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a bias in rollouts

Posted By: Matt Cohn-Geier
Date: Friday, 2 May 2008, at 5:34 a.m.

In Response To: a bias in rollouts (Chuck Bower)

If I pick and choose sentences I can talk myself into believing I understand but when I'm required to put the entire post together I feel that I don't.

Suppose that, as in Bob's example, we have a position that has an absolute equity of 0 and has only 3 legal plays. We roll out one game. The first play rolls out as +1, the second play rolls out as -1, the third play rolls out as -2. The observed equity of the position is +1. Suppose we extend the rollout to 1295 more games and the equity of the first play is +0.03, the equity of the second play is 0, and the equity of the third play is -0.03. The observed equity of the position is +0.03, even though the true equity is 0.

Could you give a more concrete example -- a real life position as illustration?

I imagine this is actually exceptionally difficult, since you would need two conditions to hold: 1) the position must have a calculable (in a reasonable amount of time) equity 2) the position must be sufficiently complex that rollouts won't arrive at the true equity

1 and 2 aren't logically incompatible, but from a practical point of view, they're pretty damn close.

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