Author: Graham Laight
Date: 05:58:12 10/14/04
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Sorry - there was an error in the above post. It has been corrected in the text below: I ran the simulator in http://www.talkchess.com/forums/1/message.html?391362 with the following parameters: Simulations: 50,000 Win probablity: 33% Draw probability: 34% Lose probability: 33% Games per tournament: 26 The results are appended after the end of this message. You can clearly see that if the two programs were equal in strength, then 11.5/14.5 is a very reasonable score (7.4% probability, when the top category is 9.6%). I then ran it for Hydra and Fritzs' performance in Bilbao: Simulations: 50,000 Win probablity: 33% Draw probability: 34% Lose probability: 33% Games per tournament: 8 Here again, results are appended. The probability of them achieving >= 7 is .0053 + .0011 + .0002 = .0066 (or 1 in 152). This strongly suggests that Hydra and Fritz are better at chess than their human opponents (Ruslan Ponomariov, Véselin Topálov and Sergey Karjakin). -g Appendix 1: Crafty v Ruffian analysis DJ won 4 points in 0% of the tournaments DJ won 4.5 points in 0% of the tournaments DJ won 5 points in 0.01% of the tournaments DJ won 5.5 points in 0.01% of the tournaments DJ won 6 points in 0.02% of the tournaments DJ won 6.5 points in 0.09% of the tournaments DJ won 7 points in 0.14% of the tournaments DJ won 7.5 points in 0.31% of the tournaments DJ won 8 points in 0.51% of the tournaments DJ won 8.5 points in 0.9% of the tournaments DJ won 9 points in 1.6% of the tournaments DJ won 9.5 points in 2.35% of the tournaments DJ won 10 points in 3.46% of the tournaments DJ won 10.5 points in 4.56% of the tournaments DJ won 11 points in 5.94% of the tournaments DJ won 11.5 points in 7.43% of the tournaments DJ won 12 points in 8.68% of the tournaments DJ won 12.5 points in 9.41% of the tournaments DJ won 13 points in 9.44% of the tournaments DJ won 13.5 points in 9.57% of the tournaments DJ won 14 points in 8.46% of the tournaments DJ won 14.5 points in 7.4% of the tournaments DJ won 15 points in 5.98% of the tournaments DJ won 15.5 points in 4.64% of the tournaments DJ won 16 points in 3.24% of the tournaments DJ won 16.5 points in 2.34% of the tournaments DJ won 17 points in 1.52% of the tournaments DJ won 17.5 points in 0.91% of the tournaments DJ won 18 points in 0.5% of the tournaments DJ won 18.5 points in 0.29% of the tournaments DJ won 19 points in 0.15% of the tournaments DJ won 19.5 points in 0.07% of the tournaments DJ won 20 points in 0.03% of the tournaments DJ won 20.5 points in 0.01% of the tournaments DJ won 21 points in 0% of the tournaments DJ won 21.5 points in 0% of the tournaments Appendix 2: Hydra & Fritz Performance in Bilbao DJ won 0 points in 0.02% of the tournaments DJ won 0.5 points in 0.1% of the tournaments DJ won 1 points in 0.49% of the tournaments DJ won 1.5 points in 1.68% of the tournaments DJ won 2 points in 3.92% of the tournaments DJ won 2.5 points in 7.61% of the tournaments DJ won 3 points in 11.95% of the tournaments DJ won 3.5 points in 15.67% of the tournaments DJ won 4 points in 17% of the tournaments DJ won 4.5 points in 15.47% of the tournaments DJ won 5 points in 12.16% of the tournaments DJ won 5.5 points in 7.6% of the tournaments DJ won 6 points in 4.04% of the tournaments DJ won 6.5 points in 1.68% of the tournaments DJ won 7 points in 0.48% of the tournaments DJ won 7.5 points in 0.11% of the tournaments DJ won 8 points in 0.01% of the tournaments
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