Games for four-year-olds

[This is a re-post of an entry originally published on 2 February 2012. The post was somehow corrupted, so I am restoring it for accessibility.] 

I was recently asked about games for very young kids.  I haven't looked at games in this age range in a while (since our youngest is eleven), so it was interesting to revisit the gamescape for the booster-seat set.

We still have two in our house that our kids enjoyed back before kindergarten:

Husker Du is essentially Concentration in a kid-friendly format.  The board consists of a number of small round "windows" through which symbols on a single rotating disc are visible.  Game set-up consists of covering the windows with checkers, then rotating the disc so that new symbols are lined up in the windows under the checkers.  Players remove checkers two at a time looking for matching symbols.  If they match, they keep the checkers; if not, the checkers cover the symbols again.  An old standard memory game, always a good parent-child past-time.

Launch Across is a cross between table-top basketball and Connect Four.  Each player has a launcher that propels colored balls against a backboard and down into one of several stacking columns.  The first to get four in a straight line row (horizontal, diagonal, or vertical) wins.  I'm not usually a fan of dexterity games, but this one is entertaining.

A search of the boardgamegeek.com database turned up a number of good options that are still available on the market:

• "Animal Upon Animal is a simple stacking game, listed for ages 4-99, with 29 cute wooden animals."
  
• Kids of Carcassone is a tile-laying game patterned after the phenomenally popular Carcassonne with simpler dynamics but, according to some parent reviews, engaging gameplay.
  
• "Viva Topo! is a [roll-and-move] family game that has players balancing risk and rewards as they attempt to outrun the cat and score for cheese. Players attempt to advance their mice to various goals. The further the goal, the more cheese it is worth. Pursuing the mice is the cat that removes the mice from the game should it catch the mice.  Movement is regulated by a die that also moves the cat. Initial cat moves are only 1 space, but become 2 spaces after once around the track, so when the cat speeds up, it's almost all over!"
  
  
  
• Boo Who? (originally Geistertreppe, now available as Spooky Stairs) has a clever feature in which players' pieces are magnetic and become hidden by "ghost" pieces over the course of the game.  Players try to remember where their pieces are and get them to the top of the castle stairs to win.
  
• "Being afraid of monsters is a normal part of growing up.  Go Away Monster! encourages kids to conquer that fear by acting it out and taking control.  It also lets them experience some of the apprehension and excitement in deciding what is real and what is imaginary.  Reach in the bag to find the puzzle pieces that fit your bedroom game board. Try to distinguish between the different puzzle pieces and decide which one feels like the size and shape of a piece you need. If you pull out a monster, don't be scared... You take charge, and the monsters will take off!"

I'd be curious to know what other games have become family favorites among parents of the pre-school generation.

A couple of funny little card games

As a get-well gift, a friend gave our convalescing family member the card game Angry Birds (Mattel), based rather tangentially on the popular app.  As games go, it's largely a function of dice and card luck, but it's a fun diversion with young kids.  We played a three-player round this evening, and we got some good laughs out of it.

Kathy's winning manipulation of the
time continuum in Chrononauts

Because Angry Birds went so quickly, Kathy and I then turned to another card game with a different bent of humor, Chrononauts (designer Andrew Looney, artist Alison Frane, publisher Looney Labs).  We like this game as an interesting twist on the Fluxx line of shifting victory condition card games that Looney Labs has put out.  As time travellers, we saved the lives of Abraham Lincoln, the Archduke Ferdinand, and John Lennon.  Kathy (as "Timmy") managed to travel back to 1918 when, thanks to the Archduke Ferdinand's narrow escape, Europe had avoided a destructive war, enabling her to "patch" the timeline with a European economic boom.  Then she traveled ahead to 1980 and saved the life of John Lennon from his would-be assassin.  She then traveled on to 1999 and engineered Senator Lennon's success in passing a Constitutional Amendment to repeal the Second Amendment and institute a nationwide gun ban.

Although some of the alternate timelines in Chrononauts are a bit tortured, the game itself is fun.  Besides manipulating history, the game can be won by collecting artifacts from history (or the future), some of which make me laugh every time I see them (such as the "Obvious Forgery of the Mona Lisa," depicted with a mustache).  The fairly simple gameplay features some tricky decision-making and risk-taking, which makes for a good overall card game.

Gaming in a hospital room - Monopoly Express

Some months ago I wrote a post on what kinds of games work when keeping someone company in a hospital room, and what kinds of games don't.  I had the occasion this week to while away time in similar circumstances, and we settled on Monopoly Express (designers Garrett Donner and Michael S. Steer, publisher Hasbro) as a not-bad alternative when conditions don't allow the kind of space that board and card games typically require.

Monopoly Express
photo Hasbro 2007

First published in 1991 as Don't Go to Jail, the dice game Monopoly Express was re-released in 2007 in a round plastic container that is rather difficult to open.  This inconvenience is a blessing in disguise, because it allows ME to be thrown into a bag and taken anywhere without concern for lost pieces.  The container also serves as a dice tray, and it was this feature that made the game work so well in a surgery waiting room.  My wife and I were able to play this game on the seat between us without worrying about pieces rolling onto the floor.

Monopoly Express board
photo posted to boardgamegeek.com
by Chris Blakely

The "board" is a round plastic disc with recesses for placing dice to score points.  The game itself is a "push your luck" game along the lines of Pass the Pigs, $GREED, or Can't Stop.  Three dice have only "Go to Jail" policemen, "Go" green arrows, or blank faces.  Seven other dice have colors and denominations on each face that correspond roughly to familiar properties on a Monopoly board.  A player's turn consists of rolling the dice, putting any policemen on the board, and then also placing on the board a combination of colored denominations that offers the best prospects for scoring points.  Completed sets are worth more points than the sum of individual dice and also offer the opportunity to add the "house/hotel" die to the mix on the next roll; houses and hotels add greatly to the score.  A player can re-roll remaining dice or stop at any time and score the results of the turn, but if a roll turns up the third policeman, then the player scores nothing that turn (like a "pig out" in PtP).

The value in this game isn't the twist on the push-your-luck format, and certainly not its very small addition to the deluge of Monopoly titles in the world.  Its real value is its extreme portability and quick play.  This week it got more action than PtP because it doesn't even need a flat playing surface.  At a time when we all needed a little cheering up, ME helped pass the time in a pleasant, undemanding way.

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...