Author: Andrew Dados
Date: 07:47:38 02/02/01
Go up one level in this thread
On February 02, 2001 at 06:59:06, Uri Blass wrote: >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 Hell(o) Uri, With all respect I think you're wrong. You can enumerate through all possible rating differences and scores. (like, for score 60-40 chance of it for rating_diff 0 is d0, for rating_diff 1 is d1 etc...) You get the function P(score,rating_diff). Factoring that through all rating_diff in some range gives you answer what is the chance that rating_diff lies in that range (you need to normalize P first). Btw if you disregard draws then one chess game equals statistically to one toss of coin (2 scores), when with draws it equals to event of 2 coin tosses (we need 2 tosses to get 3 scores). So 10 game match is equivalent of 20 coin tosses.. :) -Andrew-
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