no equilibrium at all, such as a tennis volley in which one player has to decide whether to defend a shot down the line or cross court at the same time the opponent is deciding which type of shot to attempt. If the payoff is depicted as the probability of the shot scoring a point (in which case the defender prefers as low a result as possible), there will be no combination of strategies whose result can not be improved upon by one player or the other. Best-response analysis will show that there is no strategy combination that is selected by both players.<br />
<br />
Even in the simplest simultaneous-move games, the configuration of the payoff matrix can drive very different player behavior. It will be interesting to uncover game design ramifications resulting from studying this theory, as Sam Hillier has done.<input id="idg-io-safe-browsing-enabled" oninit="true" type="hidden" />Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-49691917662559020832018-09-17T06:30:00.000-04:002018-11-15T22:47:21.533-05:00Magnificent feedback<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmZCNC1FUE0_OrPoCjxlIjowSxKNFj_IHa0hF6h72VeyZ7RwYszUltPr4D6sOLpJHOQp6Cfm06zea6_KZ8hQ-sVgTBYF6fb9tj9C_fyHygc2Wsvv_F92H_E014zdfch9Dm9T5mShPi7RT-/s1600/Integrator.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="500" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmZCNC1FUE0_OrPoCjxlIjowSxKNFj_IHa0hF6h72VeyZ7RwYszUltPr4D6sOLpJHOQp6Cfm06zea6_KZ8hQ-sVgTBYF6fb9tj9C_fyHygc2Wsvv_F92H_E014zdfch9Dm9T5mShPi7RT-/s200/Integrator.jpg" width="200" /></a></div>
Playtesting is crucial to any successful design, but the tricky part has often been which feedback to accept and which to ignore. Keith Ferguson and I really thought we had "Magnificent Marvels" nailed down when we pitched it at Origins and eventually <a href="https://paulowengames.blogspot.com/2018/08/magnificent-marvels-signed.html">signed it</a> with <a href="http://hexagram63gamesstudio.com/">Hexagram 63</a>. The publisher identified some modifications for us to explore, so Keith tested some changes out at WashingCon and again at The Island Games, our friendly local game store. The changes that Hexagram 63 requested seem to work well, but some other feedback that Keith received surprised us somewhat. We have to look hard at where to make changes and where to stick with our original design.<br />
<a name='more'></a><br />
"Magnificent Marvels" has a worker-placement aspect, with a twist that players don't get workers back until a player - any player - spends an action to clear a set of placement locations. This requirement introduces a game of "sequential chicken" in which each player may hold out in anticipation that another player will spend the action and send <u>everybody</u>'s workers back. This tension is a key aspect of the gameplay, one that Keith and I feel has become fundamental and which appealed to the publisher in the first place.<br />
<br />
Keith got some strongly negative feedback at WashingCon, however. In previous playtests, players acknowledged this conundrum as part of the game, but players at WashingCon really didn't like it, particularly when one player found themselves stuck with no other option. Players in that session wanted some compensation for the "returning workers" action.<br />
<br />
My own opinion was that the player who returns workers gets their own workers back, clears the area where they want to place workers, and improves the labor market (another mechanism I won't get into here). So it is inherently a choice that helps the player, even if it helps opponents, too. The worst case is when a player has one action left and the only option is to return workers; in that case, you've helped your opponents and done yourself very little good. That appears to be the main objection.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghRnYRUFSnw3y7QPiK8Drz2wO49JghBpkozuWFlkkgBgFdZSRrvgOkKOdgGXRcr9ZCctTJii3Pi_wjIpYVuT_EPZfsgaBl-VGuMUCWSIJNbcLcze0Xv5JM128HYL7nmXmi_swNhA8hPYSm/s1600/Starting+Player.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="173" data-original-width="265" height="130" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghRnYRUFSnw3y7QPiK8Drz2wO49JghBpkozuWFlkkgBgFdZSRrvgOkKOdgGXRcr9ZCctTJii3Pi_wjIpYVuT_EPZfsgaBl-VGuMUCWSIJNbcLcze0Xv5JM128HYL7nmXmi_swNhA8hPYSm/s200/Starting+Player.jpg" width="200" /></a></div>
Keith drew an analogy to the practice of giving a player a reward for spending an action to take the "first player" token in other worker-placement games. I can see that, although again, I consider the first-player token to have its own value and in some circumstances worth the action. But we're going to pay attention to the feedback Keith got and introduce a reward for the "return workers" action and see how it plays out.<br />
<br />
The thing I struggle with more generally is how quickly to react to a single feedback datum in the context of other playtest results. If I try to react to every comment I get from every playtester, I'll never settle on a design. If we observe a pattern (as we have with some other elements of the game), we know we need to take those results seriously and adjust the game accordingly. But sometimes, a single playtester's idea is brilliant, and other times that idea is contrary to the game's vision and shouldn't be incorporated.<br />
<br />
I think I come down to this conclusion: We need to weigh unique feedback against the vision of the game - the experience we want the players to have. If it's inconsistent with that vision, we can let it go. But the other side of the equation is that there's no harm in testing ideas. That's the part that Keith is better at than I am - the willingness to explore a new idea and see whether it has merit, even if it seems on face value as though we wouldn't like it.<br />
<br />
So we keep playtesting, we keep trying things, we keep polishing, we keep making it better - and we keep making it even more magnificent.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com1tag:blogger.com,1999:blog-4535367891237919312.post-67151431985266842172018-09-10T06:30:00.000-04:002018-09-17T20:34:43.233-04:00Bidding and game theory<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/HqTYxH2QsPkWAMCqlbuS_TQZhaY=/fit-in/900x600/filters:no_upscale()/pic1566274.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="426" height="200" src="https://cf.geekdo-images.com/imagepage/img/HqTYxH2QsPkWAMCqlbuS_TQZhaY=/fit-in/900x600/filters:no_upscale()/pic1566274.jpg" width="141" /></a>I have been thinking about the game theory construct for the share auction in <a href="https://boardgamegeek.com/boardgame/31730/chicago-express"><i>Chicago Express </i></a>(designer Harry Wu, publisher <a href="http://www.queen-games.com/en/">Queen</a>). The question isn't only one of absolute valuation but also one of the interactive decision-making in the auction. That thought led to consideration of the auction as a game-theory problem.<br />
<a name='more'></a><br />
In <i>CE</i>, players don't own railroads outright. Instead they buy shares of railroad companies at auction in anticipation of earning income from those shares later in the game. Let's simplify the problem and suppose that Anne initiates an auction for a share of Pennsylvania Railroad. Let's assume that both Anne and Bob value a share at $3. Let's further assume that Anne and Bob each have $5, and that the minimum bid with which Anne can open the auction is $1. (These aren't realistic values in <i>CE </i>but serve to illustrate this game theory case.)<br />
<br />
We can look at this auction as a game with sequential moves, which I <a href="https://paulowengames.blogspot.com/2017/04/notes-on-games-with-sequential-moves.html">wrote about</a> during our study of <i>Games of Strategy</i> by Dixit, Skeath, and Reilly. The auction is a fairly simple case of such a game that we can network fairly easily. Let's simplify the game one step further and say than on a turn, a player can either pass, or raise the opponent's bid by $1. We can create a network diagram showing the progress of the game from left to right, where each node is a player's decision point, and each arrow is the result of a decision at that point - whether the end of the game and a resultant score, or progress to an opponent's decision point. If Anne wins the auction, the value of the game is represented as the value of the share ($3) less what Anne paid for it - positive if she made a profit, negative if she paid too much for it. If Bob wins the auction, the value of the game is the opposite - how much he paid less the value of the share - so that Bob prefers a negative result, and Anne prefers a positive result.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4a9hlz1X8joiDKqYOttYmNqvwjkYfvsEoTWI3ZJsSlGDwmcm9nYhITcwygWBjB3lQ6bHtjDPD5PccWTcRkSzLiz2js5P6G6K0Ce66ezx_tXrMkwgnS_69xdX3OpGBxHPsiLdrJiV7Vqnm/s1600/Capture1.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="541" data-original-width="1463" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4a9hlz1X8joiDKqYOttYmNqvwjkYfvsEoTWI3ZJsSlGDwmcm9nYhITcwygWBjB3lQ6bHtjDPD5PccWTcRkSzLiz2js5P6G6K0Ce66ezx_tXrMkwgnS_69xdX3OpGBxHPsiLdrJiV7Vqnm/s640/Capture1.JPG" width="640" /></a></div>
Anne must bid 1 as her first move. Bob can either bid 2 or pass. If he passes, the value of the game is $3 less Anne's $1 bid, or +$2. If Bob bids 2, now Anne can either bid 3 or pass. If she passes, the value of the game is the $2 that Bob bid, less the $3 value of the share, for a result of -$1. The decision tree continues from left to right, until Anne bids $5, which ends the game because Bob does not have more than $5 to bid.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBx1nYt4Jxovtnt6Fn1M5_PH6vOa61fal5yB-UC1KHanKkacfSgS0dMlu04PAjjQXU0ZrHbpKRqWzxs89zZ7XCYANnmdnYkglnJgmGfGxcYSjSInVrlH72u6tB-z2-ZdWh94SKhzzYsPhm/s1600/Capture2.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="545" data-original-width="1473" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBx1nYt4Jxovtnt6Fn1M5_PH6vOa61fal5yB-UC1KHanKkacfSgS0dMlu04PAjjQXU0ZrHbpKRqWzxs89zZ7XCYANnmdnYkglnJgmGfGxcYSjSInVrlH72u6tB-z2-ZdWh94SKhzzYsPhm/s640/Capture2.JPG" width="640" /></a></div>
Now we can start pruning branches from the network that the players are not motivated to follow. If Bob bids $4, Anne will not bid $5 because she would lose $2; she would rather pass and see her opponent lose $1 instead (reflected as a +$1 value in the game). As we work our way backward, Bob realizes that if he bids $4, he will lose $1 because he knows Anne is motivated to pass, so he will pass instead. That means that Anne knows she will break even if she bids $3 because that is a better result than passing after Bob bids $2 and letting him gain a $1 profit. Bob likewise realizes that he is better off bidding $2 than passing and letting Anne gain a $2 profit. After pruning, the game is solved with the result that Anne will break even when she buys the share for $3.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpiiq3z-q-pzvuKytCKQ-h18DjYL15lazQj3uIuAmMsbjnxBXZ20fm0HRVat57U1hFarl7jcznpfX_2lM-gyHueNP3gCCXFkOw5BS4nwi1kuCCgESvIrPJJHt51hkmRzv6VTaq9ga9efUk/s1600/Capture3.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="541" data-original-width="1455" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpiiq3z-q-pzvuKytCKQ-h18DjYL15lazQj3uIuAmMsbjnxBXZ20fm0HRVat57U1hFarl7jcznpfX_2lM-gyHueNP3gCCXFkOw5BS4nwi1kuCCgESvIrPJJHt51hkmRzv6VTaq9ga9efUk/s640/Capture3.JPG" width="640" /></a></div>
Now, the game is actually a little more complicated, because players can raise their opponent by more than just one dollar. For Anne's first move, she can bid anywhere from $1 to $5. Bob's next move is either to pass (allowing Anne to take the share for the amount she bid) or to bid a higher value than Anne, but not more than $5. The result is a somewhat more elaborate decision network.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjte0AfWYw9XKQgYesEz8DO22hlulTmWTpfohOI6CS96v69pocpGG8XF-o81c99Ax3YBVY_p_cJX5VFhyphenhyphenOKlJe4rdDLcVmW0x0qfh_ZfGBfxYnVH07_44Vq_a4FLe3R7urlkQnPH8D9jWxL/s1600/Capture4.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="552" data-original-width="1467" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjte0AfWYw9XKQgYesEz8DO22hlulTmWTpfohOI6CS96v69pocpGG8XF-o81c99Ax3YBVY_p_cJX5VFhyphenhyphenOKlJe4rdDLcVmW0x0qfh_ZfGBfxYnVH07_44Vq_a4FLe3R7urlkQnPH8D9jWxL/s640/Capture4.JPG" width="640" /></a></div>
<br />
After going through the same pruning exercise, we find that the outcome of the game is that one player or the other will end up buying the share at its value of $3 for no profit and no loss. So at any point in the game, either player can either bid $3 to take the share, or bid $2 to force their opponent to take it. Since Anne is the first bidder, the decision is hers to make; if she bids $1, she is deferring that decision to her opponent.<br />
<br />
The game gets a little more interesting if the share has different value to the two players. If the share is worth $2 to Anne but $4 to Bob, Anne likely to bid $2 or $3. If she bids $2, Bob will buy it for $3 at a profit of $1; if she bids $3, Bob will pass and allow her to lose $1.<br />
<br />
The game is even more interesting if the players perceive the value of the share differently. If Anne believes it is worth $2 regardless of who owns it, and Bob believes it is worth $4, then Anne will bid $1 or $2, and Bob will buy it for $2 or $3.<br />
<br />
If the players misjudge how their opponents value the share, then each is essentially playing the game on a different decision tree, because they believe their opponent's decisions will be based on a different payout result. Suppose Anne values the share at $2 and believes Bob values it at $2 as well, but Bob values it at $4 and believes Anne does as well. He may bid $3 on the share to "force" Anne to bid $4, when instead she will pass and leave him with a profit of $1. If Bob had realized Anne valued the share at $2, he would have bid $2 to induce her to pass and gained a profit of $2.<br />
<br />
This observation leads to what Dr. Aaron Honsowetz of the <a href="https://dr.wictz.com/">Dr. Wictz design team </a>described to me as the <a href="https://en.wikipedia.org/wiki/Winner%27s_curse">Winner's Curse</a>, the phenomenon by which the person who most highly estimates the value of an auctioned item will bid the most and thereby win the item. Assuming that the actual value of the item is closer to the average estimate of the population of potential buyers, the winner is therefore likely to have overpaid for it.<br />
<br />
The motivation for this whole line of thinking was to consider bidding strategy in an auction game. I conclude that if a player doesn't know how his or her opponents value the share in question, it makes sense to bid or raise the minimum in the hope that all the opponents will drop out before the bid exceeds one's own valuation. But if that happens, the player is left to wonder if they've been stuck with a share that is worth less than they think. On the other hand, if the value of a share is relatively clear to all the players, then the logical play is either to bid the value of the share (to take control of it) or just a dollar less (to force an opponent to take it at essentially no profit).<br />
<br />
Sometimes I will underbid for a share by an amount equal to the number of players; <i>e.g.</i> if I value the share at $10 in a four-player game, I will bid $6. If every player raises the bid by $1, I'll still have the opportunity to buy it for $10 - or less, if anyone dropped out of the auction before my turn came up again. But that strategy can backfire if someone else jumps to a $10 bid first. So as is always the case in these games, reading the opponents is as important as valuation.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-77125659527450693162018-09-03T06:30:00.000-04:002018-09-10T07:37:51.500-04:00Magnificent spreadsheets<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGSHSNFHAB04iWFw5sh507Xv5c13I60efU3CLaQJONM5qTlYuf1mWmne6VsjOI4sxzlmMoWBkmyWAlcpZIIR5GTF0im0-ybPVD5WLifs5narcUQY2nUjOJCd2pQMZFQrzHXNzveux5LXx3/s1600/Magnificent+Marvels+spreadsheet+snip.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="336" data-original-width="901" height="74" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGSHSNFHAB04iWFw5sh507Xv5c13I60efU3CLaQJONM5qTlYuf1mWmne6VsjOI4sxzlmMoWBkmyWAlcpZIIR5GTF0im0-ybPVD5WLifs5narcUQY2nUjOJCd2pQMZFQrzHXNzveux5LXx3/s200/Magnificent+Marvels+spreadsheet+snip.JPG" width="200" /></a></div>
There was a bit of a comparative discussion on <a href="https://twitter.com/drwictz/status/1031878145270599680">Twitter </a>among a few game designers about the use of spreadsheets. For my part, I find them useful in maintaining balance in a game's economy, in the relative values of different components of the game. In "Magnificent Marvels," Keith and I recognized the need to be sure that the different components with widely varied point values would need appropriately balanced building costs, and we put together a spreadsheet to try to manage that.<br />
<a name='more'></a><br />
The core resource for player decisions is actions, which can be used to obtain money, more workers (by spending money), raw materials (by committing workers), and refined materials (by converting raw materials). So I put together the original spreadsheet of marvel components with a calculation on how many actions it would take to build each component, and then a ratio of points per action. The metric is not a perfect reflection of the cost-benefit value of each component, but it served as a helpful starting point. Very quickly, we got the game up and running based on our initial spreadsheet calculations.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXVoPvAM8HgQ5JW_bxc1j5qeYilpvO-KCi58xaxNtN3P0uaSIgHF972fWaJKfAH6_C9iTjYwMb2ZL16oaUyhq6qPDIQ3y-eXdt2X7IQEtcoIr0MtiKDmmoQcIR7imMsfJ1SLYFcjfvybty/s1600/Magnificent+Marvels+optiscope.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="186" data-original-width="279" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXVoPvAM8HgQ5JW_bxc1j5qeYilpvO-KCi58xaxNtN3P0uaSIgHF972fWaJKfAH6_C9iTjYwMb2ZL16oaUyhq6qPDIQ3y-eXdt2X7IQEtcoIr0MtiKDmmoQcIR7imMsfJ1SLYFcjfvybty/s200/Magnificent+Marvels+optiscope.JPG" width="200" /></a></div>
The Achilles heel of our design method came in our modifications to the game flow based on playtest results. One of the things we decided we needed to accelerate was refining materials, so we made the converters immediately available and more efficient in their conversions. What we didn't realize at the time was that we'd distorted the relationship between cost and point value for certain components that required several of the same refined material to build. Whereas they had originally taken perhaps six actions to assemble before (and therefore provided a high point value), the accelerating refining and other changes meant that really only three actions or so were now necessary to build the same component. It wasn't until one of our playtesters specifically pointed out the ease with which he'd built that particular component that we realized our spreadsheet hadn't kept up with our rules structure.<br />
<br />
So the lesson learned was that it is important as the game responds to playtesting results that the models used to manage the economy of the game respond along with them. We'd fallen into a classic trap of thinking all our original assumptions were still valid. Fortunately, playtesting serves to shake out those kinds of imbalances early on. That's what it's for, after all. Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-54186428215402498062018-08-27T06:30:00.000-04:002018-09-03T12:19:39.250-04:00No end in sight<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/-zggk5tD9N9HjpkR9aKhfGxB-iA=/fit-in/900x600/filters:no_upscale()/pic1558280.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="582" data-original-width="800" height="145" src="https://cf.geekdo-images.com/imagepage/img/-zggk5tD9N9HjpkR9aKhfGxB-iA=/fit-in/900x600/filters:no_upscale()/pic1558280.jpg" width="200" /></a></div>
My friends and I played <i>Axis & Allies: 1914 </i>recently, and while I had fun, I was disappointed and irked about a fundamental design flaw in the game end conditions. The rules require one side to capture two opponents' capitals, of which one must be Paris or London (for a Central Powers victory) or Berlin (for an Allied victory). After five turns and eight hours, we had reached something of a stalemate - or at least a realization that the end of the game was still a long way off.<br />
<a name='more'></a><br />
Two of the participants had played the game before, so I asked the question when we decided to call it: How often does an <i>A&A:1914 </i>game run to completion, as opposed to being called when the players were essentially tired of it or had run out of time? They estimated that nine times out of ten, participants agree to stop the game before victory conditions are achieved. In my mind, that observation indicates a poor game design - or at least, I should say that my taste in games does not easily accommodate a game that is so open-ended in its play duration.<br />
<br />
As I think about my reaction to this game, I realize that if players are looking to spend an afternoon (or longer) building armies, pushing pieces, and rolling dice, well, this game provides that experience for as long as the players like - unless the play is so mismatched between Allies and Central Powers that two capitals on one side fall before the participants have tired of it. It's been argued that role-playing games are open-ended experiences, too, which is fine, if that's what you're looking for.<br />
<br />
So what was I looking for? I think I wanted a finite, time-boxed experience. I wanted a framework in which to devise, execute, and adapt a strategy toward a resolution of success or failure. There are so many games available, and we have so little time to enjoy them along with all of our other commitments in the world, that I chafe at finding myself in an interminable and unresolved experience because a design team couldn't include a game-stop mechanism - or chose not to include one, or didn't think to. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqn_nWflf0xLY2_R_ZdTps3d2fuMTA3S_xnGPrpfcdS93OKQX-zW91pzTyKxpKvkVJhIlLY2QKvhawYc5Ly7SseocYYQgVkYhLP8rNHgd467JjAvkfMqstCdD6ho8TET1toeNOuekWf4dB/s1600/Games+of+Strategy+223+%25282%2529.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="359" data-original-width="264" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqn_nWflf0xLY2_R_ZdTps3d2fuMTA3S_xnGPrpfcdS93OKQX-zW91pzTyKxpKvkVJhIlLY2QKvhawYc5Ly7SseocYYQgVkYhLP8rNHgd467JjAvkfMqstCdD6ho8TET1toeNOuekWf4dB/s200/Games+of+Strategy+223+%25282%2529.jpg" width="146" /></a></div>
In our exploration of <a href="http://paulowengames.blogspot.com/2017/02/notes-on-games-of-strategy.html">games of strategy</a>, I've come to value the nature of a game as an interactive decision-making framework in which players prefer some results over others and execute choices accordingly. Certainly we exercised that principle in the course of playing <i>A&A:1914</i>, but we did so under the assumption that we would reach a conclusion of success or failure - that we achieved the desired result or not. If I'd thought that we'd play for eight hours and not know whether we'd won or not, I wouldn't have cared about my decisions so much (except to be sure that I didn't lose in less than eight hours).<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/gwLyip5bktcCqNbR_ecxSI8N7TM=/fit-in/900x600/filters:no_upscale()/pic1114402.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="605" height="198" src="https://cf.geekdo-images.com/imagepage/img/gwLyip5bktcCqNbR_ecxSI8N7TM=/fit-in/900x600/filters:no_upscale()/pic1114402.jpg" width="200" /></a></div>
My issue here isn't necessarily how I spent my Saturday. My real issue is that I feel as though the designers left an enormous hole in the structure of the game that meant players could play indefinitely without satisfying the end-game conditions - or at least that it might take 16 hours to do so. More to the point, it seems as though the game depends too much on the nature of gameplay for it to resolve in the expected time. I <a href="https://paulowengames.blogspot.com/2013/03/could-1955-go-on-forever.html">wrote about a similar concern</a> some time ago after playing <i>1955: The War of Espionage</i>. That post mentions that the mass-market game <i>Monopoly</i> has this problem as well. If players never trade, never assemble monopolies, and never improve properties, then the net income among the players will be positive (primarily due to the $200 for passing "Go"), rents will never be high enough for any player to go bankrupt, and the game will never end.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/dgCN4zSu58aVVGfMPmkceRr1kl4=/fit-in/900x600/filters:no_upscale()/pic2247267.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="368" data-original-width="260" height="200" src="https://cf.geekdo-images.com/imagepage/img/dgCN4zSu58aVVGfMPmkceRr1kl4=/fit-in/900x600/filters:no_upscale()/pic2247267.jpg" width="141" /></a></div>
I'm reminded of one of the improvements that <i>Bang! Halo</i> made over the original <i>Bang!</i> In the <i>Halo</i> version, players start with a fixed number of dog tags and win them from each other in combat. The game ends when one player runs out of dog tags. In itself that structure doesn't guarantee a finite game duration, but the fact that (1) players draw cards every turn and (2) whenever the deck runs out and is reshuffled, <b>each player discards a dog tag</b> means that the dog tags are guaranteed to deplete until someone runs out. The game can run at the very most four times through the deck, and rarely does so more than twice. This explicit run-out clock ensures that no matter how the participants play the game, they will finish in a finite amount of time.<br />
<br />
Out of respect for players' time, I would like to see every game design (unless it is explicitly intended as an open-ended experience) to incorporate some kind of guaranteed exit ramp so that no players find themselves wondering when and how a game would ever end. Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com3tag:blogger.com,1999:blog-4535367891237919312.post-55070371052426045602018-08-20T06:30:00.000-04:002018-08-29T19:28:03.395-04:00"Magnificent Marvels" signed<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL03bToEojcIK10WDxEVYbTARwYWRImA8TGEbJq_XZhBNreB_ScfR3LcWi475bZp6J8TDfW5YG9eUWbJM-P7dgQ_ZsVoAo_0RKYmHb6HlJQ3Q6Di82pbP4JNtp9xXXtRWfVMMpOxmscRkV/s1600/Magnificent+Marvels+marvel.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="273" data-original-width="373" height="146" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL03bToEojcIK10WDxEVYbTARwYWRImA8TGEbJq_XZhBNreB_ScfR3LcWi475bZp6J8TDfW5YG9eUWbJM-P7dgQ_ZsVoAo_0RKYmHb6HlJQ3Q6Di82pbP4JNtp9xXXtRWfVMMpOxmscRkV/s200/Magnificent+Marvels+marvel.jpg" width="200" /></a></div>
Almost two years ago, I <a href="https://paulowengames.blogspot.com/2016/09/collaboration.html">recounted</a> an initial foray into a collaborative design with Keith Ferguson. We have come a long way in those two years, and that work has paid off. On August 6, Hexagram 63 Game Studios <a href="https://twitter.com/Hexagram63GS/status/1026633010647580672">announced</a> that we had signed with them to produce "Magnificent Marvels," our contraption-inventing game. Keith and I are excited to be working with Anthony Racano and his team to make "Magnificent Marvels" a reality on the tabletop.<br />
<a name='more'></a><br />
Here's an excerpt from our sell sheet that describes the game:<br />
<blockquote class="tr_bq">
<br />
<div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;">
<span style="color: #604a7b; font-family: "gabriola"; font-size: 18.0pt; font-weight: bold;">Word has spread across the Grand Duchy of Rubetopia – the Master
Inventor has died!<span style="mso-spacerun: yes;"> </span>The Duke has issued a
summons for all inventors to gather in the capital of Goldburg. All shall have
the opportunity to build an Inspiring Invention, a Crazy Contraption – a
Magnificent Marvel – and be named as the new Master Inventor!</span></div>
</blockquote>
<blockquote class="tr_bq">
<br />
<div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;">
<span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-weight: bold;">In </span><span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-style: italic; font-weight: bold;">Magnificent Marvels </span><span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-weight: bold;">players vie to build the best Marvel by connecting components that
will synergize together. Marvels under construction can generate resources to
add more components and become magnificent in the eyes of the Duke. </span><span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-weight: bold;">Players can:</span></div>
<ul>
<li><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">Collect </span><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">component types to
enhance their Marvel </span>
</li>
<li><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">Hire </span><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">workers from a
dynamic labor market</span>
</li>
<li><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">Send </span><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">apprentices and
laborers to collect resources, add components to their Marvel – or activate the
Marvel itself!</span>
</li>
<li><span style="color: #604a7b; font-family: "calibri"; font-size: 11.0pt; font-weight: bold;">Upgrade raw
resources to refined materials to build more magnificent components</span></li>
</ul>
<div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;">
<span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-style: italic; font-weight: bold;">Magnificent Marvels </span><span style="color: #604a7b; font-family: "calibri"; font-size: 12.0pt; font-weight: bold;">will appeal to
players who enjoy action selection, worker placement, set collection, and
engine building.<span style="mso-spacerun: yes;"> </span></span></div>
</blockquote>
We've had a lot of fun designing and refining the game, and we're grateful that Hexagram 63 Game Studios has picked it up for further development and publication.<br />
<br />
Keith and I will start tagging up with Anthony on a regular basis to discuss the direction we want to take the game and plan out what we need to do to get it to production. He and his team have identified some rules questions and possible changes, some of which we had considered before and some which we hadn't. Anthony also has some ideas for art direction that he wants to pursue. It will be fun to chart the course that this game takes.<br />
<br />
Let's invent something magnificent, something marvelous!Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-7244132212200632872017-04-01T23:17:00.001-04:002018-08-18T21:32:49.496-04:00Notes on Games with Sequential MovesIn this second post in a series exploring games of strategy (begun <a href="http://paulowengames.blogspot.com/2017/02/notes-on-games-of-strategy.html">last month</a>), designers Aaron Honsowetz, Austin Smokowicz, and I explore strategic games involving sequential moves, <i>i.e.</i> those in which each player's decision happens in the context of knowing opponents' previous decisions. This exploration has its foundation in Chapter 3 of Dixit, Skeath, and Reiley's <a href="https://www.amazon.com/Games-Strategy-Third-Avinash-Dixit/dp/0393931129/ref=sr_1_2?s=books&ie=UTF8&qid=1487726418&sr=1-2&keywords=games+of+strategy"><i>Games of Strategy</i></a>.<br />
<br />
<a name='more'></a><br />
We <a href="https://ia601500.us.archive.org/34/items/PaulOwenDr.WictzColloquiumOnGamesOfStrategyEp2/PaulOwenDr.WictzColloquiumOnGamesOfStrategyEp2.mp3">recorded our discussion</a> at UnPub 7 in Baltimore, Maryland, on Friday 17 March.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://kwanghui.com/mecon/value/media%20%20files/static%20graphics/jpegs/Segment%205/5_3_static_bs_game_tree.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://kwanghui.com/mecon/value/media%20%20files/static%20graphics/jpegs/Segment%205/5_3_static_bs_game_tree.jpg" height="126" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Game tree for "Battle of the Sexes"<br />
Source: "Managerial Economics <br />
Online," kwanghui.com/mecon</td></tr>
</tbody></table>
A sequential game may be illustrated by a network of decision points, at each of which a choice is made. A <b>game tree </b>illustrates decision points (<b>nodes</b>) for all players and directional branches from those points to successive nodes or to an end game state (a <b>terminal node</b>). The game starts at an <b>initial node </b>(on the left in this illustration). Besides players' decisions, a node may represent an event of external uncertainty, <i>i.e. </i>a point that may branch in several directions due to factors outside the players' control, such as a random event. Games (<i>e.g. </i>role-playing games) don't necessarily have end states, but for those that do, the payoff for each player appears at each terminal node.<br />
<br />
Our discussion opened with a hypothetical game in which first Aaron and then Austin decides whether to go out to get ice cream. Aaron prefers ice cream but more important than that prefers not to spend time with Austin. Austin prefers ice cream. Knowing Austin's preferences (his "payoff"), Aaron "prunes" from the tree those decision branches that he knows Austin will not take, leaving Aaron with a strategy to stay home and avoid Austin's company. Austin will then go out and get ice cream.<br />
<br />
In the sample illustration for "Battle of the Sexes," a wife and a husband are choosing whether to go to the opera or to the bullfight. The wife prefers the opera with the husband (payoff 5), but would rather go to the bullfight with her husband (4) than to the opera alone (3). Going to a bullfight alone is as bad as staying home (0). The husband's payoffs are the same except that he prefers the bullfight over the opera. In this sequential game, the wife chooses first, and then knowing the wife's choice, the husband chooses second. This is not a zero-sum game, and the wife's payoffs don't necessarily compare to the husband's. Rather, each seeks to maximize her or his own payoff in isolation. So if the wife chooses "opera (O)," the husband would rather go to the opera with his wife than to the bullfight alone (even if they would be equally miserable alone), and so chooses to go to the opera (O) as well. (Later we'll see how the social concept of "fairness" can undermine game tree analysis.) <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Tic-tac-toe-game-tree.svg/330px-Tic-tac-toe-game-tree.svg.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="133" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Tic-tac-toe-game-tree.svg/330px-Tic-tac-toe-game-tree.svg.png" width="200" /></a></div>
Making a choice at a single node is called a <b>move</b>. A plan of action that governs moves in the interest of maximizing payoff is called a <b>strategy</b>. In the case of the Battle of the Sexes, since each player has only one move, the move and the strategy are essentially the same. For tic-tac-toe, a player can envision an entire game tree and can devise a strategy that maximizes his or her payoff (which will generally be zero, since optimum play by both players results in a draw). For chess, the game tree is too complex for the human brain to analyze fully, so strategic play generally involves analysis of a "foreseeable portion" of the game tree.<br />
<br />
The authors insist that a player's strategy be complete, <i>i.e.</i> that it include contingencies for nodes that perfect analysis says might be unnecessary. It's not clear in Chapter 3 why that's the case, but they refer to stability analysis in advanced game theory, and so we accept that a well-defined strategy for a player is a complete plan of action for all the player's decision nodes.<br />
<br />
Interestingly, the authors stipulate that every node have only one branch leading to it. I find that interesting, inasmuch as it is possible for different decision sequences to result in a game state that poses the same player with the same decision and the same consequences. If they are treated as different nodes, then the downstream game tree branches will be identical for both. That seems an unnecessary restriction, but I don't see it as problematic, and in fact it may simplify game tree analysis.<br />
<br />
An approach to solving a game tree, <i>i.e.</i> establishing a strategy for each player and predicting likely courses of a game, is to sequentially <b>prune </b>branches that represent decisions that are categorically not in the interest of the deciding player. So for example in the case of the Battle of the Sexes, at node <i>b</i>, the husband is faced with a payoff of 4 for the opera (O) or 3 for the bullfight (BF). So the BF branch may be pruned because in that case the husband will not choose BF. At node <i>c</i>, the husband is faced with payoffs of 0 (O) and 5 (BF), so that O branch may be pruned. The result is that now at node <i>a</i>, the wife's choices have payoffs of 5 (O), because she knows that the husband will also choose O in that case, or 4 (BF), because the husband will choose BF. So at node <i>a</i>, the lower payoff BF branch may be pruned, and the game tree has a single path in which both partners choose the opera. <br />
<br />
Instead of pruning, a different way to represent the same technique is to highlight clearly optimal choices, such as the O choice at node <i>b </i>and the BF choice at node <i>c</i>. Then highlight the O choice at node <i>a </i>to complete a path from the initial node to the terminal node. In either case, this method of working backward is called <b>rollback, </b>or <b>backward induction</b>. When all players use rollback to arrive at a strategy, the resultant set of strategies is a <b>rollback equilibrium</b>, and the resultant terminal node is the <b>rollback outcome</b>. The authors stipulate that every sequential game has a rollback equilibrium - typically exactly one, except where players have equal payoffs between two choices and are indifferent to the result.<br />
<br />
Depending on the configuration of the game tree (and the Battle of the Sexes is an example), the rollback equilibrium may result in the player at the initial node gaining the maximum possible payoff while other players gain less than their maximum. A game tree with such a configuration has <b>first-mover advantage</b>. In other cases, when reacting to the first decision yields the maximum payoff (as it would if rock-paper-scissors were a sequential game), the game is said to have <b>second-mover advantage</b>.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.publicdomainpictures.net/pictures/80000/velka/chess-pieces-clipart.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.publicdomainpictures.net/pictures/80000/velka/chess-pieces-clipart.jpg" height="113" width="200" /></a></div>
Although chess is a sequential perfect information game that can be theoretically represented and solved with a game tree, its scope exceeds both human and artificial computation. An approach to such a game is to assign values to certain characteristics of game states as a guide to decision-making. A rule that assigns such values is called an <b>intermediate valuation function</b>. Such a function typically derives from past experience of previous games; for example, maintaining a queen advantage typically results in a win. Chess analysis has led to a variety of known openings - early decision sequences - that have demonstrated intermediate value. Once the endgame is reached with fewer pieces remaining, a rollback analysis may apply. Checkers, by contrast, was <a href="http://science.sciencemag.org/content/317/5836/308.1.full">solved </a>in July 2007 and, perfectly played, will always result in a draw.<br />
<br />
Rollback analysis presupposes a clear understanding of the value of the payoffs to rational players. An "Ultimatum Game" gives 100 coins to Player A, who offers some of them to Player B. If Player B accepts the offer, both keep their shares; if not, neither keeps anything. Rollback analysis dictates that Player A offer one coin and B accept, but in social experiments, observation indicates Player A typically offers much closer to 50 and B accepts only if offered something that appears fair. So empirically, players value fairness in a way that the originally constructed game tree does not reflect. When the experiment is posed in a way that Player B does not know how the offer was derived (<i>e.g.</i> whether it was random, by computer, by Player A, or by some other method), Player B typically accepts much lower offers because the sense of fairness is less offended by an arbitrary opportunity. Going back to the "Battle of the Sexes," if the same game is played
every week and the couple goes to the opera every week, the husband
might - out of a sense of "fairness" - deliberately go to the bullfight alone rather than continue to accede to his wife's preferred event. <br />
<br />
It will be interesting to see how rollback analysis might apply to social games where signaling might induce opponents down one branch over another. For example, if the husband signals an intent to go to the bullfight regardless of the wife's decision (and if the signal is credible), the wife may choose to go to the bullfight rather than risk going to the opera alone.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://i.imgur.com/YOKJVbk.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://i.imgur.com/YOKJVbk.jpg" height="127" width="200" /></a></div>
We also discussed the game theory analysis of the last immunity challenge in the first season of the TV show <i>Survivor</i>, in which one player (Richard) evaluated the game tree and decided to step out of the immunity challenge (to the utter surprise of everyone watching) because his analysis indicated that he was likely to advance to the final tribal council regardless of which of his opponents won the immunity challenge.<br />
<br />
So we can approach sufficiently simple sequential games with game tree analysis as long as we correctly value payoffs. Game tree analysis still provides insight (if not explicit solution) for more complex games. Irrational play may undermine strict analysis, so strategies need to take into account unexpected paths that the game might follow.<br />
<br />
Next time we will discuss <i>Games of Strategy</i> Chapter 4, "Simultaneous Move Games with Discrete Strategies."Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com2tag:blogger.com,1999:blog-4535367891237919312.post-10901180662935698302017-02-22T09:56:00.001-05:002021-09-16T20:59:51.095-04:00Notes on Games of Strategy<div class="separator" style="clear: both; text-align: center;">
<a href="https://images-na.ssl-images-amazon.com/images/I/41SG2o3QGXL._SX334_BO1,204,203,200_.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://images-na.ssl-images-amazon.com/images/I/41SG2o3QGXL._SX334_BO1,204,203,200_.jpg" width="134" /></a></div>
Over three years ago, I wrote about <a href="http://paulowengames.blogspot.com/2013/09/game-theory-simple-multi-player-case.html">my effort </a>to approach a simple three-player race game using game theory. Economist and game designer Dr. Aaron Honsowetz responded, which led to his recommendation that I look up the book <i><a href="https://www.amazon.com/Games-Strategy-Third-Avinash-Dixit/dp/0393931129/ref=sr_1_2?s=books&ie=UTF8&qid=1487726418&sr=1-2&keywords=games+of+strategy">Games of Strategy</a> </i>by Avinash Dixit, Susan Skeath, and David Reiley. I finally obtained the third edition recently, and that has led Aaron, fellow designer Austin Smokowicz, and me to explore Dixit Skeath and Reiley's text in a kind of virtual book club. <br />
<a name='more'></a><br />
<b>Thinking about strategic games</b><br />
<br />
We <a href="https://www.youtube.com/watch?v=6BBI7cB93n0">live-streamed </a>last night's discussion. We start with the first two chapters, which motivate the study of game theory and then define some terms and categories. <br />
<br />
<b>Strategic games</b> depend on player decision-making, as distinguished from games of chance, which depend on luck, and from games of skill, which depend on proficiency, dexterity, quickness of mind, or practice. So, for example, chess is a game of strategy whose outcome is determined by the decisions of the players. Bingo is a game of chance, whose outcome is determined by the order of randomly selected numbers. Bowling is a game of skill, whose outcome is determined by the strength, accuracy, and proficiency of the bowlers.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.clipartkid.com/images/126/absolutely-free-clip-art-poker-clip-art-images-graphics-cards-IlWHm0-clipart.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="189" src="http://www.clipartkid.com/images/126/absolutely-free-clip-art-poker-clip-art-images-graphics-cards-IlWHm0-clipart.png" width="200" /></a></div>
The authors distinguish <b>decisions </b>that people make that are independent of the decisions of others from <b>strategic games</b>, in which people know that the results of their decisions depend on the decisions of others as well, <i>i.e.</i> that their decisions are interactive. So, for example, blackjack plays out based on the decisions of each player in isolation, regardless of the other players at the table and of the dealer, who follows strict rules and makes no independent choices. Poker, by contrast, plays out based on the interaction of the decisions among players. So poker meets the definition of a strategic game, while blackjack does not.<br />
<br />
The authors proceed to classify games in anticipation of the structure of the rest of the book:<br />
<ul>
<li>In <b>sequential </b>games, players make decisions whose immediate outcome is unaffected by other players, as opposed to games with<i> </i><b>simultaneous </b>moves, in which players must anticipate the unknown decisions of other players. Chess is sequential, while rock-paper-scissors is simultaneous.</li>
<li>Some games pose players with strictly conflicting interests while others might involve common interests among the participants. So most wargames are strictly conflicting, while <i>Dead of Winter</i> introduces both common and individual goals.</li>
<li>One-time games are distinguished from<i> </i>repeated games with the same opponents, which in turn are distinguished from games involving<i> </i>changing opponents. So a one-time-only game might be the courtship, engagement, and marriage of a couple. A bridge club plays the same game with the same opponents repeatedly. And a single-elimination game tournament generally involves playing the same game with different opponents in each session.</li>
<li>The authors define games with full and equal information <i>vs </i>partial or unequal information: <b>External uncertainty </b>applies to unknown information independent of others' decisions. <b>Strategic uncertainty </b>applies to the unknown decisions by others. A game with either or both has <b>imperfect information</b>; a game with no such uncertainty has <b>perfect information</b>. A game in which one player has more information than another has <b>asymmetric information</b>. So for example, a card game with a shuffled deck involves external
uncertainty. Rock-paper-scissors involves strategic uncertainty. Chess
is a perfect information game. <i>Scotland Yard</i> has asymmetric information. </li>
</ul>
<blockquote class="tr_bq">
Strategies that share or reveal information deliberately are called <b>signaling</b>. Strategies that seek to motivate an opponent to reveal information are called <b>screening</b>. We spent quite a bit of time discussing examples of signaling, such as playing chicken and throwing the steering wheel out the window to demonstrate to an opponent your commitment not to swerve. Aaron cited an example from Euchre in which card play signals to a partner information about your hand or about what the opponents do or don't have. To Aaron's point, the important component of signaling is the degree of commitment to a decision. Austin used an example from <i>Hanabi</i> as a method of communicating intent to fellow players.</blockquote>
<blockquote class="tr_bq">
After the chat, Aaron further refined our discussion of signaling: </blockquote>
<blockquote class="tr_bq">
<blockquote class="tr_bq">
<span class="tL8wMe EMoHub" dir="ltr" id=":jl.co" style="text-align: left;">Bluffing itself is an uncreditable signal. You claim you are committing to something (to alter player behavior). </span><span class="tL8wMe EMoHub" dir="ltr" id=":jm.co" style="text-align: left;">To
be a creditable signal, the price to make the signal must be
sufficiently high that only a person committed to the action is willing
to pay it. </span><span class="tL8wMe EMoHub" dir="ltr" id=":jn.co" style="text-align: left;">When I remove my steering wheel and toss it out the window I am saying I am willing to drive straight no matter the price. </span><span class="tL8wMe EMoHub" dir="ltr" id=":jo.co" style="text-align: left;">If
the price of making the signal is too low, than people can make the
signal without creditably committing to the action (bluffing) and destroy
the ability for the signal to indicate you are going to take a
particular action.</span></blockquote>
</blockquote>
<blockquote class="tr_bq">
Screening involves eliciting information, and one way of doing that is to make an offer like a trade in <i>Catan </i>to
see how players respond and thereby gain information about the contents
of their hand and to an extent their future intentions.</blockquote>
<blockquote class="tr_bq">
During our discussion, I provided an example of sequential interactive decision-making that led to another follow-up by Aaron regarding signaling and screening. In a game of <i>Agricola</i>, I built fences in anticipation of an opportunity to take sheep. An opponent, who had no need of sheep and no means to store or cook them, took them anyway and let them run free to deprive me of that opportunity. Said Aaron,</blockquote>
<blockquote class="tr_bq">
<blockquote class="tr_bq">
<span class="tL8wMe EMoHub" dir="ltr" id=":jv.co" style="text-align: left;">Your
sheep example from <i>Agricola </i>was (if there was no other value for that
many fences) a credible commitment that you would take sheep if they
were available. </span><span class="tL8wMe EMoHub" dir="ltr" id=":jx.co" style="text-align: left;">If that is the case it could also be part of a screening tactic. </span><span class="tL8wMe EMoHub" dir="ltr" id=":jy.co" style="text-align: left;">If
everyone is paying attention, it forces the last person before you who
has a lower value play (assuming you are competitive in the game) to
reveal that by responding to you</span><span class="tL8wMe EMoHub" dir="ltr" id=":jz.co" style="text-align: left;">. And
while you may not get the points from the sheep, it may still have been
the best move because it blocked an opponent from taking an action to
advance their score.</span></blockquote>
</blockquote>
<ul>
<li>Games can have fixed <i>vs </i>manipulable rules. Most tabletop games with which we are familiar have fixed rule-sets. I imagine games with manipulable rules to include the interactions within a legislative body, whose rules of order may be modified by a party in power. </li>
<li>The book defines cooperative games differently from the conventional use of the term that modern game-players might know. The authors refer to games in which agreements are enforceable as <b>Cooperative</b>, while games with unenforceable agreements and that allow players to act in their own best interests are called <b>non-cooperative </b>games. By these definitions, <i>Catan</i> is cooperative, inasmuch as a trade is an enforceable agreement; both parties are required by the game rules to hold up their end of the bargain. <i>Diplomacy</i> is a non-cooperative game, since a player can commit to a future action and then renege on that commitment. </li>
</ul>
Terminology and other concepts:<br />
<ul>
<li>Strategies are available choices, or more generally a set of guidelines or algorithms by which individual decisions are made - a plan for a succession of actions in response to evolving circumstances, presumably due to the actions of other players.</li>
<li>Payoffs are the outcomes of interactive decisions, including <b>expected payoff </b>based on a probability distribution of random outcomes.</li>
<li>Rationality, or <b>rational behavior</b>, assumes perfect calculating players that consistently follow the best strategy pursuant to a completely known self interest.</li>
<li>Games involve a common knowledge of rules, specifically knowing who the players are, their available strategies or choices, the payoffs for each interaction of strategies, and an assumption of rational behavior.</li>
<li>When rational players interact, the game reaches an <b>equilibrium </b>whereby each player is using the strategy that best responds to the other players' strategies. </li>
<li>As opposed to assumed perfect rationality and calculated equilibrium, an <b>evolutionary </b>approach to games allows for a dynamic process in which poor calculators are motivated to choose strategies that proved more successful in previous plays of the game through observation, imitation, and learning.</li>
<li>Observations and experiments can help structure game theory and provide a check against its results.</li>
</ul>
The book stipulates that game theory can help to <i>explain </i>observed behavior of interacting decision makers, <i>predict </i>likely choices of rational actors, and <i>prescribe </i>strategic decisions.<br />
<br />
I had one question that did not get addressed in our chat: Can a game have more than one equilibrium, <i>i.e.</i> can there be local points of optimization that could emerge in an evolutionary approach different from what an analysis of perfect strategies would indicate? The answer may come up in later discussions.<br />
<br />
Next we will explore Chapter 3, "<a href="http://paulowengames.blogspot.com/2017/04/notes-on-games-with-sequential-moves.html">Games with Sequential Moves</a>." <br />
<br /><input id="idg-io-safe-browsing-enabled" oninit="true" type="hidden" />Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com1tag:blogger.com,1999:blog-4535367891237919312.post-76685420690024679952017-01-15T21:56:00.000-05:002019-07-15T06:09:52.016-04:00Papal Pilgrimage: A preview of the sequel to Avignon<div style="text-align: right;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/EllUyi0nUW28eV592xHQmW1zLzk=/fit-in/900x600/filters:no_upscale()/pic3252924.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="429" height="200" src="https://cf.geekdo-images.com/imagepage/img/EllUyi0nUW28eV592xHQmW1zLzk=/fit-in/900x600/filters:no_upscale()/pic3252924.png" width="142" /></a></div>
</div>
The microgame format that <i>Love Letter</i> popularized poses a considerable design challenge. Fewer cards mean players face statistically fewer different situations. Pared down to a skeletal structure, a microgame really has to make every card significant and capitalize on every opportunity for interaction. John du Bois introduced a clever two-player tug-of-war in this format with the 2016 Button Shy game <i>Avignon: A Clash of Popes</i>. To that tight little design Button Shy Games is Kickstarting a sequel, <a href="https://www.kickstarter.com/projects/239309591/avignon-pilgrimage-turbo-drift-and-find-your-seats?ref=nav_search"><i>Avignon: Pilgrimage</i></a>, that introduces new characters that can stand alone as a separate game or that players can mix in with the original <i>Avignon</i> for a variety of interactions.<br />
<a name='more'></a><br />
The games are set during the Western Schism of the Catholic Church in the late 14th century, when rival popes in Avignon and Rome sought to wrest control of the Church from one another. Each player represents one of the papal factions recruiting key figures into the supporting congregation of Avignon or Rome to solidify that pope's control. <br />
<br />
<i>Avignon</i> in both its original format and its sequel constitutes a logic puzzle of card interactions with the goal of moving character cards to one's own side of the table. Available actions are simple. The complexity comes in the individual character card "Petition" actions that manipulate the positions of cards and the victory conditions. The new sequel, <i>Avignon: Pilgrimage</i>, introduces a number of mechanics relying on the relative positions of other characters on the table and thereby adds a new layer of interactive depth.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpftHZVH5zIIp2y0NwJVQJ_kdSBDq-nUUkTgHDEHhoJB9Dd244etqiha2QzaIl4UQ79SKxtFMVl4Rj3ryiYGYDnnSlRUmXGpjmJQSfmZUxtncxOpNUvZXgkHY8z8GFlUrr5gUd0zDBIzVZ/s1600/IMG_6503.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpftHZVH5zIIp2y0NwJVQJ_kdSBDq-nUUkTgHDEHhoJB9Dd244etqiha2QzaIl4UQ79SKxtFMVl4Rj3ryiYGYDnnSlRUmXGpjmJQSfmZUxtncxOpNUvZXgkHY8z8GFlUrr5gUd0zDBIzVZ/s320/IMG_6503.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The five locations on the road to papal legitimacy <br />
between Avignon and Rome. The Ascetic is shown in<br />
Genoa, which is where he really wants to be.</td></tr>
</tbody></table>
The game consists of twelve cards, each depicting one of six characters. Five cards are dealt in a row on the table between the players. The starting row represents Genoa. A card can be moved from Genoa in one direction to Florence, to Rome, and then to the Roman player's congregation. Or it can move from Genoa in the other direction to Nice, to Avignon, and then to the Avignon player's congregation. The goal is to collect three characters into one's own congregation - or to meet the special victory condition of a character in play.<br />
<br />
Available actions to a player are to pull a character one space closer, to push a character one space further, to excommunicate a character (removing it from its location and replacing it with another character from the draw deck), or to petition a character (activating its special ability). The crucial rule in <i>Avignon</i> is that although a player takes two actions per turn, they must be different actions. So only one character can be petitioned for its special effect; only one character can be pulled; only one character can be excommunicated. So good game play consists of recognizing and implementing the right combinations of actions to gain ground on the opponent in a lasting way.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhh5kDnYKABTBiJ-G2bN7UFWmteKFXhDpS7cDmWmPwGZia1JBYOontdmzV6ggWeGJYhnKmnmmU-bKMej712wvKHtgns1RnD6jg-an5vPugh2JqaEQn_LhEYUz6wOaTVcp2dEViua3T_7T2j/s1600/Avignon+Pilgrimage+-+Courtesan+Canonist+Nuncio.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhh5kDnYKABTBiJ-G2bN7UFWmteKFXhDpS7cDmWmPwGZia1JBYOontdmzV6ggWeGJYhnKmnmmU-bKMej712wvKHtgns1RnD6jg-an5vPugh2JqaEQn_LhEYUz6wOaTVcp2dEViua3T_7T2j/s320/Avignon+Pilgrimage+-+Courtesan+Canonist+Nuncio.jpg" width="149" /></a></div>
<br />
Some <i>Pilgrimage</i> characters seem more interesting than others. Petitioning the Courtesan pulls a character whose position is closer to the opponent than is the Courtesan; so her position generally benefits the player to whom she is closer. The Canonist allows switching the positions of two characters, then pulling one and pushing the other. Petitioning the Nuncio pushes him one space and then pulls all other characters that are in his new location - essentially having him trade places with everyone else in that location. <br />
<br />
Other characters seem less interesting. Petitioning the Vicar pushes a Vicar (or Bishop from the original <i>Avignon</i>) <u>two </u>spaces, excommunicates another character, and pulls that character <u>one </u>space - a move that seems to make a considerable position sacrifice in exchange for a random character replacement. An Ascetic ending the turn in Rome or Avignon automatically moves one space closer to Genoa, making him particularly difficult to recruit (and thereby less interesting). The Scribe allows a player whose turn starts with the Scribe in Genoa to win with only two characters in his or her congregation. This effect can be a game-ending (and random-feeling) consequence of pulling a character into one's congregation only to see that character replaced by the Scribe in Genoa to start the opponent's turn.<br />
<br />
Having played <i>Avignon: Clash of Popes </i>and <i>Avignon: Pilgrimage</i> separately, I look forward to mixing them together and seeing the cards from both sets interact with each other. I expect the logical conundrums to deepen even further, and I always enjoy when a small-footprint game turns into a little brain-cell-burner.<br />
<br />
Unlike many microgames, there is no hidden information (beyond the draw
deck) and no bluffing, so this is not a social game of getting inside
the opponent's head. People who like quick microgames with real logic challenges will like both <i>Avignon</i> games. <i>Pilgrimage</i> by itself is a bit more dynamic but also a bit uneven relative to the original. All in all there is a lot of game in this small footprint.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-56572959866171538052016-12-28T22:46:00.000-05:002019-05-26T18:47:09.377-04:00Getting to Know "The Grid"<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYHoGEMxZctTrySmJ39nj5jDd7Ogn6KTC8Oav_SLI9lKvyGktyYcwXzqlxcnjJXn1PzpkG355rCRRt7yrt14uGG-6js-PERW4ayGRu1shf7o_plteZ5HD_9sMuOcNFao5pOPjmI4oIuMPE/s1600/The+Grid+Game.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYHoGEMxZctTrySmJ39nj5jDd7Ogn6KTC8Oav_SLI9lKvyGktyYcwXzqlxcnjJXn1PzpkG355rCRRt7yrt14uGG-6js-PERW4ayGRu1shf7o_plteZ5HD_9sMuOcNFao5pOPjmI4oIuMPE/s200/The+Grid+Game.jpg" width="200" /></a></div>
Games in some ways, like people, have personalities. Some, like <i>Ticket to Ride</i>, are friendly, fun, and easy to get to know. Others, like <i>Two Rooms and a Boom</i>, are gregarious and a little crazy; if you can handle the energy, they are very entertaining. Some are obtuse and a little intimidating, like a Phil Eklund simulation or a heavy wargame. And some are subtle, reserved, and a little introverted; they don't want to show you everything right away, and if you base your opinion on a first impression, you'll miss what's hidden underneath.<br />
<a name='more'></a><br />
The Mexican industrial design studio Left has devised a unique abstract tile placement game with the understated title, "The Grid Game." This set of 88 hexagonal tiles in a muted color palette has a quiet beauty, like a southwestern desert at sunset. And it has a subtlety of gameplay that only emerges after patient peeling away of layers. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCksuD3_YQR7LPPBNVkKZmu9qynZ7rzhOiNUdGK-VhGGhMiQl-YcM_giFO1eJRLlzu-ZDLgSYKJrg6z5iPXWdX06avAtoF7RcbeWDsLoKMg9RPp6rKP5PfZLyDW9JX7jPwMJ6ZDD74Mooo/s1600/IMG_6500+%25282%2529.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCksuD3_YQR7LPPBNVkKZmu9qynZ7rzhOiNUdGK-VhGGhMiQl-YcM_giFO1eJRLlzu-ZDLgSYKJrg6z5iPXWdX06avAtoF7RcbeWDsLoKMg9RPp6rKP5PfZLyDW9JX7jPwMJ6ZDD74Mooo/s200/IMG_6500+%25282%2529.JPG" width="200" /></a></div>
Designed by Estudio Victor Aleman, each hexagonal wooden tile is made from three rhomboid pieces, each one of seven colors. Players will start with a set of
randomly selected tiles and play them one at a time to an array, with
the constraint that tiles may only touch if they match in color. After
the second tile is placed, subsequently played tiles must touch two
other tiles, again matching colors on the touching sides.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU2UXJMMQ7HYsQTsCjq4BwxPXR41pVyoM5fseHQ0Y4bSmtkk9c99v4J-NIwBiHyDhTusSp4aBAGge5P05IgGl77CiIamZ2qy_QzAymfEPV3B1T2fk-WSSmmXEVh10PWhZRQuExzWNh6uUp/s1600/IMG_6488.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU2UXJMMQ7HYsQTsCjq4BwxPXR41pVyoM5fseHQ0Y4bSmtkk9c99v4J-NIwBiHyDhTusSp4aBAGge5P05IgGl77CiIamZ2qy_QzAymfEPV3B1T2fk-WSSmmXEVh10PWhZRQuExzWNh6uUp/s200/IMG_6488.JPG" width="200" /></a></div>
Interestingly, the tiles are cut in such a way that the corners where
two rhomboid pieces meet are "taller" (<i>i.e.</i> stand higher above the table) than do the corners that belong to only one rhomboid piece. This vertical height of the different corners is important, because placing a tile is further constrained by having the touching corners match in height as well. It took a few plays for me to discover that this height restriction is specifically designed so that every hexagonal tile after the first one has only three legal orientations rather than six. This restriction has the nifty effect of ensuring that no tile placement results in a theoretically unplayable adjacent space.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXCozYWpz8yZ8mNgJ7VQHyq1zKFMH2Gy5pcfQrSD_f02sYLTJKjAai1puqD9H9Qlsrz38VoQbymtIJUftvUyDC0Mz8ykIl6kRlKqn3romsnad4GfuGWBM64XENHCqV5hR2tk2scKwGmRPO/s1600/IMG_6501.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXCozYWpz8yZ8mNgJ7VQHyq1zKFMH2Gy5pcfQrSD_f02sYLTJKjAai1puqD9H9Qlsrz38VoQbymtIJUftvUyDC0Mz8ykIl6kRlKqn3romsnad4GfuGWBM64XENHCqV5hR2tk2scKwGmRPO/s200/IMG_6501.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Clockwise from left: Black-sided tile <br />
(5 pts), one-color tile (3 pts), two-<br />
color tile (2 pts), three-color tile (1 pt)</td></tr>
</tbody></table>
There are several categories of tiles - those with three different colors, those with two rhomboids of one color and one of a second color, those that are all one color, and a separate category for those having two black rhomboids. The tiles with black rhomboids are unique in that no tile - not even another black-sided tile - may touch the black side of another tile when placed. <br />
<br />
Sounds simple enough - place tiles to match colored sides. Easy as <i>Carcassonne</i>, right? In fact, at the start of the game, each player has many tiles from which to choose, so the early game is especially straightforward. And the objective is simply to get rid of all your tiles. If a player has no playable tile, the turn passes to the next player. So the goal, really, is to be able to play a tile every turn and so to run out first. If the game reaches the point where no one has a playable tile, then players score points based on the tiles they have left, and fewest points wins.<br />
<br />
By the second play, it emerges that the tiles that are worth the most points - <i>i.e.</i> the ones you don't want to be stuck with - are the hardest to play. Black-sided tiles are worth five points - huge in this game - and can only be played against two tiles of a specific color and with no other adjacencies. Tiles that are all one color are worth a hefty three points but are almost as difficult as black-sided tiles to play. So there is a tendency to unload black-sided tiles as soon after the second round as possible, and one-colored tiles right away as well. The result can be a very difficult field to play, and in fact our second game ended very quickly when the entire field was essentially blocked with black-sided tiles around the entire periphery, as we each tried to unload black-sided tiles as fast as possible.<br />
<br />
At this point I was ready to write off the game as crippled by a negative feedback loop, thinking that the point values motivated players to render the field unplayable quickly by unloading the high-value tiles as quickly as possible. Our third play, however, revealed that the game can take a completely different direction, when I was able to play all my tiles without a pass. Gameplay becomes less <i>ad hoc</i>, and attention becomes more focused on how many of which colors a player has - and which colors an opponent is short on. Further reflection suggests that the tile mix has everything to do with the course of the game, so that a winning strategy can vary with the early game circumstances. Now the players must discern which direction to take depending on the kinds of tiles that are in play. Suddenly we found a new richness that did not emerge in our first two games. Such is the personality of a shy game that takes time and several encounters to get to know properly.<br />
<br />
We did establish that the tile draw at the beginning of the game is crucial to the game balance; we found that having significantly more black-sided tiles than an opponent, or more one-color tiles, makes for a considerable disadvantage. The publisher would do well to include a rule to ensure that players start with the same number of each type of tile to mitigate this effect. The actual mix that all players share can vary from game to game, and in fact a variable mix can lead to a variety of strategic options. Balance is important, however, and a disparate tile mix among players appears to bias the game significantly.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://cf.geekdo-images.com/imagepage/img/A54rTQXlsgmuGvI0t9E9Hj0Zl78=/fit-in/900x600/filters:no_upscale()/pic3287103.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="535" data-original-width="800" height="213" src="https://cf.geekdo-images.com/imagepage/img/A54rTQXlsgmuGvI0t9E9Hj0Zl78=/fit-in/900x600/filters:no_upscale()/pic3287103.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">An opened game "box" showing the four tile trays (with<br />five more games in their boxes, behind)<br />Photo by Victor Aleman posted on boardgamegeek.com</td></tr>
</tbody></table>
<div style="text-align: left;">
</div>
The physical components are remarkable. The wooden tiles are precisely cut and thoroughly glued, with only the slightest of adhesive residue visible on a number of the tiles. The game comes in a set of four foam-sided trays that each hold 22 tiles in a snug hexagonal grid. The four trays stack into a wrap-around gamebox-sized sleeve with a velcro flap that makes for a unique, snazzy-looking package.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihx1uAWcqlwM9pLbFuHZzyP8DZ05WVCe5IoKMjo7BBvF5H4lbmFQ7G1CGaBjR-5_er8uqlf3kC-8pL42bY6dVwPHRADUVyRZcs0ngs0nIPA6Cxwq2AZkOLCFmbdCialO0fKx_-on8S-0NB/s1600/IMG_4911.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihx1uAWcqlwM9pLbFuHZzyP8DZ05WVCe5IoKMjo7BBvF5H4lbmFQ7G1CGaBjR-5_er8uqlf3kC-8pL42bY6dVwPHRADUVyRZcs0ngs0nIPA6Cxwq2AZkOLCFmbdCialO0fKx_-on8S-0NB/s320/IMG_4911.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A nice table presence, almost as appealing as <i><br />Qwirkle </i>or <i>Ingenious</i></td></tr>
</tbody></table>
I mentioned the subtle Southwestern color palette, which makes for a beautiful table presence, but in anything less than very good lighting, some of the colors are difficult to distinguish, particularly brown from dark gray and dark gray from black. Many times during the game we wished for more strongly contrasted colors. And yet, when the game is done, we marvel at how pretty it is.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiXYRUS3O0bI1wpz2nZaYJpX05c4oOP0eqwo0uZ5gPNWrYyGqJPiBW_gfnqSkWJfTX2nSspXZSstGLGD9g7ffP6hfX4r-z4qWXypjrSWUITVAr7MvBtHbxXsNCzoGjNymGWwMJLvpoY8p_/s1600/IMG_6490.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiXYRUS3O0bI1wpz2nZaYJpX05c4oOP0eqwo0uZ5gPNWrYyGqJPiBW_gfnqSkWJfTX2nSspXZSstGLGD9g7ffP6hfX4r-z4qWXypjrSWUITVAr7MvBtHbxXsNCzoGjNymGWwMJLvpoY8p_/s200/IMG_6490.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">An illegal placement due to different<br />
corner height - difficult to tell until you<br />
notice this tile is oriented differently</td></tr>
</tbody></table>
In the first few games, we found it impossible to tell the difference in height between corners of the tiles until we tried to place them next to each other. Many times we would attempt to situate a tile only to discover that the corners were not aligned vertically, and it was not initially obvious why. It wasn't until we discovered that the corner heights are intended to confine all tiles to be placed in one of three possible orientations, 120 degrees apart, that we could naturally identify legal ways to place tiles that would ensure same-height corners would be lined up with each other. It seems that some stronger visual signifier might help in this respect, although such an indicator would probably change the visual aesthetic of the game.<br />
<br />
The player count is ostensibly for one to 11 players. The review copy did not include solitaire rules, though the publisher expressed an intent to include them in the final production copy. As for high player counts, I struggle to see more than five or six players around this game enjoying any kind of strategic gameplay value. With more than eight players, each person will place fewer than ten tiles in the entire game, hardly enough to feel engaged in what is otherwise a game of considerable potential depth. The publisher admits that in tests with more players, although people found it inclusive, the game slowed down, and players were often distracted.<br />
<br />
I find that this quietly attractive, subtly strategic game will appeal to people who favor abstract tile-laying games that evolve with repeated plays and who have patience to discover a game over time. I would not recommend it for more than five players. It will not appeal to those who prefer thematic games, games that they can fully appreciate in the first play, or laugh-out-loud party games.<br />
<br />
<i>Victor Aleman, Creative Director of LEFT, provided a copy of </i>The Grid Game<i> for this review. </i>Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-66262127222290516712016-10-01T15:43:00.001-04:002019-04-14T15:50:44.191-04:00Congress of Gamers 2016<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQtzkvLXMYRAjTOuU_m70Nc205NXd_Hz-i27SaCl-_O3rKsmH77X6IQ6rdx9ZLZxFPbEgM5b-4FEKGOwkIbkxHaU1JJLrKwT1Ywkwgi2KR0ZXPgykaAjyb0ptquQ6PB6TL1hM5QT_1s7dK/s1600/Congress+of+Gamers+Logo142.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQtzkvLXMYRAjTOuU_m70Nc205NXd_Hz-i27SaCl-_O3rKsmH77X6IQ6rdx9ZLZxFPbEgM5b-4FEKGOwkIbkxHaU1JJLrKwT1Ywkwgi2KR0ZXPgykaAjyb0ptquQ6PB6TL1hM5QT_1s7dK/s1600/Congress+of+Gamers+Logo142.jpg" /></a>Every fall there's a little weekend convention in Rockville, Maryland that I've always enjoyed. Hosted at the unassuming Rockville Senior Center, <a href="http://www.congressofgamers.org/">Congress of Gamers</a> features a series of Euro tournaments, an auction store, and a game design room. The <a href="https://www.gamesclubofmd.org/Default.asp">Games Club of Maryland</a> sponsored the convention, and <a href="http://breakmygamegroup.com/">Break My Game</a> ran the prototype testing event this year's session, which convened last weekend. <br />
<br />
<a name='more'></a><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggBsQuWuUQGlDPkNsfU3KHs4AMsY7GCJO5k3Q2MHGhPYzav9dMtUlmbFw5H6-zjymv4Q7GMLP1PrAW7QNzH7KaNuVoVcOyAVpZ_B520ENBbE99TJmua598DNLznFQHGg9q-4N6_aKYdVH4/s1600/Acquire.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="362" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggBsQuWuUQGlDPkNsfU3KHs4AMsY7GCJO5k3Q2MHGhPYzav9dMtUlmbFw5H6-zjymv4Q7GMLP1PrAW7QNzH7KaNuVoVcOyAVpZ_B520ENBbE99TJmua598DNLznFQHGg9q-4N6_aKYdVH4/s200/Acquire.jpg" width="144" /></a></div>
My first priority was to play <i><a href="https://boardgamegeek.com/boardgame/5/acquire">Acquire</a> </i>(designer <a href="http://gamersalliance.com/sid-sackson-special-tribute/">Sid Sackson</a>), my favorite game that I never get to play. Five of us signed up to play in a single game that was a real brain-burner. All seven companies came out within the first two rounds of play. I had no chance of keeping track of who had what. By the end, it occurred to me that I need to reconsider how I play this game. I tend to buy shares strictly in small companies that I anticipate being taken over, in the interest of pursuing bonuses with a high return on investment. Unfortunately, at the end of the game I found myself with a lot of cash but very few shares of the large high-value surviving companies. The result was that I came in a distant second to Bill, the player to my right, whose purchase timing seemed impeccable throughout the game. If I have one complaint about <i>Acquire</i>, it is that tile luck can factor strongly in the outcome, and Bill readily admitted that the right tiles came out for him. Nevertheless I'm convinced that he also made some excellent investments at the right time and capitalized on a number of other players' mergers, so he deserved the win outright.<br />
<br />
I spent most of my time in the Unpublished Gaming Room, as I usually do. I didn't bring any designs myself but spent the entire time playtesting other people's games. Highlights included<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGNRi0P-Lyqbv9y8kmeJhrOnXuCmxzaiWlB0I-W6i9syAogTC8wVBLDRpNNO-Bh15P6Jq7W3JMUK4C9uMKg3sACdwwYyl1MpndfPYqsK8o5MK9Ft1xdGU4qct0CcEWiH50nOk1DLL91aB_/s1600/Empire+by+David+Stephenson+-+Matt+Yeager.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGNRi0P-Lyqbv9y8kmeJhrOnXuCmxzaiWlB0I-W6i9syAogTC8wVBLDRpNNO-Bh15P6Jq7W3JMUK4C9uMKg3sACdwwYyl1MpndfPYqsK8o5MK9Ft1xdGU4qct0CcEWiH50nOk1DLL91aB_/s200/Empire+by+David+Stephenson+-+Matt+Yeager.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">David Stephenson explains "Empire" to<br />
Matt and Corinne Yeager</td><td class="tr-caption" style="text-align: center;"></td><td class="tr-caption" style="text-align: center;"><br /></td></tr>
</tbody></table>
<ul>
<li>Getting in a four-player game of <a href="https://twitter.com/davidysteph">David Stephenson</a>'s "<a href="http://www.stephensongames.com/game/empire">Empire</a>." I played it once head-to-head with David at <a href="http://unpub6.unpub.net/">UnPub 6</a> last spring, and I can tell now that the game is much more interesting in a larger group. Negotiation plays a big part in this abstracted nation-building game. I'm really fond of it, and it deserves attention from publishers.</li>
<li>Discovering "<a href="http://unpub.net/games/detail/?proto=597&o=544">Bring in the Birds</a>" by <a href="https://www.facebook.com/elizharg">Elizabeth Hargrave</a>, such an innocent-sounding game, and so strategic</li>
<li>Revisiting "Dichotomy" (alias "Zhongbai: Game of Balance"), by <a href="https://twitter.com/crimsynseraf/">Matthew Yeager</a>, much cleaner than its 2015 Congress of Gamers rendition and perhaps one of the best trick-taking games I've ever played (and that includes <i>Diamonds</i>) </li>
<li>Trying out "<a href="http://www.stephensongames.com/game/fealty">Fealty</a>," David Stephenson's nifty social bluffing game (that might need a new name, since Asmadi has a <a href="http://asmadigames.com/detail_fealty.php">2011 release</a> with that title) </li>
<li>Learning "Cave Paintings of Lascaux," by Corinne Yeager, a dice-driven set collector with a simple tech tree and elements of <i>Splendor</i> </li>
<div style="text-align: right;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguF_KXBAN02vIlL1GK_eShYUeGnnue02IwtDvFb1a4c4q0zjpNYB9njS9_fgXOml2DLt4Ld1_XhoaJew73nnQf3imcOSf4GiCTKUzLBoqNciiFOR4gZHmCBIzYT4egf9v_07EdRynoBDTG/s1600/Cattle+Car+-+David+Stephenson%252C+Austin+Smokowicz.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguF_KXBAN02vIlL1GK_eShYUeGnnue02IwtDvFb1a4c4q0zjpNYB9njS9_fgXOml2DLt4Ld1_XhoaJew73nnQf3imcOSf4GiCTKUzLBoqNciiFOR4gZHmCBIzYT4egf9v_07EdRynoBDTG/s200/Cattle+Car+-+David+Stephenson%252C+Austin+Smokowicz.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">David Stephenson (l.) gives feedback to <br />
designer Austin Smokowicz on <br />
"Cattle Car"</td></tr>
</tbody></table>
<li>Playing through "<a href="http://unpub.net/games/detail/?proto=465">Cattle Car</a>," by Austin Smokowicz and Aaron Honsowetz (the "<a href="http://dr.wictz.com/">Dr Wictz</a>" design team), a lean deck builder with a Western theme that I'd seen before but don't recall playing. It's got some tricky little interaction mechanics, as Josh Tempkin demonstrated in our playtest.</li>
<li>Jumping back into Adam "Alf Shadowsong" Fischer's "<a href="http://unpub.net/games/detail/?proto=893&o=191">Kahl'Shera</a>," a chaotic dice game with a whirling dervish martial showmanship dance kind of theme that I'd seen at an UnPub event somewhere before<br /><br /><br />
</li>
</ul>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi37_2j9U6VqG5ScJHE8I4HN9Zr6pAAfp3YjQIjd9X8YFkTT99kXIhIUrS5e8VUztFn3NTUkItC684Eq1ylJLNeNyrtReaU8VC3-jfpwSf974Iu00yCAJZhoYNxAUQ74KQdgvXnW58wWcxd/s1600/Asara+-+Peter+Gousis%252C+Dan+H%252C+Jessica+Wade.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi37_2j9U6VqG5ScJHE8I4HN9Zr6pAAfp3YjQIjd9X8YFkTT99kXIhIUrS5e8VUztFn3NTUkItC684Eq1ylJLNeNyrtReaU8VC3-jfpwSf974Iu00yCAJZhoYNxAUQ74KQdgvXnW58wWcxd/s200/Asara+-+Peter+Gousis%252C+Dan+H%252C+Jessica+Wade.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">(l. to r.) Peter Gousis, Dan H., and <br />
Jessica Wade schooling me in <i>Asara</i></td></tr>
</tbody></table>
Also in open gaming, I met up with <a href="https://twitter.com/MVPBoardgames">Peter Gousis</a> (<a href="https://www.facebook.com/Mvpboardgames">MVP Games</a>), <a href="http://www.nonsensicalgamers.com/author/dan-h-nad/">Dan H.</a> (League of Nonsensical Gamers), and <a href="http://www.feldfangirl.com/">Jessica Wade</a> (Dice Hate Me - <a href="http://dicehateme.com/tag/state-of-games/">State of Games podcast</a>). (Actually, I kind of invited myself to their table.) We all learned <a href="http://riograndegames.com/Game/390-Asara"><i>Asara</i></a> (designers <a href="https://boardgamegeek.com/boardgamedesigner/42/michael-kiesling" title="Michael Kiesling">Michael Kiesling</a> and <a href="https://boardgamegeek.com/boardgamedesigner/7/wolfgang-kramer" title="Wolfgang Kramer">Wolfgang Kramer</a>, publisher <a href="http://riograndegames.com/">Rio Grande</a>), which turns out to be a nifty area control game. Fun and clever, if not life-changing.<br />
<br />
I also sat in on a demonstration of <i><a href="https://boardgamegeek.com/boardgame/68425/eminent-domain">Eminent Domain</a> </i>(designer <a href="http://sedjtroll.blogspot.com/">Seth Jaffee</a>, publisher <a href="http://playtmg.com/">Tasty Minstrel Games</a>), which I'd always been curious about since its seminal success on <a href="https://www.kickstarter.com/projects/627547359/eminent-domain-the-next-evolution-of-deck-building?ref=nav_search">Kickstarter</a> in the fall of 2010 as one of the ground-breaking boardgames of those early crowd-funding days. As it happens, I found it to be rather a love-child of <i>Dominion </i>and <i>Race for the Galaxy</i>, both games that I wish I liked more than I do, and so I was left similarly unexcited by <i>ED. </i>That's okay; that's why we do demos.<br />
<br />
So Congress of Gamers was a fun, low-key gaming weekend. Such a nice little convention. I look forward to next year. Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com2tag:blogger.com,1999:blog-4535367891237919312.post-71262860544544603692016-09-09T06:30:00.000-04:002019-11-15T06:37:01.624-05:00Collaboration<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/mDO1lCO9kZ9zpBlKFGi9ZiKgfi0=/fit-in/900x600/filters:no_upscale()/pic116113.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="527" height="200" src="https://cf.geekdo-images.com/imagepage/img/mDO1lCO9kZ9zpBlKFGi9ZiKgfi0=/fit-in/900x600/filters:no_upscale()/pic116113.jpg" width="175" /></a>Having always approached game design as a solitary creative activity, I've been curious about successful design teams like Inka and Markus Brand (<i>Village</i>), or Kramer and Kiesling (<i>Tikal</i>). My friend Keith Ferguson recently spoke about the collaborative process with Ben Pinchback, who said that he and Matt Riddle meet on a weekly basis and just work on games for a dedicated regular session.<br />
<a name='more'></a><br />
That notion got us thinking, and the timing was right, so Keith and I have decided to get together on a biweekly basis to try our hand at collaborating on a game project. Our first session was Wednesday night, and in two hours we went from having a couple of vague ideas to sketching out the initial concepts of what could actually develop into a fun game. The best part is that I'm excited about game design all over again, and I think we'll have fun seeing what we come up with, whether or not our efforts amount to anything worthwhile.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-5422050441194279242016-09-05T13:52:00.001-04:002018-10-10T23:07:31.568-04:00Summer vacation gamingOur friends gave us access to their beach house in Rodanthe, North Carolina, for a week this summer. For me, the best part of a summer vacation is simply sitting without a care in the world and reading a book or playing a game, and we did plenty of both. I finished three books (including <a href="https://www.kickstarter.com/projects/625614616/girls-on-games-a-look-at-the-fairer-side-of-the-in"><i>Girls on Games</i></a>, reviewed in my <a href="http://paulowengames.blogspot.com/2016/08/hearing-women-tell-it-review-of-girls.html">last post</a>), and we played games every day, including my sons, who are not normally enthusiastic gamers.<br />
<a name='more'></a><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Kk-hnzb510RzjmMzrZr3JIM_LYsqlIlnBUkbGFCGYbGJA1WREprcT06tQadFA_-0aLgBHXbsOMLg6YbFH4TqbCWEAEK-NIcHtpyPe7oPQNKnqB9zuyNGEPK9DB0GEP0vvhutGrYL2Txj/s1600/0819+Dead+of+Winter.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Kk-hnzb510RzjmMzrZr3JIM_LYsqlIlnBUkbGFCGYbGJA1WREprcT06tQadFA_-0aLgBHXbsOMLg6YbFH4TqbCWEAEK-NIcHtpyPe7oPQNKnqB9zuyNGEPK9DB0GEP0vvhutGrYL2Txj/s320/0819+Dead+of+Winter.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">In <i>Dead of Winter</i>, we "Find a Cure," and two players <br />
satisfy "Justice" and "Collector" objectives</td></tr>
</tbody></table>
Our 20-year-old Liam had discovered <a href="http://www.plaidhatgames.com/games/dead-of-winter"><i>Dead of Winter</i> </a>(designers <a href="https://twitter.com/IsaacsAshes">Isaac Vega </a>and <a href="https://twitter.com/JonGilmour">Jon Gilmour</a>, artist <a href="https://fernandasuarez.carbonmade.com/about">Fernanda Suarez</a>, publisher <a href="http://www.plaidhatgames.com/">Plaid Hat Games</a>) on Tabletop Simulator with friends online, so we picked up a copy from Amazon and brought it with us on vacation to try as a family. It was a huge hit, and we ended up playing twice. There were plenty of B-movie moments - like when the principal and the student are searching the school for supplies, and the zombies are outside, and the principal says, "I think I can take out one of them" - you can hear the audience shouting along with the student, "No, don't go out there, it's too dangerous" - and he gets bitten and turns and kills the student, too. We ended up playing <i>DoW</i> twice that week, and we plan to play again this Labor Day weekend.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgH-ke_BMG-aC6qJpTnzuTXleqnG_OXmOGB6Hk4DKl2Tf4ak1LBsshylcWKxZR08IiznjSYZuiT8m3YludFew-dJTHWsyPIzyMf7AmNPaJ_kx_LgJm8O3LtNhN5HM5f5TQht3Q2cEpvEWx/s1600/0815+Evolution+Climate.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgH-ke_BMG-aC6qJpTnzuTXleqnG_OXmOGB6Hk4DKl2Tf4ak1LBsshylcWKxZR08IiznjSYZuiT8m3YludFew-dJTHWsyPIzyMf7AmNPaJ_kx_LgJm8O3LtNhN5HM5f5TQht3Q2cEpvEWx/s320/0815+Evolution+Climate.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">First game of <i>Evolution: Climate</i>, in which I finished last</td></tr>
</tbody></table>
The big hit of the week, though, was <a href="http://www.northstargames.com/collections/strategy-games/products/evolution-climate"><i>Evolution: Climate</i> </a>(designers <a href="http://www.northstargames.com/pages/dominic-crapuchettes" title="Dominic Crapuchettes">Dominic Crapuchettes</a>, <a href="https://scholar.google.com/citations?user=E6Gk8ogAAAAJ&hl=en" title="Dmitry Knorre">Dmitry Knorre</a>, and <a href="https://boardgamegeek.com/boardgamedesigner/9247/sergey-machin" title="Sergey Machin">Sergey Machin</a>; artists <a href="http://mydogoscar.com/birdspot/" title="Catherine Hamilton">Catherine Hamilton</a> and <a href="http://www.jacobyodesign.com/" title="Jacoby O'Connor">Jacoby O'Connor</a>; publisher <a href="http://www.northstargames.com/">North Star Games</a>), which my friend Glenn Weeks had picked up for me at Gen Con (even though I did not expect North Star to have it yet). We absolutely love this game, and in our first session Liam rocked us all with a burrowing pack-hunting carnivore that we just couldn't beat. Carnivores are tricky - more than once I had a carnivore go extinct just one or two turns after bringing it in. Sometimes we just had lots of fat herbivores sitting around the table seeing who could eat the most, until the climate dragged down the food supply and suddenly there were populations starving. We like this game so much that we've played again several times since we got back, and it remains on the top of my "want to play next" list.<br />
<br />
The other family games we played were old favorites that included <i>Survive: Escape from Atlantis</i>, for the first time using the Giant Squids expansion.<br />
<br />
Kathy and I played a number of two-player games as well, including <i>Splendor</i> and<i> </i>a 2p-variant of <i>Puerto Rico</i><i>.</i><br />
<br />
So, yes, it was a relaxing vacation.<i> </i>Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-20105942144516085212016-08-28T22:08:00.001-04:002019-12-01T22:58:48.909-05:00Hearing Women Tell It: A Review of "Girls on Games"<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc-mPv6kCUB2SAaz4TeWdRrQ2XKV17q68f4YVhcfvlAzwJXxuiI0eAW4wFy4ZKsiLPn_2r4FAKJ368IvMceDy-iGvfuo6yCjR-D6xsImZ2QBP6YAlxYIfIbDCwOrMTV0W7Ot4XS5eRsSnU/s1600/Girls+on+Games.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc-mPv6kCUB2SAaz4TeWdRrQ2XKV17q68f4YVhcfvlAzwJXxuiI0eAW4wFy4ZKsiLPn_2r4FAKJ368IvMceDy-iGvfuo6yCjR-D6xsImZ2QBP6YAlxYIfIbDCwOrMTV0W7Ot4XS5eRsSnU/s320/Girls+on+Games.PNG" width="215" /></a></div>
At a time when the board game community has become gradually
aware of the unique experiences of women in the hobby, the gently feminist <i style="mso-bidi-font-style: normal;">Girls on Games</i>, an anthology on gender
perspective in gaming particularly and in geekdom more generally, successfully
Kickstarted in 2014 with over 900 backers. <span style="mso-spacerun: yes;"> </span><a href="https://twitter.com/geekypinup">Elisa Teague </a>- designer of games, events, costumes, and props - compiled 15 essays by women
and a foreword (by a man) and<i> </i>herself wrote six more plus an afterword.<span style="mso-spacerun: yes;"> </span>She also interleaved “Share My Story
Spotlight” anecdotes by two women, three men, and a girl, plus a poem – or
perhaps a song lyric – by “The Doubleclicks.”<span style="mso-spacerun: yes;">
</span>And to read and hear women tell it, despite a consistently optimistic
tone throughout their essays, they experience some ugly behavior in our gaming hobby<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><span style="mso-special-character: comment;"> </span></span></span>
– from condescension, to scorn, to challenges to their <i style="mso-bidi-font-style: normal;">bona fides</i> as game lovers.<span style="mso-spacerun: yes;"> </span>After
reading of these experiences, frankly,
I don’t know how they put up with it.<br />
<span style="mso-spacerun: yes;"> </span><br />
<a name='more'></a></div>
<div class="MsoNormal">
I suppose not all women do put up with it.<span style="mso-spacerun: yes;"> </span>We hear from the passionate gamer women who
share their stories with an enduring hope to make future experiences better,
more welcoming, more inclusive, more accepting, and less judgmental.<span style="mso-spacerun: yes;"> </span>We don’t, on the other hand, hear much
first-hand or in social media from the women<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_4" id="_anchor_4" name="_msoanchor_4"></a><span style="mso-special-character: comment;"> </span></span></span>who
gave up after the first confrontation, who were intrigued by <i style="mso-bidi-font-style: normal;">Catan</i> among friends but were put off by
their first unwelcome visit to a game store and so turned their backs on gaming
as a hobby thereafter. <span style="mso-spacerun: yes;"> </span>In this
discourse, those voices are silent.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Is it an exaggeration
to say that if the gaming community were aware of the women who have walked
away, we would mourn them – or at least mourn the opportunity to share games
with them and to grow the hobby that much further?<span style="mso-spacerun: yes;"> </span>Every one of us brings something to the
hobby.<span style="mso-spacerun: yes;"> </span>Some of us design, some publish,
some review and constructively criticize, some volunteer, some write, some
podcast, but most of us simply play.<span style="mso-spacerun: yes;"> </span>We
all bring something to the table – except for those of us who don’t feel
welcome at the table and stop coming altogether.<span style="mso-spacerun: yes;"> </span>Those self-ostracized bring nothing, and we
miss what they might have brought.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I should mention that this anthology’s fascinating perspective
and insight suffer, regrettably, as a roughly hewn text in need of professional
attention from both an editor and a formatter.<span style="mso-spacerun: yes;">
</span>In the Kickstarter reward edition on my Kindle, the atrociously laid-out
Table of Contents – with each page number appearing at the end of a ridiculous
string of periods – did not get the same convenient, nicely hyperlinked
treatment that the end notes did.<span style="mso-spacerun: yes;"> </span>Headers
and footers appear in the middle of pages of text.<span style="mso-spacerun: yes;"> </span>I lost count of spelling and grammatical
errors.<span style="mso-spacerun: yes;"> </span>Page breaks do not separate
chapters, which instead begin in the middle of a page.<span style="mso-spacerun: yes;"> </span>A series of <i style="mso-bidi-font-style: normal;">Dork Tower </i>comic strips interleaved among the chapters appear too
small on the screen to read and do not respond to magnification attempts.<span style="mso-spacerun: yes;"> </span>Many paragraphs intended to lead with an
over-sized capital letter instead appear as simply a word with its first letter
separated from the rest of the word by two spaces.<span style="mso-spacerun: yes;"> </span>These formatting and editorial issues make
the book read like a first draft and distract from the collection’s otherwise
compelling thesis.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<div style="text-align: right;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.looneylabs.com/sites/default/files/pictures/kristin.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://www.looneylabs.com/sites/default/files/pictures/kristin.png" height="200" width="184" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Kristin Looney<br />
Source: Looney Labs</td></tr>
</tbody></table>
And yet, for all of those distractions, a compelling thesis
it has indeed.<span style="mso-spacerun: yes;"> </span>As I read Kristin
Looney’s “Life Without Boxes,” I found myself mindful of my own
prejudices.<span style="mso-spacerun: yes;"> </span>When I met Andrew Looney at
UnPub 5 in Baltimore, I assumed that he ran Looney Labs – even though I’d seen
Kristin Looney identified as Chief Executive Officer (CEO) on the company
website.<span style="mso-spacerun: yes;"> </span>I took her to be actually his
business manager and attributed the quirky application of the “CEO” title to
the offbeat, unconventional personality<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"></span></span>
of Looney Labs.<span style="mso-spacerun: yes;"> </span>Kristin Looney’s account
of her gaming and business life, however, makes clear that it is Andrew that
has a creative role in <u>her</u> company and not she that has a business role
in his.<span style="mso-spacerun: yes;"> </span>Looney Labs is successful in no
small measure because Kristin Looney remained true to herself and brought her
full knowledge and talent to bear, rather than accept the boxes into which
people sought to put her as a woman in business.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf9geajkOKmLkkN5hdPirv4NryZVfQnNjFYFVYjSG7Ts0SAvAcHNyRS7ffu_Bk7HQWKGa4DgS4aYrKgKYMVuew4f-aDesYR9ng7_eS7_U7zyDfCLaOT1tKqI4LDSJEibfjlyljOKldhcKO/s1600/Girls+on+Games+-+Fake+Geek+Girl.PNG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf9geajkOKmLkkN5hdPirv4NryZVfQnNjFYFVYjSG7Ts0SAvAcHNyRS7ffu_Bk7HQWKGa4DgS4aYrKgKYMVuew4f-aDesYR9ng7_eS7_U7zyDfCLaOT1tKqI4LDSJEibfjlyljOKldhcKO/s200/Girls+on+Games+-+Fake+Geek+Girl.PNG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Source: Girls on Games</td></tr>
</tbody></table>
Several of the essays recount frequent male accusations of some women as
“fake geek girls,”<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_7" id="_anchor_7" name="_msoanchor_7"></a><span style="mso-special-character: comment;"> </span></span></span>a
notion foreign to me.<span style="mso-spacerun: yes;"> </span>I have no familiarity
with this concept.<span style="mso-spacerun: yes;"> </span>Perhaps I play among
well-behaved gamers.<span style="mso-spacerun: yes;"> </span>Perhaps it comes up
more frequently in comic and video game conventions than at board game
conventions.<span style="mso-spacerun: yes;"> </span>Or perhaps I have something
of a blind eye to the misbehavior around me, as one male admits in his “Share My Story
Spotlight” to having heard but not noticed a woman being hit on at his own game
table.<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_8" id="_anchor_8" name="_msoanchor_8"></a></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The women contributors consistently describe having to prove
themselves qualified to participate in the gaming community, whether as
creators, businesspeople, or even players. <span style="mso-spacerun: yes;"> </span>In numerous random encounters, men dismissed women’s
gaming experience or challenged their “geek credentials” by quizzing them as if
their commitment to the hobby were on trial and men were the gatekeepers.<span style="mso-spacerun: yes;"> </span>These challenges undermine – perhaps
deliberately – women’s confidence and sense of acceptance in a community that
ostensibly enjoys games with such like-minded fellow hobbyists.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Women feel targeted by these credibility challenges, but
they may not realize that male gamers – particularly wargamers, in my opinion –
cred-check each other continually in a kind of knowledge one-upmanship.<span style="mso-spacerun: yes;"> </span>The most egregious example I can recall was
at a War of 1812 re-enactment event, where one uniformed expert insisted that
someone had pronounced “huzzah” incorrectly. The self-identified expert
informed everyone in earshot of the correct 19<sup>th</sup>-century celebratory
exclamation.<span style="mso-spacerun: yes;"> </span>His elucidation of an
obscure historical fact served a tacit but painfully obvious effort to
establish a position in a geek<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"></span></span>
knowledge pecking order.<span style="mso-spacerun: yes;"> </span>Male geeks test
each other in their command of obscura the same way that boys race to see who
is fastest or arm-wrestle to prove superior strength.<span style="mso-spacerun: yes;"> </span>Wargame geeks read avidly, remember
voluminously, and expound proudly, sometimes obnoxiously and ostentatiously,
for the sake of credibility and superiority among their peers. <span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<div style="text-align: right;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://ksr-ugc.imgix.net/assets/002/612/162/3d4ab5bf24a7a8211e2ff4ebc0a985c3_original.jpg?ixlib=rb-2.1.0&w=680&fit=max&v=1411181344&auto=format&gif-q=50&q=92&s=2755d34dc081f543901382dc5712157d" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="300" data-original-width="300" height="200" src="https://ksr-ugc.imgix.net/assets/002/612/162/3d4ab5bf24a7a8211e2ff4ebc0a985c3_original.jpg?ixlib=rb-2.1.0&w=680&fit=max&v=1411181344&auto=format&gif-q=50&q=92&s=2755d34dc081f543901382dc5712157d" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Trin Garritano<br />Source: Kickstarter.com</td></tr>
</tbody></table>
Trin
Garritano’s “The Greatest Game of ‘I’ve Never’” best illustrates the inherent
one-upmanship among male hobbyists by turning the practice on its head.<span style="mso-spacerun: yes;"> </span>She recounts an almost accidental conversation
with a male stranger at a convention that turned into comparing notes on which
canon video games they had <u>not</u> played – as if to say, “See, I’m an
outsider just like you,” only to illuminate the point that no minimum gamer qualification
checklist exists to enjoy the hobby and participate in the community.<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_10" id="_anchor_10" name="_msoanchor_10"></a></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<div style="text-align: left;">
</div>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="http://geekandsundry.com/wp-content/uploads/2017/02/15592288_10210007651699506_1467005097_n-e1486002803528.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://geekandsundry.com/wp-content/uploads/2017/02/15592288_10210007651699506_1467005097_n-e1486002803528.jpg" data-original-height="424" data-original-width="300" height="320" width="226" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Elisa Teague<br />
Source: elisateague.com</td></tr>
</tbody></table>
Still,
given the need for a sense of superiority in a climate of a geek hierarchy that
challenges the male’s validity as a gamer, a woman represents a target of
opportunity against which a male may compare himself and elevate his geek
standing.<span style="mso-spacerun: yes;"> </span>Teague personally undermined
one such effort that she recounts in “The Cred-check: Set Up to Fail,” when a
CVS clerk challenged her on the <i style="mso-bidi-font-style: normal;">Firefly</i>
t-shirt she was wearing on the way to Gen Con.<span style="mso-spacerun: yes;">
</span>She put the fellow in his place, and arguably, he asked for it, inasmuch
as every such challenge carries a risk of failure and inferior standing against
the opportunity to demonstrate superiority.<span style="mso-spacerun: yes;">
</span>He thought he was picking on a weakling but instead woke up a tiger.<span style="mso-spacerun: yes;"> </span>The cred-check backfired, and he had it
coming.<span style="mso-spacerun: yes;"> </span>Guys understand – or should
understand – that issuing a challenge risks losing.<span style="mso-spacerun: yes;"> </span>Women that beat men at this game should
understand that they do not need to feel badly for them.<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_11" id="_anchor_11" name="_msoanchor_11"></a></span></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Except, that is, for<span class="MsoCommentReference"><span style="font-size: 8.0pt; line-height: 107%;"><a class="msocomanchor" href="https://www.blogger.com/blogger.g?blogID=4535367891237919312#_msocom_12" id="_anchor_12" name="_msoanchor_12"></a></span></span> the fact that the whole social construct
of geek hierarchy undermines the hobby in the first place.<span style="mso-spacerun: yes;"> </span>“The Desiderata” warns us against comparing
ourselves to others, lest we become both vain and bitter, because there will
always be those greater and lesser than we.<span style="mso-spacerun: yes;">
</span>We male geeks risk vanity and bitterness in seeking validation through
mutual comparison, but the male beast by nature seeks to challenge others to
prove ourselves.<span style="mso-spacerun: yes;"> </span>To fulfill our
potential as intelligent, morally aware, enlightened beings, however, we need
to transcend our primal tendency to push ourselves up by pushing others down and
instead protect the dignity of every member of the community that would join us
in our mutually enjoyable hobby, male and female alike.<span style="mso-spacerun: yes;"> </span>Games, after all, constitute a fundamentally
social activity.<span style="mso-spacerun: yes;"> </span>We compete not to test ourselves
against each other but to enjoy the company and the competition.<span style="mso-spacerun: yes;"> </span>We embrace a social contract in the rules of
the game and in entering the magic circle that envelopes our experience and structures
our personal interactions.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i style="mso-bidi-font-style: normal;">This reviewer backed
Teague’s <a href="https://www.kickstarter.com/projects/625614616/girls-on-games-a-look-at-the-fairer-side-of-the-in/description">Kickstarter project</a> to fund publication of </i>Girls on Games<i style="mso-bidi-font-style: normal;">.<span style="mso-spacerun: yes;"> </span>This
review addresses the .</i>mobi<i style="mso-bidi-font-style: normal;">-formatted
ebook reward copy from that crowd-funding campaign.<span style="mso-spacerun: yes;"> </span></i></div>
Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com1tag:blogger.com,1999:blog-4535367891237919312.post-60157681052282499122016-08-12T07:00:00.000-04:002016-09-04T16:02:48.432-04:00Fifth annual-ish "What to pack for a vacation"This summer we're headed to the North Carolina Outer Banks for a week at a beach house. We just threw together a list of games to bring based partly on recent acquisitions, partly on old favorites, and partly on family stand-byes that we think we can get the normally reluctant sons to play. Here's this year's packing list:<br />
<a name='more'></a><br />
<blockquote class="tr_bq">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBU4lUHFqFNchYE2tOvgUiPrZFCI399uhFnXbHNXYTh9B2xyIjo_TrV-P8bltJlETHrJEgvfLTZcGk9J-EG9iaQPtTxYzSi07CJyo6K9oyoZ0sR_5XJ1W-LA9Tp7zLuUjkPkRnq74hTqt0/s1600/LS-Sleeve-front.tif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBU4lUHFqFNchYE2tOvgUiPrZFCI399uhFnXbHNXYTh9B2xyIjo_TrV-P8bltJlETHrJEgvfLTZcGk9J-EG9iaQPtTxYzSi07CJyo6K9oyoZ0sR_5XJ1W-LA9Tp7zLuUjkPkRnq74hTqt0/s320/LS-Sleeve-front.tif" width="242" /></a></div>
<i>- Splendor<br />- Jaipur<br />- Dead of Winter<br />- Evolution: Climate<br />- Last Spike<br />- New Bedford<br />- Bang! Halo<br />- Survive: Escape from Atlantis<br />- Munchkin</i>
<br />
<i>- Qwirkle Cubes<br />- Pie Factory<br />- Diner<br />- Incan Gold<br />- PowerMage 54<br />- Love Letter<br />- Loot Letter</i></blockquote>
Past years' vacation packing lists:<br />
<blockquote class="tr_bq">
<a href="http://paulowengames.blogspot.com/2015/08/fourth-annual-ish-what-to-pack-for.html">2015 Bermuda cruise</a><br />
<a href="http://paulowengames.blogspot.com/2014/08/third-annual-ish-what-to-pack-for.html">2014 southwest Virginia</a><br />
<a href="http://paulowengames.blogspot.com/2011/07/what-to-pack-for-vacation.html">2011 West Virginia mountains</a></blockquote>
Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0tag:blogger.com,1999:blog-4535367891237919312.post-50425780287886059032016-07-22T23:17:00.000-04:002019-12-28T02:24:18.138-05:00Can one house rule make an old game new again?<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/Df4qKZlLrXPNrlrSbQAdcl390Xg=/fit-in/900x600/filters:no_upscale()/pic205804.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="492" height="200" src="https://cf.geekdo-images.com/imagepage/img/Df4qKZlLrXPNrlrSbQAdcl390Xg=/fit-in/900x600/filters:no_upscale()/pic205804.jpg" width="163" /></a>Replacing the dryer with one that was two inches wider led to having to move a shelf unit. Which meant unloading all the old games from the shelves. Which meant going through all the old games and deciding which to keep and which to dispose of. Which meant rediscovering games that perhaps deserved a second look. Which led to trying a 20-year-old game that I'd picked up at a PrezCon auction thinking my wife would like it but never actually played - <a href="https://boardgamegeek.com/boardgame/2119/221b-baker-st-sherlock-holmes-time-machine">221B Baker Street: Sherlock Holmes and the Time Machine</a> (designer Jay Moriarity, publisher <a href="http://johnhansenco.com/">John N. Hansen Co</a>).<br />
<a name='more'></a><br />
The game includes 20 different mysteries that appear to be actual historical cases (hence the loosely-applied "time machine" theme). My wife and I played the first one, The Mystery of the Black Dahlia. We read the opening story introduction and then raced among about 20 locations to uncover clues and determine the four elements of the crime - the killer, the motive, the weapon, and the victim's secret. The first of us to solve the problem and then return to the "time machine" (the space in the center of the board) would win the game.<br />
<br />
What I appreciated about this game over all other "deduction / crime-solving" games is that the game does not abstract the mystery among a set of discrete options with a process of elimination in the way that <i>Clue, Alibi</i>, and <i>Mystery of the Abbey</i> do. All the elements require some degree of actual reasoning and inferring logical conclusions from available piecemeal facts as they emerge. Even the opening story hints at which locations on the board might provide significant early clues. There is a real tension in trying to tie the evidence together and make sense of it before the opponent does.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<a href="https://cf.geekdo-images.com/imagepage/img/lNp86gL1fwnOcYXD0aSRnPHKIYs=/fit-in/900x600/filters:no_upscale()/pic201212.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="532" data-original-width="800" height="132" src="https://cf.geekdo-images.com/imagepage/img/lNp86gL1fwnOcYXD0aSRnPHKIYs=/fit-in/900x600/filters:no_upscale()/pic201212.jpg" width="200" /></a>The only interaction among players is in the use of badges (locks, really) and keys. Each player may hold at most one lock and one key, and starts with one of each. Upon leaving a location, a player can leave a lock on the door, which requires an opponent to spend a key to enter the location. More locks are available at the FBI Building (we're not in London any more) and keys at the Locksmith. In a two-player game, this interaction doesn't amount to much, other than to slow down an opponent from discovering a valuable clue (or to bluff as to the significance of a location). I can imagine locks and keys getting a little more activity with more players.<br />
<br />
The weakness in the game is that like <i>Clue</i>, the game forces players to roll a die and move on a grid to get from one clue-revealing location to another. A sequence of bad die rolls can leave a player with several consecutive unproductive turns. And the movement decision is not generally arbitrary. Clue distribution
among the locations appears to have at least some significance to the
locations themselves. Sometimes clues refer to other locations. So
there is some real reading between the lines when deciding where to go
next. Depending on die rolls becomes all the more bothersome when movement is so crucial to the process of solving the crime. This adherence to an obsolete mechanism would hold the game back significantly - if it were not for one fortunate aspect of the game board design.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://cf.geekdo-images.com/imagepage/img/ytd--u0I5gEcVjbYB3hDzj3SL-4=/fit-in/900x600/filters:no_upscale()/pic107048.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="800" height="480" src="https://cf.geekdo-images.com/imagepage/img/ytd--u0I5gEcVjbYB3hDzj3SL-4=/fit-in/900x600/filters:no_upscale()/pic107048.jpg" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
Every location on the board is exactly six spaces from at least two other locations on the board. That means that on a roll of six, a player can simply decide to which nearby location to move next and read the corresponding clue. The simple and obvious solution to getting bogged down with die rolls between rooms is not to roll the die at all but allow players to move six spaces every turn. Then area movement rather than roll-and-move governs the game (perhaps more in the manner of <i>Mystery of the Abbey</i>), and the board becomes a simple network of locations in which each move is a commitment toward one part of the board and away from another.<br />
<br />
One reviewer actually <a href="https://boardgamegeek.com/thread/190451/good-fun-despite-absence-eloi-and-morlocks">suggested</a> this assignment of six spaces to every roll. I'm convinced that it will speed up play and eliminate the caprice of dice luck. Kathy and I are looking forward to our next play of this game <i>sans </i>dice.<br />
<br />Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.com0