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Variance reduction is unbiased but may be skewed

Posted By: Phil simborg
Date: Saturday, 11 April 2015, at 1:22 a.m.

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

While I do not question the logic of your hypothesis I do question that the end result is quite so predictable as you have concluded.

There is an assumption that in every rollout that XG plays every roll and cube decision perfectly, and since we know that is not possible, there is good reason to believe that no rollout is exactly correct. Therefore we should assume that any result we see from a rollout is likely to be a certain degree off, and which way we don't know. However my intuitive guess is that the factor that it might be off is far greater than the amount it might be off as a result of the variance reduction. In fact some times the VR might tilt the results slightly more correct and some times slightly more wrong.

My point is that if you start with the assumption that the rollout result represents a small range of possible results and you factor in something far smaller than what a few checker or cube errors would make, then the impact of the variance you describe is probably even smaller than you would estimate. If the rollout result was "perfect" without VR then a small shift in one direction because of VR would be meaningful.

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