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Oops...cube in the wrong position

Posted By: Bob Koca
Date: Saturday, 12 September 2009, at 9:37 p.m.

In Response To: Oops...cube in the wrong position (Timothy Chow)

Kleinmann's formula was based on the pipcount and was intended for long low wastage races. There is math based on Normal limit theory that supports it. Recently Art Benjamin wrote more about it and extended it to take into account that the limit is not quite reached. Look at http://www.math.hmc.edu/~benjamin/papers/BackgammonRacing.pdf

He also incorporates adjustments but here the stack and straggler goes beyond the range of his adjustments. So I used Trice count instead. Positions with checkers down low have a lower variability in number of turns to bear off than a more typical race with the same Trice count and for either side reducing the variability in number of turns to bear off while keeping the average number of turns to bear off the same is good for the leader in the race. That is where my two one pip adjustments come in. It seems to be about right from looking at those situations but I didn't do any formal tests for it. The other adjustment was for what to use for the sum. Since his formula used the pipcount I wanted to use the pipcount for a typical race that would have the same Trice count as the given positions.

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