Author: Uri Blass
Date: 09:16:52 01/26/02
Go up one level in this thread
On January 26, 2002 at 10:00:44, Sune Fischer wrote: >On January 26, 2002 at 09:50:17, Uri Blass wrote: > >>On January 26, 2002 at 09:32:43, Albert Silver wrote: >> >>>On January 26, 2002 at 09:27:03, Sune Fischer wrote: >>> >>>>On January 26, 2002 at 09:07:51, Albert Silver wrote: >>>> >>>>>>>>Realisticly a 2800 player probably has a branchfactor of no more than 2, ie. he >>>>>>>>is able to always choose the best or second best move (on average). >>>>>>>>If the average game lasts 100 moves, then that is still 10^30 plausible games of >>>>>>>>which only a handfull will be good enough against *perfect* play. >>>>>>>>Poor odds I agree with you :) >>>>>>> >>>>>>>You're presuming that anything other than one move, the best move, will lose >>>>>>>forcibly to best play. I believe that more than one move is available to a >>>>>>>non-loss thus perfect play would be often a flip of the coin between a few >>>>>>>(perhaps three as I hypothesized in another post in the thread) moves. I have >>>>>>>seen no evidence to suggest there is only one path to a non-loss and that a >>>>>>>single path of perfect play is needed to avoid it. Everything we know whether >>>>>>>from personal research or from the current tablebases suggests there are several >>>>>>>paths. If this were accepted to be true, the question would be whether the 2800 >>>>>>>player is incapable of hitting on _one_ of these non-losing moves (according to >>>>>>>perfect play). >>>>>>> >>>>>>> Albert >>>>>> >>>>>>You could interpet in an similar way; there is a 50% chance of the 2800 chooses >>>>>>a move that is *good enough*. >>>>>>It was just an estimate, probably way off :) >>>>>> >>>>>>Suppose that a *correct* move is done with 95% certainty (on average) and that >>>>>>the average game length is only 60 moves, then he has a 0.95^60 = 4.6% chance of >>>>>>a draw! >>>>>> >>>>>>This is perhaps more realistic? >>>>>> >>>>>>-S. >>>>> >>>>>Well, a few things come to mind. One is that there would be more than one >>>>>correct move to hit on. >>>> >>>>Yes, and that why I rephrased it to be a *correct* move rather than *the best* >>>>move, by *correct* I mean a move that isn't losing. >>>> >>>> >>>>>Second that I wasn't aware that his chances changed with >>>>>each move, so I don't think that the longer the game the worse his chances. Give >>>>>a 2800 player a dead equal dry game and I don't think he will suddenly be in >>>>>danger of losing just because it can take 40 moves to trade off the pieces and >>>>>pawns and play the endgame to the end. There is more to chess than probability. >>>>> >>>>> Albert >>>> >>>>What I meant was, that at every move he has a 5% chance of _not choosing the >>>>correct move_, ie. he "blunders" by playing inaccurate. >>>>That is an average percentile taken out of the blue of cause, but the tablebase >>>>test could give us a hint whether we are talking 95% or 50%, it would allow us >>>>to calculate the rating of a perfect player, which was the goal I believe. >>>> >>>>-S. >>> >>>I was addressing two things: Dann's statement that against perfect play, >>>Kasparov (or any other 2800 player) would lose 1000 games in 1000. And your >>>statement that against perfect play in a game of say 60 moves he only had a 4.6% >>>chance of surviving. I think both statements are completely unreal and show >>>little understanding of certain realities of both chess and their ability. You >>>could also take a dead equal rook endgame where there is no chance for the >>>mighty player to calculate a line to the very end and I would still adamantly >>>state that his chances of losing are _zero_ and not some percentage that grows >>>exponentially with each move played. >>> >>> Albert >> >>I agree > >Well I don't, I don't see what there is to object to, I specificly said they >where estimates and averages. >Albert talks about a dead drawn endgame with rooks that is easy to hold, then >yes in _that case_ the factor goes to 1.00. But that is only one single case and >why would the perfect player choose to end up in such a position? > >>The probabilities are not independent numbers. > >True, I also never said that, I only said average. > >>The probability can go down from 5% to 0% and can go up from 5% to 20%. > >I agree, they most probably will, some endgames are dead draw and in some >tactical middelgame positions it is very easy to blunder, even for a super GM. > >>The probability may be 95% to be right for every move but more than 0.95^n to be >>right in n moves when the events are not independent. > >I'm not sure what you mean? > >-S. I meant that it is possible that the probability not to blunder is 95% at move 1,2...9,10,11,12,13...40 but the probability not to blunder in all of the first 40 moves is not 0.95^40. I admit that I thought about regular games and not about games against the perfect player(in regular games between kasparov and kramnik if I know that the sides blundered it means that the position is complicated and the side have good chance to continue to blunder). The problem is that in games against the perfect player there may be only one blunder that change the theorethic result from draw to a win for the perfect player so if the probability not to blunder in every move is 0.95 then the probability not to blunder in the game must be 0.95^n assuming that n is the number of moves. practically I believe that the probability not to blunder is an increasing function(except the openings when most of the opening lines lead to draw) and if kasparov played well enough not to blunder in the middle game the probability for kasparov to play the correct moves in the endgame is bigger. practically there are positions when kasparov can be almost sure not to blunder(for example rook and 3 pawns against rook and 3 pawns in the same side and even some positions with rook and 2 pawns against rook and 3 pawns in the same side when one pawn advantage of the perfect player is not enough to win) Uri
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