Author: Sune Fischer
Date: 04:44:27 02/09/02
Go up one level in this thread
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) :) -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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