Author: Dieter Buerssner
Date: 13:43:13 05/24/04
Go up one level in this thread
On May 24, 2004 at 16:16:15, Uri Blass wrote:
>On May 24, 2004 at 16:04:23, Peter McKenzie wrote:
>
>>I would say that if Crafty's expected score against Shredder in around 25-30%
>>then in a 10 game match there is still a reasonable chance of getting a 50%
>>score. Someone else can probably give the exact probability but I'd guess it is
>>at least 10%, in which case it certainly seems worth 'hoping for'.
>We need to know the probability for draw and the probability for a win for white
>to calculate.
For example these values (which may include different probabilities for draws as
white and as black). Or some other combination of the winning/drawing
probabilities for white and black.
>If we assume that white has 80% chances to win and 20% to draw in case that
>white is shredder when it is 100% draw in case that white is Crafty then the
>expected result is 7-3 but the probability for 5-5 is 0.2^5 that is very
>small(0.032%).
>
>If we assume 70% for shredder 30% for crafty in every game then the probability
>for 5-5 is 0.7^5*0.3^5*10!/(5!^2) and it is more than 10%.
A bit more. 15% for the probability of the weaker player to get 5-5 or better.
For some intermediate values (that I guessed could be realistic for a typical
match) I get:
Result of chess matches
Player A as white wins 65.0%, draws 20.0% and loses 15.0%
Player A as black wins 50.0%, draws 30.0% and loses 20.0%
Expected result: 70.00% (as white 75.00%, as black 65.00%)
A match of 10 games was simulated 10000000 times by a Monte Carlo method
result probability p <= res. p > res.
0.5 - 9.5 ( 5.0%): 0.0000% 0.0000% 100.0000%
1.0 - 9.0 ( 10.0%): 0.0004% 0.0004% 99.9996%
1.5 - 8.5 ( 15.0%): 0.0019% 0.0023% 99.9977%
2.0 - 8.0 ( 20.0%): 0.0092% 0.0115% 99.9885%
2.5 - 7.5 ( 25.0%): 0.0371% 0.0486% 99.9514%
3.0 - 7.0 ( 30.0%): 0.1312% 0.1798% 99.8202%
3.5 - 6.5 ( 35.0%): 0.3777% 0.5575% 99.4425%
4.0 - 6.0 ( 40.0%): 0.9686% 1.5261% 98.4739%
4.5 - 5.5 ( 45.0%): 2.1569% 3.6830% 96.3170%
5.0 - 5.0 ( 50.0%): 4.2293% 7.9123% 92.0877%
5.5 - 4.5 ( 55.0%): 7.2307% 15.1430% 84.8570%
6.0 - 4.0 ( 60.0%): 10.8662% 26.0092% 73.9908%
6.5 - 3.5 ( 65.0%): 14.2511% 40.2603% 59.7397%
7.0 - 3.0 ( 70.0%): 16.1705% 56.4309% 43.5692%
7.5 - 2.5 ( 75.0%): 15.6930% 72.1238% 27.8762%
8.0 - 2.0 ( 80.0%): 12.8393% 84.9631% 15.0369%
8.5 - 1.5 ( 85.0%): 8.5445% 93.5075% 6.4925%
9.0 - 1.0 ( 90.0%): 4.4780% 97.9855% 2.0145%
9.5 - 0.5 ( 95.0%): 1.6511% 99.6366% 0.3634%
10.0 - 0.0 (100.0%): 0.3634% 100.0000% 0.0000%
Average result of simulation 70.0009%
So about 8% probability for the weaker player to get 5-5 or better. Using
somewhat different values for the probabilities still gives simar results
between 7% and 9%.
Regards,
Dieter
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