Author: Angrim
Date: 10:42:57 08/08/03
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On August 08, 2003 at 12:27:34, Erik Bergren wrote: > As to your question of "assurance" that 85 wins out >of 100 shows one to be superior to the other: >Just model the problem with pennies: >assume an equal chance to a flip resulting in a heads up landing >of the penny. Thus getting 85 heads out of 100 would be >quite unlikely indeed ( just have your computer calculate >all possible out comes, and find the ratio of the total >of all of those, to those that have more than or equal to >85 heads out of 100). You will thus be shown that >one program not being better than the other (thus them being >equal in strength), after 85 wins out of 100, is >less likely than 1 in 1000000 ( I do not have a >computer with me to find the exact number).Now I do: > >The equation is: >integral (from x=85 to 100) of >[(.5)^x*(.5)^(100-x)*(100!)/((x!)*(100-x)!)] >divided by >integral (from x=50 to 100) of >[(.5)^x*(.5)^(100-x)*(100!)/((x!)*(100-x)!)] > > >which equals 2^25. >Thus the probability (or "strangeness") of a computer >winning 85 (or higher) out of 100 games from one of equal strength >( or against an identical computer, say ) is >one in 10^25. Thus such a result would conclusively >show that one of those computers was better than it's opponent. This assumes that both have large books, and pick moves from them in a somewhat random fashion rather than just playing the "best" move each time. many(most?) amateur engines will repeat the same game over and over vs the same set of moves, so seeing a result of 100:0 between two engines that are the same strength is quite possible. simply the same game being played out 100 times. learning rocks. Anyway, I was too lazy to work out the math to find the odds of getting a score of 85/100 between two equal randomized engines, so I wrote a simple program. Here are the results. It might be interesting to compare these with what your formula says you should get. out of 10000000 trials, 795183 scored 50 out of 10000000 trials, 793723 scored 51 out of 10000000 trials, 764336 scored 52 out of 10000000 trials, 703845 scored 53 out of 10000000 trials, 621736 scored 54 out of 10000000 trials, 521374 scored 55 out of 10000000 trials, 416639 scored 56 out of 10000000 trials, 316655 scored 57 out of 10000000 trials, 227297 scored 58 out of 10000000 trials, 153369 scored 59 out of 10000000 trials, 97752 scored 60 out of 10000000 trials, 58311 scored 61 out of 10000000 trials, 32417 scored 62 out of 10000000 trials, 16796 scored 63 out of 10000000 trials, 7973 scored 64 out of 10000000 trials, 3548 scored 65 out of 10000000 trials, 1417 scored 66 out of 10000000 trials, 495 scored 67 out of 10000000 trials, 187 scored 68 out of 10000000 trials, 56 scored 69 out of 10000000 trials, 17 scored 70 out of 10000000 trials, 6 scored 71 out of 10000000 trials, 2 scored 72 out of 10000000 trials, 1 scored 74 Angrim
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