Author: Uri Blass
Date: 03:59:06 02/02/01
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On February 02, 2001 at 02:55:44, Andrew Dados wrote: >On February 01, 2001 at 10:21:43, Uri Blass wrote: > >>On February 01, 2001 at 07:39:11, Leen Ammeraal wrote: >> >>>On January 31, 2001 at 20:17:17, Bruce Moreland wrote: >>> >>>>I expressed very forcefully that a 10-0 result was more valid than a 60-40 >>>>result. >>>> >>>>I've done some experimental tests and it appears that I'm wrong. >>>> >>>>I have no idea why. >>>> >>>>bruce >>> >>>According to the little Windows app Whoisbetter by Steve Maugham, >>>the certainty of being better for the winner is >>>97% with the score 60 - 40, and >>>99% with the score 7 - 0 >> >>It is clearly wrong. >>The probablities that you talk about are not the probability that the winner is >>better. >> >>We cannot know the probability that the winner is better unless we have more >>knowledge. > >We can calculate this and if we disregard draws the chance that winner of 60-40 >is better is indeed 97.4%. Even without draws we cannot calculate it because we need information about the apriori distribution of the probability of the better player to win. If we assume that it is 0.51 then we get 0.51^20/(0.51^20+0.49^20) If we assume that it is 0.6 we get 0.6^20/(0.6^20+0.4^20) If we assume that the probability of the better player to win has 50% probability to be 51% and 50% probability to be 60% then we get something else. Uri
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