Author: Christoph Fieberg
Date: 11:56:42 06/15/99
Thanks a lot for all the interesting and fascinating postings and discussions on the topic. Here is a new thought from the newsgroup "rec.games.chess.computer". I quote Michel Grimminck: ------------------ One way to compute this is, is to asses how well Kasparov would play against a perfect computer. How many points would Kasparov score? Well in order to score even he would have to play each of his moves flawless. If the 'average' chance of Kasparov playing the correct move is P and the average number of moves before it is clear the Kasparov won't make mistakes anymore, (for example when it is a clear draw) is M, his score would be P^M. (Any move that does not affect the game-theorectical value of the position is correct) Elo formula's says: score = 1/(10^[-(rating difference)/400] + 1) If the rating difference is large (and negative) one can estimate the rating difference required to obtain a certain score: (rating difference)=-400*log10(score) for score near 0 if we insert Kasparov's rating into this we get: (rating difference)=-400*log10(P^M)=-400*M*log10(P) If we assume the M=60, one gets: (rating mr. perfect)=(rating Kasparov)+24000*log10(P) P is hard to estimate, but lets try some some value's P rating mr. perfect 0.05 31244 0.1 26800 0.25 17249 0.5 10024 My *guess* would be that half Kasparov's moves are perfect, yielding a rating of 10000 This calculation is ofcourse a gross extrapolation and actually I don't think it is valid to extrapolate this much. Michel Grimminck ----------------- Remark: I think it is a very good approach - even if it is probably not accurate to extrapolate that much. The rating 10024 for the perfect machine means that Kasparov would score just 0.5 points in 1,152,921,504 billion games! And that is with a (high) 50% chance of picking a move that will not lose and a (low) expected average game of 60 moves. I think my prediction of Elo 7000 is wrong. The perfect machine will reach a much better rating. Regards, Christoph Fieberg
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