Author: Dieter Buerssner
Date: 16:22:47 11/22/03
Go up one level in this thread
On November 22, 2003 at 04:32:32, Gian-Carlo Pascutto wrote:
>Hmm, makes sense I guess as with more games there's more chances to diverge
>from the average. I never tests 1000 games though :) You can calculate the
>probability after the match, but for the range of say less than 100 games it
>should be pretty high as far as I remember.
Depends on the number of draws. In general, I would say - no: +6 is not very
significant with say 50 games.
C:\e\dcrand>cmatch 50 40 30 30 1000000
Result of chess matches between equal opponents
White wins 40.0%, black 30.0% and 30.0% draws
A match of 50 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
25.0 - 25.0 ( 50.0%): 6.758% 6.758% 93.242%
25.5 - 24.5 ( 51.0%): 13.304% 20.062% 79.938%
26.0 - 24.0 ( 52.0%): 12.751% 32.813% 67.187%
26.5 - 23.5 ( 53.0%): 11.959% 44.772% 55.228%
27.0 - 23.0 ( 54.0%): 10.811% 55.584% 44.416%
27.5 - 22.5 ( 55.0%): 9.390% 64.974% 35.026%
^^^^^^^
28.0 - 22.0 ( 56.0%): 8.076% 73.050% 26.950%
28.5 - 21.5 ( 57.0%): 6.736% 79.786% 20.214%
29.0 - 21.0 ( 58.0%): 5.395% 85.181% 14.819%
29.5 - 20.5 ( 59.0%): 4.233% 89.415% 10.585%
30.0 - 20.0 ( 60.0%): 3.207% 92.621% 7.379%
30.5 - 19.5 ( 61.0%): 2.384% 95.005% 4.995%
31.0 - 19.0 ( 62.0%): 1.722% 96.727% 3.273%
31.5 - 18.5 ( 63.0%): 1.182% 97.909% 2.091%
32.0 - 18.0 ( 64.0%): 0.786% 98.695% 1.305%
32.5 - 17.5 ( 65.0%): 0.521% 99.216% 0.784%
33.0 - 17.0 ( 66.0%): 0.322% 99.538% 0.462%
33.5 - 16.5 ( 67.0%): 0.198% 99.736% 0.264%
34.0 - 16.0 ( 68.0%): 0.119% 99.854% 0.146%
34.5 - 15.5 ( 69.0%): 0.068% 99.923% 0.077%
35.0 - 15.0 ( 70.0%): 0.036% 99.959% 0.041%
35.5 - 14.5 ( 71.0%): 0.020% 99.979% 0.021%
36.0 - 14.0 ( 72.0%): 0.011% 99.990% 0.011%
36.5 - 13.5 ( 73.0%): 0.005% 99.995% 0.005%
37.0 - 13.0 ( 74.0%): 0.002% 99.997% 0.003%
37.5 - 12.5 ( 75.0%): 0.002% 99.999% 0.001%
Assuming above shown win/draw ratios, the probability of a result with a
difference of >= 6 in 60 games (seen as independent - no learning, etc.) between
opponents of equal strength is 35%. With 100 games it would be around 37%.
Regards,
Dieter
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