Author: Dieter Buerssner
Date: 13:43:13 05/24/04
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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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