Author: blass uri
Date: 01:36:22 07/29/00
Go up one level in this thread
On July 29, 2000 at 03:50:59, Terry Ripple wrote: >On July 28, 2000 at 15:45:15, Christophe Theron wrote: > >>On July 28, 2000 at 01:05:53, Terry Ripple wrote: >> >>>Used an AMD K6-2, 266Mhz, 64Ram, Ponder off, 16Mb Hash per engine. >>> >>>If anyone cares to see some or all of the games, i will be glad to post them. >>> This match shows how close the strengths are between these two fine engines! >>> >>>Best regards, >>>Terry >>> >>>Blitz:5' 2000 >>> >>> >>>1 Fritz 6 158.0/306 >>>2 Hiarcs 7.32 148.0/306 >> >> >> >>No offense intended Terry, but you cannot say with this match which program is >>the best. >> >>The result of this match is 51.63% in favor of Fritz. >> >>I don't have the typical margin of error for 306 games, but I know that for 400 >>games it is +/-2.5% (80% confidence) and +/-2.1% (70% confidence). >> >>So even if you got this 51.63% with a 400 games match, you couldn't say which >>program won because 51.63% is between 47.5% and 52.5% (80% confidence). You >>couldn't even say Fritz is better with 70% confidence. >> >>That's the problem with chess matches results... You have to apply some >>statistic formulas and sometimes you discover that the match does not say which >>is best... >> >> >> >> Christophe > > Please explain where you may get a margin of error when there isn't a human >operator making any moves on the chess board? Please, i would like to learn more >about this! > >Regards, Terry You can get the margin of error by the following experiment: Throw a coin 400 times and count the number of heads. repeat the experiment again and again. The best guess is 200 heads in every experiment. In 80% of the cases this guess will be wrong by not more than 2.5% and in 70% of the cases you will be wrong by not more than 2.1% This is not correct for chess because there are draws so the coin should have 3 results. The following explanation may not be clear to you if you did not learn statistics but I will give it. Let assume that the probability for white to win is 40%,the probability for a draw is 30% and the probability for black to win is 30%. The variance in one game is 0.4*0.45*0.45+0.3*0.05*0.05+0.3*0.55*0.55=0.081+0.00075+0.09075=0.1725 The variance in 400 games(assuming the events are independent) is 0.1725*400=69. It gives standard deviation of about 8.3 that is 2.075%. The probability to be in a distance of one standard deviation from the right number assuming normal distribution is about 80%(I think 83% but I am not sure). binomical distibution with 400 games is close to be normal distribution so you get +-2.1% with about 80% confidence. I got different result relative to christhophe results probably because my model is more comlicated but 1.63% is not significant even if you have 400 games I should look at the right tables to see the probability to be at distance of 1.63/2.1~=0.78 standard deviations and I have not the right tables near me. Uri
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