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a bias in rollouts

Posted By: Matt Cohn-Geier
Date: Friday, 2 May 2008, at 6:40 a.m.

In Response To: a bias in rollouts (Stick)

Well if the true equity of all the 3 plays is 0, and the method we use (best play/rollouts/GNU/whatever) gives an equity of +0.03, the method is biased, i.e., we get a higher number than we ought to. Bob's point is that the method in general is biased in favor of higher equities.

So, in the example, we got three equities: -0.03, 0, and +0.03. If we took the average we'd get 0, the true equity. By taking only the highest equity we get +0.03, which means we ignore 0 and -0.03. This leads to a general bias.

In order for us to get a number at or below the true equity, we would have to get all three plays as negative equity (or 0). This is much more unlikely than getting just one play as positive equity.

As to whether or not the bias is a problem in practice, I don't know. I'm certain that you wouldn't care whether a play was actually +.5506 or +.5505. But it might be a problem on a larger scale, like when coding GNU or the like--but I'm way out of my expertise there.

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