Author: Uri Blass
Date: 11:35:32 02/26/02
Go up one level in this thread
On February 26, 2002 at 13:16:48, Robert Hyatt wrote: >On February 26, 2002 at 10:56:12, Sune Fischer wrote: > >>On February 26, 2002 at 09:09:17, Robert Hyatt wrote: >> >>>On February 26, 2002 at 06:11:05, Graham Laight wrote: >>> >>>>If two players were above ELO level 4000 (approx), they would always draw. >>>> >>> >>>What is this assumption based on? Certainly not scientific research. IE >>>who has proven that the game is a draw. >>> >>>And the question was about _one_ "perfect player". Not two. If there is just >>>one, his rating will continually rise over time and since he never loses, it >>>has no real upper bound. >> >>It is not enough that he never loses, drawing is also losing points, and so >>would give him a finite rating. >>The question is, do you need to play perfect to draw the perfect player? >> > > >I would assume yes to your question, assuming that he always wins from the >white side and a non-perfect player can't win from the white side because >of the mistakes. > >But it is too philosophical to waste much mental energy on. > >:) > > > > >> >>>>This is derived by extrapolating from the following graph, which is drawn by a >>>>former secretary of the USCF: >>>> >>>>http://math.bu.edu/people/mg/ratings/Draws.jpg >>>> >>>>-g >>> >>>That has nothing to do with "perfect play". It is assuming the game is >>>drawn, which is not a given. >> >>Doesn't matter if it is drawn or a win, the perfect player can only be certain >>of a win if he has white and the chess is a win for white, or vice versa with >>black. >>I suppose we could ask a different question, if chess is a win for white and the >>perfect player is allowed always to play white, will he still have a finite >>rating? Probably not...! >>However, that is not *fair*, he should play both sides, so it is hard to prove >>he would always score a 100%. > > >true. It depends on the mistake(s) made by the imperfect player. I am >simply assuming someone that plays "perfect" wins every game because making >a mistake as white to turn the win into a draw probably still requires perfect >play to avoid one more mistake that turns it into a loss. > >Would be nice to have 32-piece EGTBs and we could answer this easily. :) > > > > >>What if he playes an almost perfect player, one that only makes a mistake in 1 >>in a million moves? Clearly that guy will have a finite rating, and he should >>stand a good chance against the perfect player, probably scoring close to 50% => >>the perfect player will also get a finite rating. >> >> >>-S. > >If the perfect player doesn't win every game then yes, he has a finite >rating. I agree. The only issue is whether he wins all or not... The perfect player is not going to win every game if he plas enough games. even the strategy to xhoose a random move is going to socre more than 0% against the perfect player. The difference in elo in order to win a match 2*10^1000-1 is certainly finite and I believe that choosing a random move is going to be enough for better score because I believe that it is possible to get at least a draw in less than 500 moves and the probability to be lucky and choose every one of them is more than 1/100 in every move because I believe that the number of moves in every ply is going to be less than 100 when the opponent choose the perfect strategy. It suggest the following question suppose that A has rating 0(I believe that the player who choose random move will have rating that is lower than 0). suppose B wins against A 2*10^1000-1 What is going to be the rating of B based on the elo formula? This rating is probably an upper bound for the rating of the perfect player if you assume that the perfect player plays only against A. Uri
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