The Game Theory of Games

I’ve been witnessing a Twitter Battle play out over weeks, days, and now over the course of minutes.  The subject is Machi Koro.  The debate is about whether Machi Koro is fun (or even a game).

I boil it down to two perspectives:

1.  There are lots of ways to play and win
2.  There are few decisions/you play the same way every time

I think both of these are true.  I made a simulation of the game (reducing quite a bit of it out) to examine probabilities/payoffs of various strategies.

What did I find?  There are dominant strategies.  That is, while there are many ways to play the game, if you want to maximize your chance of winning you should make a single best decision based on the circumstances (how many players is the most important followed by what personal cards have been flipped (like the Shopping Mall).

So people that hold perspective #1 above don’t feel constrained by the dominant strategies.  They have fun trying out different things — even though, in the long run, most of those “things” are sub-optimal.

For the people that hold #2 the game is sort of on autopilot.  You play the odds.  And every game really is just the same thing repeated over and over again. [Interesting side note, could add betting to MK to add some spice to playing the odds]

Many deck builders solve this problem by having a wide variety of potential cards to build with — then randomizing a subset to play with.  This changes the context every game.  And in each game you’re trying to figure out the dominant strategy — rather than just implementing it.

That approach is okay.  But an even better fix is to create more interaction between players.  The Red and Purple cards just don’t do enough to change the probabilities on the choices to make.

I’m eager to see the expansion with new cards and new rules/variants that might address the above.  There’s much to like about the potential of Machi Koro.  But in terms of game theory, if your game has dominant strategies — and even worse, equilibrium of dominant strategies, they aren’t going to be fun in the long run.

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