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Answering Paul Weaver: 7777 vs. 7776

Posted By: Timothy Chow
Date: Saturday, 23 December 2023, at 9:53 p.m.

In Response To: Answering Paul Weaver: 7777 vs. 7776 (Jason Lee)

Jason Lee wrote:

If we ask for 7777 trials, some sequence will be overrepresented, introducing a bias.

Wait a minute. I don't think any bias will be introduced, assuming GNUBG does not deterministically select a particular sequence more often than others. For example, if each of the 7777 trials is an independent random trial, then it will give an unbiased estimate (i.e., the mean value of the estimate will be correct), or even if the 7776 trials are quasi-random and the 7777th trial is chosen uniformly at random, the estimate will still be unbiased.

I can believe that 7777 independent random trials might have lower variance than 7776 quasi-random trials, though.

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