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How to count MWC here,and how much i need to re-double?

Posted By: Bob Koca
Date: Tuesday, 8 June 2010, at 3:31 p.m.

In Response To: How to count MWC here,and how much i need to re-double? (Chuck Bower)

Part of being an n-roll position means that if you get 2-1 n times you bear off all the checkers and that all doubles including 11 save a roll. Vanilla is worse by enough to worry about.

Can you show your work for the 4.2 value? I am not getting the same. There are a couple problems I see with the technique here. First is that the Kleinmann method is not meant to apply to positions where one side has many checkers on low points. The reason is that the technique is based on a estimates of the expected number of turns to bear off (which the Trice count accounts for very well) and also the variability in the number of turns to bear off (which it doesn't). Vanilla here has a lower wastage position than one in which the EPC is equal but without many checkers on the lower points. That is a change which favors the leader over the Kleinmann technique estimate. For example the given position gives 3.9% win chance to the trailer with vanilla having 29.76 Trice count but changing Vanilla's position to 1 2 1 1 0 0 (from 6 point to ace point)decreases Vanilla's Trice count to 29.08 yet increases the trailer's win %age to 5.1%. If you want to use the Kleinmann technique I think the pipcount difference should be increased by one if one side has many checkers on low points. From expereince that seems to work o.k. usually.

A second problem is what to use in the equation for the total pipcount. The technique uses the raw pipcounts (remember that it is mainly meant for longer races) but here what should be used the raw pipcount or the effective pipcounts? The raw will be too small since the wastage for Vanilla is much higher than for a long race and should be accounted for somehow but the EPC is too high. Note that the formula for long races uses the raw and not adjusted pipcounts.

http://www.math.hmc.edu/~benjamin/papers/BackgammonRacing.pdf has more about the Kleinmann technique and some refinements.

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