
BGonline.org Forums
Half as wild
Posted By: Timothy Chow
Date: Thursday, 22 April 2010, at 5:01 p.m.
In Response To: Half as wild (Daniel Murphy)
Daniel Murphy wrote:
If, for instance, we want to combine the relative equities of the XG 4ply and Gnubg 2ply rollouts, even though their absolute results are out of each other's 95% confidence intervals, is there a rationale for doing that, other than the old standby
I don't believe so. In fact I would be in favor of averaging absolute equities.
And another question: a rollout of two plays reports standard deviations or 95% confidence intervals for the absolute equity of each play. But what's the confidence interval of the relative equity?
If A and B are independent random variables then the variance of A – B is the sum of the variances of A and B. In terms of standard deviations, if s is the standard deviation of A and t is the standard deviation of B, then the standard deviation of A – B is the square root of s^{2} + t^{2}. In particular if s = t then the standard deviation of A – B is going to be larger than s by a factor of sqrt(2).
The assumption that A and B are independent is a subtle one. In this context it means, roughly speaking, that the positions that arise after play A are "unrelated" to the positions that arise after play B. It's probably a reasonable assumption though I'm unaware of anyone who has studied it thoroughly.

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