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stronger RO gives expected result (362k trials)

Posted By: Maik Stiebler
Date: Friday, 24 November 2017, at 11:14 a.m.

In Response To: stronger RO gives expected result (362k trials) (Nack Ballard)

I wouldn't call 63.7% the "expected result"

I wouldn't call it unexpected. Well, "expected" in the mathematical sense means something like "average", so in that sense 50% would be "expected", but I suppose that's not the sense you have in mind.

Best I can tell, the way XG constructs this number is such that if you set up two plays A and B which are exactly equal in the sense of equal equity found in a rollout of inifinitely many trials, but not obviously equal (lookahead/variance reduction/dice rotation can not "prove" that they are, there is still variance left after variance reduction and dice rotation), the reported confidence for play A being best after a rollout of N trials, where N was specified in advance, will be a random number from a uniform distribution in the interval between 0% and 100%. However, if you continue extending the rollout, you can expect that number to cross the 50% line infinitely many times.

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