Author: Robert Hyatt
Date: 07:50:29 02/09/02
Go up one level in this thread
On February 09, 2002 at 07:44:27, Sune Fischer wrote: >On February 09, 2002 at 07:08:35, Uri Blass wrote: > >>returns. >> >>Imagine the following simple game: >>Every side need to say in it's turn if it resigns or not resign. >>The game is finished only when one side resigns. >> >>If both sides never resign the game is never finished. >> >> >>Imagine the following 3 programs for that simple game: >> >> >>Program A resigns with probability of 10% in every move >>Program B resigns with probability of 1% in every move >>Program C never resigns. >> >>program C finds better move than program B only in 1% of the cases but in games >>C always wins against B(B will do a mistake of resigning after enough moves). > >No, this is where you get it wrong IMO. >See C will not _always_ beat B, because the games will end at some point and >this will give B a winning probability greater than zero. > >>Program B finds better move than program A in 9% of the cases but program A has >>positive chance to beat program B. > >I assume finding "a better move" is the same as winning, or at least drawing >from a lost position? Anyway, that was my assumption, it may be too simplistic >for chess. > >>I think that this is a convincing argument to prove that reducing the >>probability to find a better move in the next ply has nothing to do with >>diminishing resturns. > >This is the way I see it: >1) At 2-ply you can improve on about 50%(?) of the moves found at 1-ply. This >corresponds to some decent rating difference, 100-200 points? Because obviously >2-ply will win a lot more games. > >2) At 369-ply you will almost _never_ get a better move than that found at >368-ply. Maybe this happens in 1/10000 moves, so probably 99.99% of all games >will end in draw (or equal win-lose ratio), remember the games do not go on >forever, sooner or later there will not be enough material to mate (for >instance). The rating difference here will be virtually unmeasurable. > >3) We know chess has a limited number of positions, so we _know_ there is no >difference between a 12345678-ply search and a 12345677-ply search, probably >they have both solved the game. > >I challenge you to draw the curve between a 1-2 plies and 368-369 plies without >this showing diminishing returns! >You claim it is a straight line (ie. no DR), which means there is a constant >improvement on the rating at every ply you go deeper. >This in in direct conflict with 1)+2) and 3), so I guess you disagree on those, >which brings us back to the claim, that the elo boost from 368 to 369 is >identical to the one given by going from 1 to 2. This is definitely incorrect >due to 3) :) It is pretty straight thru 15-16 plies... By experiment. Which means at least "for a while" deeper is better. And it _could_ be straight all the way to the depth where we discover the game-theoretic value. Beyond that point searches can't improve things of course... > >-S. > >>In practical games programs never do a mistake when they say resign but part of >>the stupid moves are practically the same as say resign. >>It is more complicated because losing moves from theoretical game do not finish >>the game when the opponent can blunder and there are also draws but the idea is >>similiar. >> >>Uri
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