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Answering Paul Weaver: 7777 vs. 7776

Posted By: Timothy Chow
Date: Wednesday, 3 January 2024, at 2:51 a.m.

In Response To: Answering Paul Weaver: 7777 vs. 7776 (Sam Pottle)

Sam Pottle wrote:

Would a rollout of 15553 trials be more accurate, on average, than a rollout of 7776?

Even without doing any careful calculations, I'm sure the answer is yes. Doubling the number of trials should approximately reduce the statistical error by a factor of about √2 ≈ 1.4. The variance reduction from pseudorandom dice is not going to make nearly that much difference. In fact, I recall that one reason Xavier didn't bother to implement pseudorandom dice is that he found, empirically, that it didn't make that much difference for rollouts with thousands of trials.

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