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DQ: Consider the bar point? *** Rollout ***

Posted By: Timothy Chow
Date: Friday, 18 July 2014, at 10:00 p.m.

In Response To: DQ: Consider the bar point? *** Rollout *** (Tom Keith)

That's how people tend to think of those numbers, but that's not what they are, strictly speaking. To compute a "probability of being best" you have to adopt a Bayesian framework and postulate a prior probability distribution, but that's not what the bots do.

To simplify matters, suppose there are only two candidate plays. Then a 99% probability means that there is only a 1% probability that you would observe the top play coming out as far ahead as you observe (or more) if the plays were actually identical. Informally, this can be described as "99% confidence that the plays do not have identical equity."

In the limit of infinitely many trials, everything converges to the same thing anyway, so you might complain that I'm being pedantic to point out that the computer's calculation is a standard confidence interval calculation and not a Bayesian calculation. But either way, the main point is that the only thing that percentage gives you information about is whether the plays differ in equity and not how accurate the equity estimate is.

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