Author: Robert Hyatt
Date: 19:24:21 05/11/01
Go up one level in this thread
On May 11, 2001 at 15:49:19, Angrim wrote: >On May 11, 2001 at 03:29:43, Dann Corbit wrote: > >>On May 11, 2001 at 01:49:03, Angrim wrote: ><snip> >>>If your goal is to determine how hard it is to solve chess, then yes. >>>Rather then go into a lengthy rant here, let me give an example. >>>The following position has pawns advanced a total of 4 squares, so >>>subtract 4*50 from the max depth, and your math suggests that there are >>>38^(5900 -200) total games of chess that can result from this position. >>>However, the position is trivial. No need for sqrt(38^(5900 -200)) >>>positions to be searched or stored... >>> >>>[D]rnbqkbnr/pppp1ppp/4p3/8/6P1/5P2/PPPPP2P/RNBQKBNR b KQkq g3 0 2 >> >>Yet there are many quintillions of quintillions of qintillions of games that can >>sprout from here. >> >My point being that if your goal is to solve this position, then all >but 1 of those games is totally irrelevant.\\\\\ Unfortunately they are _not_. Because you have to _prove_ that the best move is best. And to the best of my knowledge, there is no "oracle" that will give us perfect move ordering so it is not just likely, it is highly probable that the winning move won't be searched first. Maybe it will be searched by the 1/2 way mark at this play, maybe it will be last. But if it isn't first, you have a HUGE tree to search first... That's the way alpha/beta works... not best-first but alpha/beta... > >>Unless we assume optimal play. >We only need to assume optimal play for one side, unless chess turns out >to be a draw. I'm not actually good enough at chess to determine whether >or not the game is a theory draw :-) . > >>Positions like this one are intensely interesting, however. We could formally >>trim all forward branches from here. Unless I am missing something. >> >>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". > >Angrim >ps. so much for my attempt to avoid a lengthy rant. But at least I >left out the 2 pages of 9s ;)
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