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Varianace Reduction for Dummies
Posted By: rambiz
Date: Thursday, 11 August 2016, at 12:34 p.m.
Assume it is the last roll of a game and we want to find out the probability of winning for the guy on roll.
Evaluation Engine:
We firstly count the wins in,say, 100 games and divide that number by 100 to get p'. p' is henceforth our estimated winning chance.
Rollout with Variance Reduction:
Now we start observing an infinitely long series of games. Every time the player on roll wins, we write down 1(1p'), that is, we subtract the tentative "luck" from the actual result. Similarly, every time he loses, we write down 0(p').
VR Rollout Result:
Now in the looong run, the probability of having written dowm 1(1p') is equal to true winning chance, that we call p. Silimiarly, the probability of having written down 0(p') equals (1p).
Thus, the rollout will report: p(1(1p'))+(1p)(0(p'))=pp'+(1p)p'=p'as the winning chance of the player on roll.
Conclusion: Variance Reduction doesn't work with an imperfect evaluation engine.

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