Author: Bruce Moreland
Date: 17:02:20 06/09/00
Go up one level in this thread
On June 09, 2000 at 06:26:17, Amir Ban wrote: >On June 08, 2000 at 16:10:16, blass uri wrote: > >>On June 08, 2000 at 15:25:22, Amir Ban wrote: >> >>>Ok, here's my two cents: >>> >>>The most likely estimate for the game outcome is the overall match result >>>(33.5/41). The probability for any *particular* sequence of 10 games (say the >>>last 10) to be 10-0 is (33.5/41)^10 = 13.3%. >>> >>>If you want probability for any sequence anywhere, the probability is larger, as >>>you point out. >>> >>>If you suspect the 10-0 result, you can argue that the most likely estimate >>>should discount this result, so this gives you a probability of (23.5/31)^10 = >>>6.3%. >> >>If you use the most likely estimate >>The probability for 10:0 is smaller than (23.5/31)^10 because there are draws. >> >>The result was +20, =7.-4 so if you use the most likely estimate you get >>probability (20/31) for Junior to win >>7/31 for a draw and 4/31 for a loss >> >>(20/31)^10=0.012493... so the probability is less than 2% >> >>I ignored the fact that the white probability is different from the black >>probability but not ignoring it does not change much the result because you get: >> >>(10/15)^5*(10/16)^5 that is 0.012558... >> >>If you do not ignore the last 10 games and ignore the colours you get >>(30/41)^10=0.043992... >> >>Uri > >All right, you are right about the draws. > >My presentation of the problem was more complicated than necessary. Here is the >question in its simplest form: > >A match of 41 games concluded with 30 wins, 7 draws and 4 losses. It is unknown >in which order these wins/draws/losses occurred. > >Out of all possible permutations with the same result, what percent of the >permutations have a sequence of at least 10 wins ? > >This is clear cut question for the combinatorics gurus in this newsgroup. > >There seems to be gross difference of opinion about the result of this, so until >we get an answer, we can have an opinion poll about the result. > >My guess: 40%. > >Amir I modified my monte carlo thing and it says about 31.5% bruce
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