Author: Dieter Buerssner
Date: 09:46:13 06/12/02
Go up one level in this thread
On June 11, 2002 at 12:18:14, Uri Blass wrote:
>On June 11, 2002 at 09:47:31, Tina Long wrote:
>
>>30 games, result 18-12, difference 50% = 18/12 -1.
>>You say this would never happen (revised to "very limited")
>>I say it (or greater than 50% difference) would happen around 16.6% of the time.
>>
>>Tina Long
>
>I think that it is dependent on the programs that you test.
>
>If the program that you test draw 90% of the games then I expect it almost never
>to happen.
Yes:
Result of chess matches between equal opponents
White wins 5.0%, black 5.0% and 90.0% draws
A match of 30 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
15.0 - 15.0 ( 50.0%): 23.899% 23.899% 76.101%
15.5 - 14.5 ( 51.7%): 39.315% 63.214% 36.786%
16.0 - 14.0 ( 53.3%): 22.749% 85.963% 14.037%
16.5 - 13.5 ( 55.0%): 9.712% 95.676% 4.324%
17.0 - 13.0 ( 56.7%): 3.239% 98.915% 1.085%
17.5 - 12.5 ( 58.3%): 0.857% 99.772% 0.229%
18.0 - 12.0 ( 60.0%): 0.192% 99.963% 0.037%
18.5 - 11.5 ( 61.7%): 0.032% 99.995% 0.005%
19.0 - 11.0 ( 63.3%): 0.004% 99.999% 0.001%
19.5 - 10.5 ( 65.0%): 0.001% 100.000% 0.000%
20.0 - 10.0 ( 66.7%): 0.000% 100.000% 0.000%
>If the programs that you test win with white in 90% of their games and lose with
>black in 90% of the games then I also expect it almost never to happen(I assume
>that you are fair and gives every program 15 games with white.
White wins 90.0%, black 5.0% and 5.0% draws
A match of 30 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
15.0 - 15.0 ( 50.0%): 17.020% 17.020% 82.980%
15.5 - 14.5 ( 51.7%): 27.783% 44.803% 55.197%
16.0 - 14.0 ( 53.3%): 23.286% 68.090% 31.910%
16.5 - 13.5 ( 55.0%): 14.460% 82.550% 17.450%
17.0 - 13.0 ( 56.7%): 9.079% 91.629% 8.371%
17.5 - 12.5 ( 58.3%): 4.556% 96.186% 3.814%
18.0 - 12.0 ( 60.0%): 2.271% 98.457% 1.543%
18.5 - 11.5 ( 61.7%): 0.935% 99.392% 0.608%
19.0 - 11.0 ( 63.3%): 0.394% 99.786% 0.214%
19.5 - 10.5 ( 65.0%): 0.140% 99.926% 0.074%
20.0 - 10.0 ( 66.7%): 0.053% 99.979% 0.021%
20.5 - 9.5 ( 68.3%): 0.015% 99.994% 0.006%
21.0 - 9.0 ( 70.0%): 0.005% 99.999% 0.001%
21.5 - 8.5 ( 71.7%): 0.001% 100.000% 0.000%
>In the practical case I expect it to happen but I did not calculate how often it
>is going to happen.
White wins 35.0%, black 25.0% and 40.0% draws
A match of 30 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
15.0 - 15.0 ( 50.0%): 9.435% 9.435% 90.565%
15.5 - 14.5 ( 51.7%): 18.333% 27.768% 72.232%
16.0 - 14.0 ( 53.3%): 16.934% 44.702% 55.298%
16.5 - 13.5 ( 55.0%): 14.690% 59.392% 40.608%
17.0 - 13.0 ( 56.7%): 12.169% 71.560% 28.440%
17.5 - 12.5 ( 58.3%): 9.373% 80.933% 19.067%
18.0 - 12.0 ( 60.0%): 6.902% 87.835% 12.165%
18.5 - 11.5 ( 61.7%): 4.793% 92.628% 7.372%
19.0 - 11.0 ( 63.3%): 3.150% 95.778% 4.222%
19.5 - 10.5 ( 65.0%): 1.939% 97.717% 2.283%
20.0 - 10.0 ( 66.7%): 1.111% 98.828% 1.172%
20.5 - 9.5 ( 68.3%): 0.601% 99.429% 0.571%
21.0 - 9.0 ( 70.0%): 0.313% 99.742% 0.258%
21.5 - 8.5 ( 71.7%): 0.148% 99.890% 0.110%
22.0 - 8.0 ( 73.3%): 0.068% 99.958% 0.042%
22.5 - 7.5 ( 75.0%): 0.025% 99.984% 0.017%
23.0 - 7.0 ( 76.7%): 0.010% 99.994% 0.006%
23.5 - 6.5 ( 78.3%): 0.004% 99.997% 0.003%
So results of 18-12 or more extreme will happen under these conditions in about
19% of the matches.
>In the match between Fritz and Junior the result was 5-0 after 5 games and
>Fritz won the next 19 games 13-6.
>
>I believe that 18-12 has bigger probability than both 5-0 and 13-6 between equal
>programs and if you assume that the programs were not equal then it is clear
>that in at least one of these results the inferior program won.
White wins 35.0%, black 25.0% and 40.0% draws
A match of 5 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
2.5 - 2.5 ( 50.0%): 22.546% 22.546% 77.454%
3.0 - 2.0 ( 60.0%): 38.580% 61.126% 38.874%
3.5 - 1.5 ( 70.0%): 24.427% 85.552% 14.448%
4.0 - 1.0 ( 80.0%): 10.861% 96.414% 3.586%
4.5 - 0.5 ( 90.0%): 3.133% 99.547% 0.453%
5.0 - 0.0 (100.0%): 0.453% 100.000% 0.000%
White wins 35.0%, black 25.0% and 40.0% draws
A match of 19 games was simulated by 1000000 Monte Carlo tries
result probability <= this > this
9.5 - 9.5 ( 50.0%): 11.806% 11.806% 88.194%
10.0 - 9.0 ( 52.6%): 22.564% 34.369% 65.631%
10.5 - 8.5 ( 55.3%): 19.937% 54.307% 45.694%
11.0 - 8.0 ( 57.9%): 16.001% 70.307% 29.693%
11.5 - 7.5 ( 60.5%): 11.795% 82.102% 17.898%
12.0 - 7.0 ( 63.2%): 7.943% 90.046% 9.954%
12.5 - 6.5 ( 65.8%): 4.854% 94.900% 5.100%
13.0 - 6.0 ( 68.4%): 2.740% 97.639% 2.361%
13.5 - 5.5 ( 71.1%): 1.374% 99.014% 0.986%
14.0 - 5.0 ( 73.7%): 0.615% 99.628% 0.372%
14.5 - 4.5 ( 76.3%): 0.250% 99.878% 0.122%
15.0 - 4.0 ( 78.9%): 0.083% 99.961% 0.039%
15.5 - 3.5 ( 81.6%): 0.030% 99.990% 0.010%
16.0 - 3.0 ( 84.2%): 0.007% 99.998% 0.003%
16.5 - 2.5 ( 86.8%): 0.002% 100.000% 0.000%
Dieter
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