Author: Uri Blass
Date: 06:50:17 01/26/02
Go up one level in this thread
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 The probabilities are not independent numbers. The probability can go down from 5% to 0% and can go up from 5% to 20%. 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. Uri Uri
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