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Smallest Possible Chance to Win? - Mochy

Posted By: Timothy Chow
Date: Tuesday, 18 May 2010, at 2:29 a.m.

In Response To: Smallest Possible Chance to Win? - Mochy (mochy)

O.K., I finally understand the question! And just to be sure, we're assuming it's DMP, right? The checker play could differ in a money game and that might affect the winning chances.

I don't know if nori's position has higher winning chances, but one way to get a lower bound on the winning chances is to specify a sequence that leads to a hit, calculate the probability of that sequence, and then work forwards from there. For example, in nori's position, the most likely way to get a hit is "dance, doublet, dance, doublet, dance, doublet, dance, non-doublet, hit." The probability of this happening is

(1/36)*(1/6)*(1/36)*(1/6)*(1/36)*(1/6)*(1/36)*(5/6)*(11/36)

Actually the non-doublet doesn't have to come last so we should really multiply the above by 4. Now that you have a hit, the winning chances should go way up. Unfortunately it's not so easy to estimate this number because the bot may not play the game so well, but again since we're just trying to get a lower bound, we can assume a favorable sequence of events, such as making a 6-prime and rolling it home while the opponent fails to leap. One has to work this out in detail to be sure, but I would be surprised if this were not much larger than the non-contact position, where you have many more factors of 36 in the denominator.

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