Author: Uri Blass
Date: 15:06:44 02/27/02
Go up one level in this thread
On February 27, 2002 at 16:05:58, Robert Hyatt wrote: >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. I agree that there is no practical chance by playing random moves to draw against the perfect player but if we talk about reality then there is no chance to get a perfect player. If we assume that the perfect player does not live forever then the perfect player cannot get an infinite rating so the only relevant question is what is the rating of the perfect player when we assume that she lives forever. If she lives forever and plays every day a game against a player with random stategy then she also cannot get infinite rating. Uri
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