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Variance reduction is unbiased but may be skewed

Posted By: Maik Stiebler
Date: Saturday, 11 April 2015, at 7:31 a.m.

In Response To: Variance reduction is unbiased but may be skewed (Timothy Chow)

If the luck is skewed, it doesn't follow that the luck-adjusted aka varianced-reduced result is.

In the ideal case, the variance-reduced result of a single rollout trial is just the real rollout equity, thus the distribution of total luck must simply be the distribution of raw results with a sign change and shifted. The total luck inherits the skew of the raw results.

As deviation from the ideal case, noise is added to the variance-reduced result on every roll due to imperfect evaluations. I can't say how the imperfections of evaluations are skewed.

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