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In defense of single trial rollouts

Posted By: Tom Keith
Date: Tuesday, 19 October 2010, at 2:54 p.m.

In Response To: In defense of single trial rollouts (Maik Stiebler)

Let me elaborate on the second point because I think it's interesting.

If you rollout an entire game, one trial, you might get an equity of, say, +0.03 for the starting position (before the first roll). We know that's wrong. The equity of the starting position is zero. Where did this error come from?

It comes from errors in the luck evaluation during variance reduction. (If the luck evaluation had been perfect during variance reduction, then the rollout equity of the starting position would be zero.) It is reasonable to assume the errors in luck evaluation are distributed somewhat evenly across all the positions of the game.

We could just assume an equal amount of error in the calculation of luck in all positions. This won't be true in any particular case but if we adjust the luck evaluation of each position by 1/n times the total error we will get equities that are closer, on average, to the true equity.

And we can do better than that. Calculating luck is easier in some types of positions than others. For example, if all rolls in a particular position lead to the same result, then the error in the luck estimate of that position must be zero. So we can ignore that position when dividing up the error of the rollout.

This is a second type of variance reduction. Unfortunately, it works only with single-trial rollouts.

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