Author: Dieter Buerssner
Date: 09:36:09 06/12/02
Go up one level in this thread
On June 11, 2002 at 07:37:52, Peter McKenzie wrote:
>Ask yourself this question:
>
>"If I ran this very same match 100 times, but with Crafty 18.15 vs Crafty 18.15,
>then how many times would I see this score (22.5 - 13.5)?"
>
>What answer do you come up with?
I am not Jorge, but I got an answer:
E:\dcrand>cmatch 36 35 25 40 1000000
Result of chess matches between equal opponents
White wins 35.0%, black 25.0% and 40.0% draws
A match of 36 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
18.0 - 18.0 ( 50.0%): 8.582% 8.582% 91.418%
18.5 - 17.5 ( 51.4%): 16.799% 25.381% 74.619%
19.0 - 17.0 ( 52.8%): 15.748% 41.129% 58.871%
19.5 - 16.5 ( 54.2%): 14.058% 55.187% 44.813%
20.0 - 16.0 ( 55.6%): 11.950% 67.136% 32.864%
20.5 - 15.5 ( 56.9%): 9.670% 76.807% 23.193%
21.0 - 15.0 ( 58.3%): 7.436% 84.243% 15.757%
21.5 - 14.5 ( 59.7%): 5.508% 89.751% 10.249%
22.0 - 14.0 ( 61.1%): 3.878% 93.629% 6.371%
22.5 - 13.5 ( 62.5%): 2.555% 96.184% 3.816%
23.0 - 13.0 ( 63.9%): 1.646% 97.830% 2.170%
23.5 - 12.5 ( 65.3%): 0.992% 98.822% 1.178%
24.0 - 12.0 ( 66.7%): 0.557% 99.379% 0.621%
24.5 - 11.5 ( 68.1%): 0.309% 99.688% 0.312%
25.0 - 11.0 ( 69.4%): 0.164% 99.852% 0.148%
25.5 - 10.5 ( 70.8%): 0.084% 99.936% 0.064%
26.0 - 10.0 ( 72.2%): 0.036% 99.972% 0.029%
26.5 - 9.5 ( 73.6%): 0.018% 99.990% 0.010%
27.0 - 9.0 ( 75.0%): 0.007% 99.997% 0.003%
27.5 - 8.5 ( 76.4%): 0.002% 99.999% 0.001%
28.0 - 8.0 ( 77.8%): 0.001% 100.000% 0.000%
28.5 - 7.5 ( 79.2%): 0.000% 100.000% 0.000%
So, assuming that on average white will win 35% of the games, black will win 25%
of the games, and 40% of the games are draw, one can expect in 6.4% of such 36
game matches a result of 22.5 - 13.5 and more extreme.
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