The Tao of Gaming

Boardgames and lesser pursuits

Can’t Stop Theory

I’ve been thinking that I should write a simple computer opponent to explore various AI techniques (neural nets, genetic algorithms). Of course, I’m mainly in the ‘thinking about’ stage.

Can’t Stop seems like a good choice because the rules are simple. If you could value a position then it’s simple — split the dice to maximize your position, then check
[% failure to advance] * [current unbanked gains] is greater than [expected gain when you succeed]. If the first number is greater, stop.

But the real issue is — how to quantify a position. A zeroeth order approximation is to call capping a column 1, and then each step on a column is worth 1/X, where X is the length of the column (counting the cap as a space).

Michael Keller’s “World Game Review” [Issue 7, page 5] analyzes the game with this formula and provides a mnemonic for when to stop (“Math is hard”).

But that doesn’t seem right. The value depends on how far up the column everyone else is? [The WGR admits this as a problem, but offers no solution]. If ‘7’ is almost capped, the first few steps of ‘7’ should be basically valueless (so your advancement on other columns count).

So tweak the formula. I’m wondering how. I suspect that the best bet is to perhaps develop a generic formula per column(mybase, mycurrent, opponents bases) and then use a genetic algorithm to see where the coefficients drift toward (you can also have an ‘aggressiveness’ gene, that biases a strategy towards rolling or stopping….)

It should be possible to write a reasonable opponent, but I’ll admit that I have no idea what the ‘best’ algorithm will look like….[it may also vary based on # of players].


Written by taogaming

February 16, 2005 at 7:29 pm

Posted in Strategy

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One Response

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  1. Brian, do you have the “Roll or Don’t” computer application? This is a Can’t Stop program created by good guy and good gamer Jim Cobb. Anyway, a few of us were talking about the possibility of him doing an updated version and he said that he got his AI algorithm from a fellow who did an analysis of the “optimal” way of playing Can’t Stop. Unfortunately, it doesn’t take the opponents’ positions into account, but it does play a reasonable game. You might want to get in touch with him; I can give you his contact information if you need it.

    As far as the worth of a step of a column, I agree they should be variable. One thing you may want to consider is what kind of position you want to leave yourself with. For example, I often like to keep going until I am three spots from the top. I’ll make this four from the top for 7 and two from the top for 4 and 10. My reasoning is that I don’t want to make it too hard for me to complete these columns in a future turn. The worst thing you can do is stop one or two spaces from the top; even if an opponent isn’t in position to steal it from you, you’ll have to “waste” another turn to finish it off. So I usually push when I’m in that position, and if I crap out, I don’t want to lose too much ground that turn. So I judge these “stopping” points higher than the steps above or below them. I’m not saying this is optimal, but I suspect that something along these lines is and that this kind of reasoning should go into developing a good strategy.

    Larry Levy

    February 17, 2005 at 6:33 pm

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