Author: Roger D Davis
Date: 19:25:02 12/26/00
Go up one level in this thread
On December 26, 2000 at 22:24:00, Roger D Davis wrote: >On December 26, 2000 at 14:28:15, Bruce Moreland wrote: > >>On December 26, 2000 at 09:59:45, Uri Blass wrote: >> >>>It seems that there are more draws between humans. >>> >>>If you look at the match between kramnik and kasparov there were 13 draws out of >>>15. >>> >>>If you assume probability of 25% for the winner,5% for the loser and 70% draws >>>then the standard deviation is smaller and you need less games to get >>>significant result. >> >>If the draw percentage is 70%, you are right. 75 points should win that one out >>about 87% of the time. >> >>But Kasparov should have been about to get 7.5 out of 15.0 93% of the time, and >>win it outright 82% of the time. >> >>How many did he get, 6.5? He should have gotten that score 0.5% of the time. >> >>But I don't think you can assume these huge draw percentages are "normal" >>either. GM games are usually in some larger context. They achieve a winning >>advantage in a match or tournament, then force draws to maintain this margin. >> >>>Another point is that the games are not independent events. >> >>Yes, I'm sure this messes everything up, but note that I'm not arguing for >>statistical accuracy when choosing champions, either. >> >>I think it's more powerful for *us* if we apply it to computer chess, where >>there is much less match strategy. >> >>bruce >> >> >>>The first match between kasparov and karpov demonstrated it when karpov was >>>leading 5-0 and decided to quit the match when he was leading 5-3 because he was >>>tired. >>> >>>The reason that he decided to quit is that he knew that he was tired and that >>>kasparov has bettter chances if the match continues. >>> >>>Karpov did not think about the games as independent events(otherwise he could >>>prefer to continue and be almost sure of winning even if kasparov is slightly >>>better). >>> >>>Even if you assume that the probability for kasparov to win a game is 0.2 and >>>the probability of karpov to win a game is 0.1(I ignored white and black for >>>doing the problem more simple) karpov had probability of 19/27 to win but karpov >>>understood that the situation is worse than that and starting a new match from >>>0-0 result is better for him. >>> >>>Uri > >Another problem for your argument is that ELOs are based on play across a pool >of players. Match play is often (but not always) much different. > >If the two players reached some arbitrary large number of games with no >statistical difference between the results, then there would simply be no >statistically-significant champion, only a match winner. The fact that the >winner is awarded the title of champion does not void the fact that there is no >statistically significant difference between the two players, no matter how much >you might like it to. What is at stake is simply whether the statistical >equality of the two players is recognized (my point), or whether it remains >obscure (your position). > >Roger The "your argument" is addressed to Bruce, not to Uri. Roger
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