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Gappy stacky bearoff cube

Posted By: Bob Koca
Date: Friday, 21 December 2007, at 7:10 p.m.

In Response To: Gappy stacky bearoff cube (Chuck Bower)

Kleinmann's method is based on calculations from a normal distribution. Roughly one estimates the number of rolls to bear off for each player as being normal and then calculates the probability that one is larger than the other. His numbers come from that calculation.

The expected value of turns to bear off is based on the pipcount plus adjustments if needed. Using Ward to do this is o.k.. The problem is not there.

The problem in this situation is that his numbers are based on assuming a certain deviation in the number of rolls needed to bear off. This value is based on a more typical race in which there are few checkers on low points. When there are checkers on the low points it is correct that the wastage is larger than typical. This aspect is accounted for in the adjustments though. The other important thing to realize is that the deviation in the number of rolls to bear off will be smaller. The great rolls tend to be less great and the terrible rolls tend to be less terrible.

What to do in practice? I haven't studied this that carefully but my guess in a position like the above, and supported by a small amount of spot checking, is to penalize the trailer 1 pip to compensate for the decreased deviation.

Bob Koca

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