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a bias in rollouts

Posted By: David Montgomery
Date: Friday, 2 May 2008, at 9:11 p.m.

In Response To: a bias in rollouts (Stick)

No, it really can be due to luckier dice.

Here's another experiment. Let's say we're rolling two dice, tallying the pips (no doubles), and wondering both "What is the expected value?" and "Is it better to roll harder, or to roll softer?"

So we set up a rollout. We roll out a zillion times play 1 ("roll hard") and play 2 ("roll soft"). At the end, we see which of those two strategies is best, and take the equity for that strategy as our answer for "What is the expected value?"

On average, our answer will be greater than seven, because this process is biased.

If you have two equivalent plays in bg, this is what you are doing in a rollout.

As the difference between the plays becomes larger, the bias is less. (Analogous experiment: Is it better to roll and take the sum as is, or roll, take the sum, and subtract X? For X=0.0001 and small sample sizes, the bias is still there; For X=11 the bias will be gone.)

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