Author: Sune Fischer
Date: 11:54:07 02/09/02
Go up one level in this thread
On February 09, 2002 at 14:12:18, Uri Blass wrote: >On February 09, 2002 at 11:37:41, Sune Fischer wrote: > >>On February 09, 2002 at 11:14:05, Uri Blass wrote: >> >>>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. >> >>Well you mentioned 1%, not me:) >>Chess _is_ statistics, the weaker side always has a chance, a 2400 player can >>beat a 2700 player once and a while (why else even play the match?). >> >>Maybe I misunderstood your game, in your game it seems B will resign even in a >>completely drawn positions such as K-BK because, C will never stop playing the >>game so B might resign before the 50 move rule. That is a strange game I think. >> >>-S. > >In my game there is no 50 move rule and it is not chess. > >The point is that even if the probability to change your mind is smaller you >cannot learn from it that the rating difference is smaller. > >I cannot give a correct model of what happens in chess so I try to look at a >simpler game. > >I can also look at chess and look at a simple strategy assuming that you know >the right moves. > >imagine that chess is a draw and >imagine the following players in chess: > >player A:always plays the correct move > >player B: always plays the correct move after move 60 when in the first 60 moves >plays the correct move in 95% of the cases and resigns in the rest of the cases. > >player C:the same as B when 89% is used instead of 95% > >It is clear that if you do a match between A and B you will get higer result >than the case that you do a match between B and C inspite of the fact that you >can say that B is 6% better than C when A is only 5% is better than B. > >Uri I think something is wrong with your example. Since all games can last infinite, it means A can drag the game on forever and just wait for the opponent to make a mistake, so A _always_ wins. I don't know the rating formula, but it seems to me A must have an infinite rating since it will never even draw. This is a complete breakdown, A is beyond Godness, even God would not have an infinite chess rating, so something needs to be fixed. The game must end, in fact this is probably a non-trivial rule about chess. -S.
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