This is a terrific tool that will help you understand your odds. Thanks to the great Paul Weaver for working this out for us.
Assume that X gets hit while bearing off. Assume that O has a closed board with ideal spares, one each on the 6pt, 5pt and 4pt. Assume that X’s remaining checkers are evenly distributed on his 1pt and 2pt, with the odd extra checker on X’s 1pt. In the chart below, X is the number of checkers that X bore off before getting hit. The XG number gives the probability that X will win the game, according to a 1296 XG 3-ply rollout. The difference column shows the differences between the numbers in the XG column. The right column shows the application of the formula below, for values of X between 5 and 12. I am not pretending that this formula is always exact. It could not possibly be totally accurate because the differences are not exactly 9%. However, it is never wrong by more than 1.15%. All I am claiming is that if you know nothing else, this formula is a bit better than nothing. Difference (9x – 23) X = 0 XG: 2.66% 1.76% formula not applicable X = 1 XG: 4.42% 2.40% formula not applicable X = 2 XG: 6.82% 3.66% formula not applicable X = 3 XG: 10.48% 4.68% formula not applicable X = 4 XG: 15.16% 6.63% formula not applicable X =
5 XG: 21.79%
8.36% X =
6 XG: 30.15%
8.70% X =
7 XG: 38.85% 10.54%
X =
8 XG: 49.39%
8.89% X =
9 XG: 58.28%
9.64% X = 10
XG: 67.92%
8.55% X = 11
XG: 76.47%
7.70% X = 12
XG: 84.17% X = 13 XG: 78.66% blot in home board X = 14
XG: 93.11% formula not
applicable |