Agricola close-up

Spanish boardgame geek Roberto Méndez has started a game photography project he calls, "52 Weeks 52 Photos."  This week's photo of Agricola reminded me that I'd taken a few photos of a game Kathy and I had played recently but never posted.

Kathy's very successful wild boar farm in our Agricola game two weeks ago 

So here's today's Agricola close-up, inspired by Roberto Méndez.

Tsuro close-up

I've been trying my hand at some boardgame photography, so tonight I thought I'd post a shot I took at the end of our game of Tsuro (designer Tom McMurchie; artists* Shane Small, Cathy Brigg, and Sarah Phelps; publisher Calliope Games).

Kathy's winning position at the end of Tsuro.  My just-eliminated black stone languishes on the board edge in the background.  Had I been able to last one more turn, she would have been eliminated on her next tile play.

I have to say that this is one of the most aesthetically pleasing games we own, and I'm very fond of it.  As a game, it is a very quick play with only a few decision options each turn, but it certainly requires some thought and planning ahead.

Tonight I gambled on having the right tile come up to extricate my piece from a bind into which I'd put myself, trying to corner my wife's piece and lock her out of the more open side of the board.  My gamble didn't pan out, and she ended up beating me with just one open space left.

Since Tsuro ostensibly accommodates up to eight, I'd love to play this game with a bigger group, but seldom do we get more than three to the table for it.

*Boardgamegeek.com entry gives artist credits to Franz and Imelda Vohwinkel.  I can't figure out why.

Design inspiration

Working trademark for
"Gold on Mars"

Missing Unpub2 on Saturday inspired me to set aside a "designer day" of my own.  Since I had today off from work, I decided to sit down with "Gold on Mars" and nail down all the loose ends in my design.  My goal was to have a playable prototype by the end of the day.  I didn't quite get there, but I did get a good draft of rules for the commodities market written up and settled on the actual commodities and price structure that I think will work.  Everything will change with playtesting, of course, but I like my first cut to represent enough thought and planning that when it goes to table for the first time, it plays at least roughly well.

Space travel is still my major sticking point, and I wish I'd spent more time on it.  I think I finally settled on some rules for how much fuel is required to get to each planet, and how much fuel must be carried (or produced in situ) for the return trip.  I just don't want to get hung up on making players do too much math, or end up with such widely disparate transit costs among planets that a degenerate strategy develops to ignore distant mining sites in favor of those closer to Earth.

Another concern I have is the risk of a jackpot mining operation resulting in a runaway leader.  Mining is necessarily speculative, and has to have a major upside potential to justify the expense and risk of space travel, but if one player hits it big and others have mines that run dry, then the game simply ends up being an exercise in dice and card luck.  So once I do have a prototype, the first few playtests will have to expose the luck factors and point me in the direction of redesigning and reworking game elements to make it a contest of thoughtful risk management, more than just luck or puzzle-solving.

I do love a challenge.

***

Beer, wine, and Citadels

We did a fair amount of family gaming over the long weekend.  Saturday night saw us break in my dad's copy of Trains Planes and Automobiles.  We had a fun five-player session that saw the lead change hands several times before I finally won - almost entirely with railroad cities and without a single airport.  Sunday night we played a seven-player Sour Apples to Apples (publisher Mattel, strangely missing from mattel.com).   A Christmas gift from our oldest son, SAtA, like the original AtA, is a fun game for a big group.  (Lesson learned:  There's a big difference between the adjectives "immoral" and "immortal.")  And this evening, Kathy and I played another two-player session of Citadels in which she proved once more that she is living rent-free inside my head - and sometimes she even pulls the levers, tugs the strings, and pushes the buttons in there.

Risk management and pigs: Running the numbers

Pig on left demonstrates the very
difficult "leaning jowler" while pig on
right wallows on table, unimpressed

In my last post I discussed the personal thresholds that my wife and I have when playing the push-your-luck game Pass the Pigs.  For those not familiar with the game, it consists simply of two little rubber pigs that can be rolled like dice.  Each will come to rest in one of six positions, and the resulting score depends on the combination of the two resulting positions from one throw.  A player can elect to keep rolling the pigs and racking up the score, but if on any throw one pig lands on its left side and the other on its right, the result is a "pig out" and no points are scored on that turn.  So the push-your-luck aspect comes in deciding how far to go before stopping to keep the points scored on that turn rather than risk pigging out on the next throw.

My habit has been to stop rolling when I've reached a score of 11 or higher (unless I'm behind, in which case I'll take a chance on catching up).  Kathy's personal threshold is a score of 15.  Our friend "SPC" commented back to say that his threshold is 18.  But all of that was pretty much based on a qualitative sense of risk tolerance, not any real actuarial analysis.

As it happened, back in October, the intrepid boardgame geek Mike W. actually kept track of 895 rolls of two pigs over ten games and posted the resulting statistics.  These data provided a golden opportunity to do some real optimization analysis.  Release the spreadsheets!

I started with Mike's breakdown of 1790 individual pig results:

Result, Number of Occurrences, Percentage

On Side, 1243, 69.4%
Razorback, 388, 21.7%
Hoofer, 112, 6.3%
Snouter, 30, 1.7%
Leaning Jowler, 17, 0.9%

I broke out the "On Side" results and assumed half were on the left, half on the right, then made a matrix of all possible combinations of two pigs:

Probability	Left side	Right side	Razorback	Hoofer	Snouter	Leaning jowler
Left side	0.120409	0.120409	0.075299	0.021861	0.005899	0.003123
Right side	0.120409	0.120409	0.075299	0.021861	0.005899	0.003123
Razorback	0.075299	0.075299	0.047089	0.013671	0.003689	0.001953
Hoofer	0.021861	0.021861	0.013671	0.003969	0.001071	0.000567
Snouter	0.005899	0.005899	0.003689	0.001071	0.000289	0.000153
Leaning jowler	0.003123	0.003123	0.001953	0.000567	0.000153	0.000081

Now, given a starting score s, I treated a result of one left-side pig and one right-side pig as have a value of -s, and all other results having the positive score value in the game (five points for a razorback, 20 points for a double hoofer, etc).  The expected value of a roll of two pigs is the linear combination of probabilities and corresponding scores, where the "pig outs" have a value of -s for a given starting score s.

For the first roll of the turn, s = 0, and the expected value turns out to be +4.17.  For every point of s at risk, the expected value goes down by 0.24 (the probability of a "pig out").  So for any initial score s, the expected value of the next roll is

s		Expected value
0		4.17
1		3.93
2		3.69
3		3.45
4		3.21
5		2.97
6		2.72
7		2.48
8		2.24
9		2.00
10		1.76
11		1.52
12		1.28
13		1.04
14		0.80
15		0.56
16		0.32
17		0.08
18		-0.17

These results really surprised me.  They indicate pretty clearly that my instinct for stopping at 11 points is way too conservative.  With only 11 points at stake, the next roll still has an expected value of 1.52 - better than a sider.  Even my wife's threshold of 15 is a bit safe, since the subsequent roll would still have an expected value of 0.56.  But most amazing is that "SPC's" risk tolerance is perfect (according to these data).  If he rolls on 17 but stops on 18, he is playing PtP right down to the tip of the snout.  On scores of 18 or higher, the downside risk outweighs the upside, and it's time to stop (unless the opponent has a significant lead and the game is in jeopardy).

This revelation of my own conservative play reminds me again of my poor showing in Can't Stop at Congress of Gamers (and before that at PrezCon).  I think I'm going to have to run the numbers on CS some time and see what I can discover about my risk threshold there.

Luck, risk management, and pigs

Beer, wine, pretzels, and pigs -
my final losing "pig out"

My wife and I were playing Pass the Pigs (designer David Moffatt, publisher Winning Moves) this evening before dinner, and my son happened by and said, "I thought you didn't like games based on luck."

What a great question.  I don't like games based on luck - games like Life, Sorry, War, and any other game in which luck renders decision-making moot.  But I certainly do like risk management games, and PtP is squarely in that category.  I've posted before about my early observations on how the teenage brain works in assessing risk.  In our first family game of Incan Gold,

[My son] bolstered my working hypothesis on teenagers and risk assessment.  He was always still in the expedition when the second monster of a suit came up, so he ended up with no treasure after five rounds.

On the other hand, I remember getting my butt kicked in Can't Stop at Congress of Gamers last fall because of that very phenomenon.

One brilliant element of PtP is that since the pigs aren't really dice, it's very difficult to calculate probability in the conventional sense.  The pigs are oddly shaped, and because I'm too lazy to run 1000 trials of pigs to estimate the expected value of a roll (although somebody else wasn't), well, I just wing it on the risk assessment.  My "wing it" threshold for PtP is typically eleven points.  (Actually, maybe I shouldn't post that number online.)  If I'm significantly behind, I'll take bigger chances, but overall, I'm still pretty conservative.  My wife said her threshold was 15 points, but after I told her mine was eleven, she started stopping at eleven, too.  And she won.  So what does that tell you?

***

So now that I've been thinking about the fact that somebody else actually did run the numbers on the pigs, my inner mathematician compels me to calculate the optimal threshold for rolling again vs. not rolling again.  I think that will be a topic for a future post...

Playing with Christmas toys

This evening, Kathy and I played two games that we received as Christmas presents this year.  First was a gift from our gaming buddy Glenn called Ingenious Challenges (designer Reiner Knizia, publisher Fantasy Flight Games).  This little box actually contains three games - "Card Challenge," "Dice Challenge," and "Tile Challenge" - that are based on Knizia's clever board game Ingenious.  We tried the Dice Challenge, whose scoring is based on the same "advance all six colors" principle of Ingenious but by rolling dice to match those of the opponent.  Right away, we began to appreciate that this is more than just "Yahtzee with colors and shapes."  The roll you decide to use for your score is also the roll that your opponent(s) will try to match and use to score as well.  So like the board game, it is as important to keep an eye on your opponents' scoring needs as it is your own when deciding the position you want to leave at the end of your turn.  In this case, each of us tried to avoid leaving dice that the other needed to score.  It turned out to be a very close game that Kathy won with some judicious re-rolls.

24/7: The Game - near the end of this evening's session

Our second game was a gift that I picked up for Kathy based on a recommendation (I wish I could remember from whom) as a "spouse" game - 24/7: The Game (designer Carey Grayson, publisher Sunriver Games).  This game for two to four players appeals to me in two respects - the gameplay challenge and the physical quality, much as do the two-player games Quarto and Hive.  In 24/7, players take turns laying tiles onto a board in a kind of crossword fashion, similar to Scrabble, except that the tiles are numbered from one to ten, only one tile is laid in a turn, and scoring comes from completing runs, matching sets, or sums adding to seven or 24.  In our game this evening, again, the importance of not leaving the opponent an opportunity to score became evident.  I had one big bonus score - completing both a seven and a 24 on a double-score space - that turned out to be the game-winner.  (In the photo, that was the '6' tile in the upper left corner of the picture.*)  I have been pleasantly surprised that my right-brained mystery-writer wife likes this arithmetic-dependent game as much as I do.

Incidentally, I'm inspired by GamerChris's new Picture of the Week series and Roberto Mendez's 52-weeks-52-photos geeklist to renew my amateur interest in boardgame photography.  So I hope to have the camera out more often and resort less frequently to stock box art images in the future.

*The astute observer and aficionado of 24/7 will observe that one of us made an illegal tile placement at some point during the game.  I will leave it to the reader to find the error.

Family games - what works for both adults and kids?

As parents of boys spanning eight years in age difference, we've struggled to find family activities that work for all of us.  Naturally, my first choice for an indoor occasion is to play a boardgame - anything we can all agree on and enjoy.  In my experience, a game that appeals to kids as well as the adults in the family does not come along often.

The other day we tried a little game that my son got for his birthday called Pictionary Card Game (designer Brian Yu, publisher Mattel).  Unlike the original Pictionary, which requires players to draw diagrams and pictures, the card game has a set of pictographs - little cards with icons, sketches, and other abstract or symbolic drawings that can be combined or manipulated to prompt teammates to come up with the intended answer.  There are two levels of play - adult level, where the answers that teammates need to guess require a certain familiarity with culture and turns of phrase (like "Yellow Submarine"), and kid level, where the answers are more generic (like "ruler").  Each answer has an associated category (like "school supplies" for "ruler") so that players have a general idea of what they're trying to guess.

Sample pictograph cards used
in Pictionary Card Game

What we found was that when adults play with kids at the kids level, the adults will start shouting a range of generic answers to the category before the "clue-giver" has much chance to assemble the pictographs into any kind of clue.  For example, when "school supplies" was announced, people started calling out "paper," "pencil," "eraser," "chalk," etc.  In several cases, the right answer was stumbled on in a matter of seconds.  So the conclusion I reached is that PCG probably works well for kids among kids, and for adults among adults, but not in a mixed setting of adults and kids.  Other word-association games that have not always succeeded to bridge the adult-kid gap include Catch Phrase (which the kids love but which the adults tend to dominate) and Taboo.

Games that have worked well for us in a broad age range setting include Clue, Apples to Apples Junior (though not the original Apples to Apples), Pirateer, and Guillotine.  In larger groups, we've had success with Are You a Werewolf? as long as the participants are comfortable in a player-elimination game.  (If the group includes kids who are sensitive about getting "voted out," then Werewolf won't work.)

Trains Planes and Automobiles fits the bill as a family past-time in a group spanning a broad mix of ages - even more successfully than I expected when I first conceived and developed the game.  I am frequently and pleasantly surprised by the positive reactions I get from both children and adults when I demonstrate it at conventions or hear from people who have played it at home.  I mentioned in my last post that it had become a favorite of our friends' son and that they love the fact that they can get together and play it as a family without having to drag people to the table.  I think the principle reason is that TPA rewards good decision-making enough to keep grown-ups engaged but also has enough luck and balancing elements to keep everybody in contention for the whole game.  Kids feel as though they have a good chance to win, while adults enjoy playing a real game that is more than just a roll-and-move luck exercise.

Familia quod ludit una manet una.

New year of boardgame socializing

To me, boardgaming is primarily a social experience, and our new year celebrations this weekend have been no exception.

Last night, on the occasion of celebrating the new year, we visited our friends Brion and Theresa H. for dinner, drinks, and several games.  We opened with Citadels, the card game that has emerged as my very favorite discovery of 2011.  Theresa won handily with something like 27 points scored in an eight-district citadel that included all five colors.  Next we played Trains Planes and Automobiles, which I was pleased to learn had become a favorite among Brion and Theresa's family.  Yours truly managed to stay just ahead of Theresa for the win, helped by four consecutive air travel assignments facilitated with a frequent flyer and clear skies.  We wrapped up the New Years Eve gaming with Storming the Castle (designer Aaron Watson, publisher Toy Vault), a light-hearted card-driven race game based on the 1987 film Princess Bride.  My wife Kathy won as the giant Fezzek taking advantage of "four white horses" to beat us all to the castle.

Today I invited several friends over to play a couple of games and share some good company.  Grant G., his brother W.J., and Glenn W. joined me in rewriting the History of the World (designers Gary Dicken, Steve Kendall, and Phil Kendall - artists Charles S. Jarboe Jr, Steve Kendall, and Jason Spiller - publisher Avalon Hill), an old favorite that never seems to get enough play time.  Grant achieved a fairly commanding victory, in no small part to his success in holding on to his acquisitions and generating victory points for multiple epochs, particularly with the Romans in southern Europe and several Asian civilizations and a big scoring turn with the Arabs.  I had a strong early game with the Assyrians and a strong finish with the Mongols, Ottoman Turks, and Britain, but was nearly wiped off the map in the middle of the game around Epoch IV from which I never fully recovered.  I finished third behind Glenn.

If HotW can be subject to the vagaries of card luck, not so the brilliantly-designed Puerto Rico.  We invited my wife Kathy to join us for a five-player session.  PR has become one of my favorite games for its nearly pure dependence on player decisions for the course of the game.  I managed to pull out a win with some very heavy shipments of corn, tobacco, and sugar, just two points ahead of Kathy's dominant building performance.

This kick-off to the new year inspires me to revitalize my focus on boardgames and design.  Although I will miss Car Trunk Entertainment's Unpublished Games Festival "UnPub II" in Dover, Delaware later this month, I look forward to PrezCon in Charlottesville, Virginia in late February.

Here's to a whole new year of gaming developments and discoveries.

Ludero ergo sum.