Author: Sune Fischer
Date: 05:26:42 01/21/03
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On January 20, 2003 at 21:15:53, Dann Corbit wrote: >>But what you were saying was, that you could _never ever_ know the answer. There >>is a fundamental difference I think and this is where the null event theorem >>saves us. It _is_ possible to make an accurate statement if you have reduced it >>to a null event. After 1 trillion games I think we have a clear winner, whom >>ever that may be. > >I would be utterly astonished if it were true. > >After a trillion coin flips, we will still have random walk problems, and it >could (on rare occasions) be considerable. How will we discern the random walk >drift from a very tiny change in strength? At the top, the strength of the >programs appears to be very close. This is the exact region where random walk >will give us the most trouble. > >In other words, I think we will not be able to discern (on a blind test) whether >we pit top program A against top program B or whether it was A against A or B >against B. Well, first step is to agree that they can't be equally strong, that would be a null event so it doesn't happen. Ok, the probability of a Tiger win is p in [0;1]. This gives us a serie of Bernoulli experiments. With such a sequence of Bernoulli experiments you have the "the law of great numbers" (not sure what's it's call in english). It states, to make it short, that for all epsion>0 limes n->0 Prob(abs(S/n-p))>epsilon)=0 . In other words, going towards infinity we find p, as an exact result. Of course it is a theoretical result, but there is an enhanched version more complex (I will spare you the details, has to do with Chebyshev's inequality) where you only do a limited number of trials and get a delta on the estimation. -S.
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