Author: Dieter Buerssner
Date: 09:42:32 10/13/04
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On October 13, 2004 at 06:45:50, Graham Laight wrote: >OK - here's a program to use the statistical technique called, "Monte Carlo >Simulation". I hope that this satisfies everyone that I am not statistically >illiterate. Nice. Until now, I had no idea, that one could write such a thing so easily (at least the source looks rather straight forward) in a scripting language that runs under any (?) Web browser. I had written a very similar program some years ago. It gives the same results as your program (within the expected noise of ~sqrt(n)). You could tickle out a bit more, by using the knowledge that typically chess players perform differently with white and black, and that matches have the same number of white and black games. A constructed example: One player as white wins 90%, 5% draw, 5% losses. As black he wins 5%, draws 5% and loses 90% (against the same opponent). We expect 50% in a match. A result of say 7-3 or more extreme is rather unlikely. If we however take the overall probabilities (47.5% win, 5% draw, 47.5% loss), a 7-3 result is not very unlikely at all. Regards, Dieter Output of your program (1 million tournaments, your default values otherwise): DJ won 0 points in 0.16% of the tournaments DJ won 0.5 points in 2.23% of the tournaments DJ won 1 points in 12.06% of the tournaments DJ won 1.5 points in 30.84% of the tournaments DJ won 2 points in 36.04% of the tournaments DJ won 2.5 points in 15.37% of the tournaments DJ won 3 points in 3.02% of the tournaments DJ won 3.5 points in 0.27% of the tournaments DJ won 4 points in 0.01% of the tournaments My prog: C:\e\dcrand>cmueoa 4 1 7 2 1 7 2 1000000 Result of chess matches Player A as white wins 10.0%, draws 70.0% and loses 20.0% Player A as black wins 10.0%, draws 70.0% and loses 20.0% Expected result: 45.00% (as white 45.00%, as black 45.00%) A match of 4 games was simulated 1000000 times by a Monte Carlo method result probability p <= res. p > res. 0.0 - 4.0 ( 0.0%): 0.1639% 0.1639% 99.8361% 0.5 - 3.5 ( 12.5%): 2.2384% 2.4023% 97.5977% 1.0 - 3.0 ( 25.0%): 12.0312% 14.4335% 85.5665% 1.5 - 2.5 ( 37.5%): 30.8543% 45.2878% 54.7122% 2.0 - 2.0 ( 50.0%): 36.0153% 81.3031% 18.6969% 2.5 - 1.5 ( 62.5%): 15.3896% 96.6927% 3.3073% 3.0 - 1.0 ( 75.0%): 3.0155% 99.7082% 0.2918% 3.5 - 0.5 ( 87.5%): 0.2814% 99.9896% 0.0104% 4.0 - 0.0 (100.0%): 0.0104% 100.0000% 0.0000% Average result of simulation 45.0024% And some longer runtime (now the numbers should come rather close to the exact numbers): A match of 4 games was simulated 100000000 times by a Monte Carlo method result probability p <= res. p > res. 0.0 - 4.0 ( 0.0%): 0.1596% 0.1596% 99.8404% 0.5 - 3.5 ( 12.5%): 2.2387% 2.3983% 97.6017% 1.0 - 3.0 ( 25.0%): 12.0859% 14.4842% 85.5158% 1.5 - 2.5 ( 37.5%): 30.8014% 45.2856% 54.7144% 2.0 - 2.0 ( 50.0%): 36.0047% 81.2903% 18.7097% 2.5 - 1.5 ( 62.5%): 15.4025% 96.6928% 3.3072% 3.0 - 1.0 ( 75.0%): 3.0176% 99.7104% 0.2896% 3.5 - 0.5 ( 87.5%): 0.2797% 99.9901% 0.0099% 4.0 - 0.0 (100.0%): 0.0099% 100.0000% 0.0000% Average result of simulation 44.9986%
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