Author: Angrim
Date: 22:20:59 05/11/01
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On May 11, 2001 at 17:16:26, Dann Corbit wrote: >On May 11, 2001 at 15:49:19, Angrim wrote: > >>On May 11, 2001 at 03:29:43, Dann Corbit wrote: >>>Which brings up another thought. What percentage of moves are so horrible that >>>they are not even worth considering. Is it 99.99999999999999999999999999%? >> >>not of moves, but of the set of all possible games, the percentage that contain >>an error of that magnitude is roughly 99.999<insert 2 pages of 9s>99% >>Even if you define such an error as "any move which can be shown to lose >>with a 1 second search" rather than the possibly unsound "any move which >>crafty would score as 10 points lower than the favorite after a 1 second >>search". > >I don't think that such a percentage can really be quite so high. I notice in >the middle game that there are usually about 35 choices that can be made. Super >GM's will usually pick about 3 different options in such an example. So that's >about ten percent from a given node. Now, it is interesting that it is a sort >of exponential trimming, since (.10)^k grows towards zero quickly. But then, >that's just another way of saying that the average branching factor is about 3, >which means we are right back in exponential-ville. > a 90% prune rate is much more optimistic than I was thinking. Even allowing for the fact that "random" positions will generally have much less king defenses than positions reached by solid play, I doubt that more than 50% of the legal moves would lose trivially. However, if you estimate that most of the legal games are at least 5000 moves long, and 50% of the moves at each ply are errors, then the fraction of those games which include an error would be 1-(0.5^5000) which has a lot of 9s in it :) <big snip of factoring stuff> wow, you really are bored. Whats the address for the factoring message board? :) Angrim
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