Author: Uri Blass
Date: 08:14:05 02/09/02
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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. Not in the game that I described. I agree that at some point there is diminshing returns in chess and I believe that it happens a lot before chess is solved but the point is that using statistics about the probability to change your mind is a wrong way to get a conclusion. > >>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. I also believe that at 368-369 plies there is probably no returns because chess is practically solved at this point(Inspite of the fact that we cannot be sure about from a theoretic point of view) but we are not close to that depth and my point is that we cannot decide that there is a diminishing returns in the practical depthes that programs search even if we prove that program tends to change their mind more at smaller depthes. > >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. I did not say it. It may be constant in the first 20 plies and start go down at ply 21. It also may show increasing returns at some small depthes. I do not know. I believe that it may be dependent on the opening and if you play a match from the right fixed positions then you may even find increasing returns. I used the nunn match as a match from fixed positions and did not find clear evidence for diminishing returns at small depthes. Both program had to play the same position as white and as black and none of these positions is an endgame or a forced perpetual check when there are cases when book lead to an endgame or to a forced perpetual check. I guess that when you use an opening book the book has increasing returns and this is the reason that the experiment of Ernst Heinz found deminition returns when Fritz played against itself because there were cases when the draw was a result of the book only if you search deep enough. There are also cases when a win is a result of the book but these cases are more rare. Uri
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