Author: Dieter Buerssner
Date: 10:51:07 10/14/03
Go up one level in this thread
On October 14, 2003 at 06:19:17, Gerhard Sonnabend wrote:
>The current matches is (after 120 games per Level):
>Chess Tiger 15.0(CB) "Normal" vs Beta-WIN-Rebel 12 (style=Test12a)
> Total (+ 1/2 -)
> 5min/game 83.0-37.0 (68-30-22)
> 10min/game 80.0-40.0 (63-34-23)
> 30min/game 68.5-51.5 (48-41-31)
>120min/game 65.5-54.5 (41-49-30)
>(Played on a Cel. 1.8GHz / 128MB HTs / ...the rest look above)
This looks statistically significant. If we assume, that there is no influence
of the time control, and it is just statistical noise, we can take the average,
which would be 61.875% for Tiger. The average draw rate is 32.0833%. For my
match simulation, I would need to know the probabilities for white/black
draws/wins seperately, but it won't make a big difference in the outcome. I just
guessed some values (I took white wins for Tiger as 47% - average wins for Tiger
is 45.8%, so just a bit more for white. I took white and black draw ratio as
equal). A Monte Carlo simulation of the match yields:
Result of chess matches
Player A as white wins 47.0%, draws 32.1% and loses 20.9%
Player A as black wins 44.7%, draws 32.1% and loses 23.3%
Expected result: 61.88% (as white 63.04%, as black 60.71%)
A match of 120 games was simulated 10000000 times by a Monte Carlo method
result probability p <= res. p > res.
[...]
60.0 - 60.0 ( 50.0%): 0.0227% 0.0719% 99.9281%
60.5 - 59.5 ( 50.4%): 0.0330% 0.1049% 99.8951%
61.0 - 59.0 ( 50.8%): 0.0471% 0.1520% 99.8480%
61.5 - 58.5 ( 51.3%): 0.0638% 0.2158% 99.7842%
62.0 - 58.0 ( 51.7%): 0.0901% 0.3059% 99.6941%
62.5 - 57.5 ( 52.1%): 0.1223% 0.4282% 99.5718%
63.0 - 57.0 ( 52.5%): 0.1650% 0.5932% 99.4068%
63.5 - 56.5 ( 52.9%): 0.2180% 0.8112% 99.1888%
64.0 - 56.0 ( 53.3%): 0.2869% 1.0981% 98.9019%
64.5 - 55.5 ( 53.8%): 0.3757% 1.4738% 98.5262%
65.0 - 55.0 ( 54.2%): 0.4826% 1.9564% 98.0436%
65.5 - 54.5 ( 54.6%): 0.6021% 2.5585% 97.4415%
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
66.0 - 54.0 ( 55.0%): 0.7510% 3.3096% 96.6904%
66.5 - 53.5 ( 55.4%): 0.9246% 4.2342% 95.7658%
67.0 - 53.0 ( 55.8%): 1.1306% 5.3647% 94.6353%
67.5 - 52.5 ( 56.3%): 1.3564% 6.7211% 93.2789%
68.0 - 52.0 ( 56.7%): 1.6066% 8.3278% 91.6722%
68.5 - 51.5 ( 57.1%): 1.8854% 10.2132% 89.7868%
69.0 - 51.0 ( 57.5%): 2.1769% 12.3901% 87.6099%
69.5 - 50.5 ( 57.9%): 2.4906% 14.8807% 85.1193%
70.0 - 50.0 ( 58.3%): 2.8062% 17.6869% 82.3131%
70.5 - 49.5 ( 58.8%): 3.1245% 20.8114% 79.1886%
71.0 - 49.0 ( 59.2%): 3.4311% 24.2425% 75.7575%
71.5 - 48.5 ( 59.6%): 3.7234% 27.9659% 72.0341%
72.0 - 48.0 ( 60.0%): 3.9903% 31.9561% 68.0439%
72.5 - 47.5 ( 60.4%): 4.2288% 36.1849% 63.8151%
73.0 - 47.0 ( 60.8%): 4.3965% 40.5814% 59.4186%
73.5 - 46.5 ( 61.3%): 4.5335% 45.1149% 54.8851%
74.0 - 46.0 ( 61.7%): 4.5996% 49.7146% 50.2854%
74.5 - 45.5 ( 62.1%): 4.6008% 54.3154% 45.6846%
75.0 - 45.0 ( 62.5%): 4.5524% 58.8678% 41.1322%
75.5 - 44.5 ( 62.9%): 4.4536% 63.3214% 36.6786%
76.0 - 44.0 ( 63.3%): 4.2746% 67.5960% 32.4040%
76.5 - 43.5 ( 63.8%): 4.0686% 71.6647% 28.3353%
77.0 - 43.0 ( 64.2%): 3.8112% 75.4759% 24.5241%
77.5 - 42.5 ( 64.6%): 3.5223% 78.9982% 21.0018%
78.0 - 42.0 ( 65.0%): 3.2173% 82.2155% 17.7845%
78.5 - 41.5 ( 65.4%): 2.8879% 85.1034% 14.8966%
79.0 - 41.0 ( 65.8%): 2.5592% 87.6626% 12.3374%
79.5 - 40.5 ( 66.3%): 2.2455% 89.9081% 10.0919%
80.0 - 40.0 ( 66.7%): 1.9340% 91.8421% 8.1579%
80.5 - 39.5 ( 67.1%): 1.6428% 93.4849% 6.5151%
81.0 - 39.0 ( 67.5%): 1.3769% 94.8619% 5.1382%
81.5 - 38.5 ( 67.9%): 1.1343% 95.9962% 4.0038%
82.0 - 38.0 ( 68.3%): 0.9239% 96.9201% 3.0799%
82.5 - 37.5 ( 68.8%): 0.7446% 97.6646% 2.3354%
^^^^^^^
83.0 - 37.0 ( 69.2%): 0.5838% 98.2485% 1.7515%
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
83.5 - 36.5 ( 69.6%): 0.4559% 98.7044% 1.2957%
84.0 - 36.0 ( 70.0%): 0.3519% 99.0562% 0.9438%
84.5 - 35.5 ( 70.4%): 0.2620% 99.3183% 0.6817%
85.0 - 35.0 ( 70.8%): 0.1980% 99.5162% 0.4838%
[...]
Average result of simulation 61.8778%
Now, if we look at the 2 extreme results of the actual match, we see, that under
the above assumption (no depencence on time control) the probability for a
result of 65.5-54.5 or less for player A (Tiger) has a probability of only 2.6
%. A result of 83-37 or more has a probabilty of 2.3%. With good confidence, we
can say, that the assumption is wrong, and for the 2 results the two opponents
were of different strength.
One would get much more extreme numbers, if one would phrase the question
slightly different: I have one result of 83-37, and take this as given. Is it
likely, that a match between the same opponents will come out as 65.5-64.5?
Result of chess matches
Player A as white wins 58.0%, draws 25.0% and loses 17.0%
Player A as black wins 55.3%, draws 25.0% and loses 19.7%
Expected result: 69.16% (as white 70.50%, as black 67.83%)
A match of 120 games was simulated 10000000 times by a Monte Carlo method
result probability p <= res. p > res.
61.5 - 58.5 ( 51.3%): 0.0001% 0.0001% 99.9999%
62.0 - 58.0 ( 51.7%): 0.0001% 0.0002% 99.9998%
62.5 - 57.5 ( 52.1%): 0.0000% 0.0002% 99.9998%
63.0 - 57.0 ( 52.5%): 0.0002% 0.0004% 99.9996%
63.5 - 56.5 ( 52.9%): 0.0003% 0.0007% 99.9993%
64.0 - 56.0 ( 53.3%): 0.0004% 0.0011% 99.9989%
64.5 - 55.5 ( 53.8%): 0.0006% 0.0017% 99.9983%
65.0 - 55.0 ( 54.2%): 0.0012% 0.0028% 99.9972%
65.5 - 54.5 ( 54.6%): 0.0015% 0.0043% 99.9957%
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
66.0 - 54.0 ( 55.0%): 0.0027% 0.0071% 99.9929%
66.5 - 53.5 ( 55.4%): 0.0038% 0.0109% 99.9891%
67.0 - 53.0 ( 55.8%): 0.0053% 0.0161% 99.9839%
[...]
Average result of simulation 69.1646%
Regards,
Dieter
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