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BGonline.org Forums
eXtreme Gammon question
Posted By: Timothy Chow In Response To: eXtreme Gammon question (Maik Stiebler)
Date: Friday, 28 August 2009, at 5:46 p.m.
Mark Stiebler wrote:
I'm also for a more Bayesian viewpoint in backgammon statistics.
In fact I rashly assumed that the bots were already using a Bayesian viewpoint. That is, again assuming DMP, we take two candidate plays and choose a uniform prior (i.e., before any rollouts are performed, the probability of winning is assumed to be uniformly distributed between 0 and 1). Then each time we sample one of the distributions by rolling out a game, we update the probability distribution in the usual Bayesian manner. We end up with a probability distribution over the unit square (the two axes are the win percentages of the two plays) and we're at 95% confidence if 95% of the volume under the surface lies on one side of the plane y = x.
Bob Koca says that instead, the bots take 95% confidence to mean that there's only a 5% chance that we would observe a separation between the scores as large as or larger than what we in fact observe, if the plays were actually equal. If that is so, then indeed what I said before was wrong. But I have to say that it strikes me as a rather strange thing to report. The hypothesis that we are really interested in ruling out isn't that the plays are equal.
The Bayesian viewpoint does suffer from the usual problem that you can quibble with the choice of prior. However, if you roll the thing out enough, any reasonable choice of prior will converge to the same thing, so this shouldn't matter much in practice.
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