Author: Robert Hyatt
Date: 13:05:58 02/27/02
Go up one level in this thread
On February 26, 2002 at 14:35:32, Uri Blass wrote: >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. Do the math. at any point in the game, the "random player" will have about 40 moves to choose from, and for this case I assume exactly one is "perfect". That means he has a probability of .025 of choosing the "perfect" move in a random fashion. Compute .025^50 (assuming a game lasts 50 moves for simplicity). You get roughly 7 e-81. I don't believe that a real human can play enough games to give the "random player" any chance at all for a draw, much less playing perfectly enough for a win. The human simply won't live long enough to play enough games at one game per day. The random player has no chance. > >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. See above. If a human could live forever, the random player would eventually win a game. But the human doesn't, and the random player has no chance whatever to win. > >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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