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Kleinman count investigation

Posted By: rambiz
Date: Thursday, 21 April 2011, at 5:19 a.m.

In Response To: Kleinman count investigation (Timothy Chow)

By asserting the variance to be implied in EPC, I actually meant the EPC is indeed indifferent to the variance, in the sense that, it is a proper measure for the length of the race, no matter what the variance.

The simple position below shows definitely, that two totally different positions regarding their variances, can have very close EPCs, meaning the same average number of rolls are needed to bear all the checkers off.

White's EPC: 15.11 SD: 0.521


' ' '1X '1X ' ' ' ' ' '

4O ' ' ' ' ' ' ' ' ' ' '

Position ID: SAAAeAAAAAAAAA Match ID: cAkgAAAAAAAA

Blue's EPC: 14.97 SD: 0.373

However, Kleinman has assumed the same variance for both players, which is apparently not necessarily the case. I think, if we assign the "true" variances to the two positions and solve the problem for the joint distribution, there will be a general solution for the "middle long" races. The "middle long" condition being necessary for the Gaussian approximation to work. I know, my idea isn't well formulated or fully developed yet, but with a little help from my friends , I'm rather optimistic, something useful can be devised.

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