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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-(1-p'), 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-(1-p') is equal to true winning chance, that we call p. Silimiarly, the probability of having written down 0-(-p') equals (1-p).
Thus, the rollout will report: p(1-(1-p'))+(1-p)(0-(-p'))=pp'+(1-p)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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