3000
The rating of a perfect player
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Karpov:Kasparov, what does the computer say about his rating?
Kasparov:IT'S OVER 9000!!!!!!!!!!!!!!!!!
Karpov: WHAT?!?!!?!?!?!? THERE'S NO WAY THAT CAN BE RIGHT!!! O_O
Aug 10, 2011
0
#145
When you think of the 32 piece tablebase of chess, the bound 13^64 on its size doesn't sound that big (if you say it quickly and don't think about it too much). Heck, it's only about 237 bits. Similar number to the number of particles in the universe. But its also quite an overestimate, as there have to be 1 king of each colour, no more than 15 other pieces of each colour, various bounds on combined numbers of pawns and pieces of different types, not so mention positions that you can't reach.
But first, keeping the kings separate gets the bound down to 64*60*(11^62). Much better. Well, actually over 1000 times smaller.
But that only accounts for the number of possible positions (and quite a number of impossible ones). Setting aside the fact that you'd have to double that figure (whether it's white or black to move makes two identical looking positions different), a table base also includes all of the possible transitions between those potions -- in effect it's actually a directed graph with each of the possible positions as nodes. Something that vastly increases its complexity.
Ziryab wrote:
cyrobro wrote:
3000
+2
There are computer programs better than 3000; the perfect player is at least as good as the best computer --> the perfect player is better than 3000.
If the perfect player plays the perfect game every time, he will use the same openings each time because it is "perfect". Given enough games, someone would play his black repertoire against his white repertoire and get a draw (Im assuming in the perfect game its a draw). Then anyone who wanted a draw could get one, because the perfect player would be forced to play the same perfect game over and over, as to stray from it would be imperfect. His rating would then become dependant on his opposition, and assuming he only player super tournaments, it would be something like 2740, just by scoring 50% against an average opponent of 2740 every time.
Grated thats very hypothetical, but then again, so is the perfect player.
thekibitzer wrote:
If the perfect player plays the perfect game every time, he will use the same openings each time because it is "perfect". Given enough games, someone would play his black repertoire against his white repertoire and get a draw (Im assuming in the perfect game its a draw). Then anyone who wanted a draw could get one, because the perfect player would be forced to play the same perfect game over and over, as to stray from it would be imperfect. His rating would then become dependant on his opposition, and assuming he only player super tournaments, it would be something like 2740, just by scoring 50% against an average opponent of 2740 every time.
Grated thats very hypothetical, but then again, so is the perfect player.
The better everybody plays, the lower rating the perfect player will have, since the system is relative and there is a "conservation of rating" of sorts.
Since the perfect player is outside this system (it's perfect regardless of relation to anything in the system), the rating of this player really measures how close everybody is to being perfect. The lower the rating, the closer we all are to perfection. The truth is, if everyone plays perfectly, this rating will be 1200 (or whatever "average" is).
thekibitzer wrote:
If the perfect player plays the perfect game every time, he will use the same openings each time because it is "perfect". Given enough games, someone would play his black repertoire against his white repertoire and get a draw (Im assuming in the perfect game its a draw). Then anyone who wanted a draw could get one, because the perfect player would be forced to play the same perfect game over and over, as to stray from it would be imperfect. His rating would then become dependant on his opposition, and assuming he only player super tournaments, it would be something like 2740, just by scoring 50% against an average opponent of 2740 every time.
Grated thats very hypothetical, but then again, so is the perfect player.
Thats assuming that there is only one perfect game, when there are most likely many, in may openings.
For those of you who have no idea where the "over 9000" came from...
http://www.youtube.com/watch?v=SiMHTK15Pik
Apr 16, 2013
0
#152
it's only just occurred to me on glancing back at this topic that there is a reasonable bound on the highest possible rating given by understanding of the practical size of the game of chess. If it is assumed that chess games at an extraordinarily high level would be not much longer than current games between two top computers or world class humans, and also that the current empirical fact that a doubling in speed of a computer provides about 40 elo points in results (but gradually decreasing?), you can combine the two by consideration of how much computing you need to compute right to the end of a game. In practical terms it appears that a ply takes about one doubling in speed (very rough, for an incomplete but almost perfect search). Now, if we need perhaps 200 ply (about 2^200 in speed) this could not be more than about 8000 elo points. (Probably quite a lot less due to diminishing returns, but surely not by more than a single figure factor?) If so, the rating of perfect chess is probably at least 4000. Seems outrageous!
Assuming chess is a draw, a perfect player's best move would actually be to play the move which would cause an imperfect player the most trouble based on the percentage of all possible games beyond that move that lose for the imperfect player. Or am I just talking out of my ***?
Jun 4, 2014
0
#154
No, you're not wrong. I've seen computer programs that, faced with a theoretically drawn K+P vs K position, will not even try to defend their pawn because their database says it's a draw. I can't imagine a "perfect" player giving up when a win was still technically possible.
This guy thinks it's 3600, he says his computer model thinks so. It goes into plenty of detail.
http://www.uschess.org/content/view/12677/767/
It's an interesting perspective & the article can get boring but maybe you'll want to see it.
When I get back to Buffalo, I'm going to ask IM Regan ("this guy") myself, see if he can spare some time to talk to me; he works in the CSE department at my university~
Very intersting discussion. Back in 2004 I had a similar discussion on the Arimaa game forum. To estimate the rating of a perfect player I proposed using the increasing percentage of draws as players get stronger to extrapolate the rating when that percentage reached 100%. Using data from human games I concluded it would be 3500. Using data from computer games I concluded it would be around 4000. The reason for the difference is that humans tend to offer and accept draws more often rather than playing the game as far as possible until it reaches a natural draw.
One of the interesting conclusions from this discussion was that even among perfect players it is possible for some perfect players to have a higher rating than other perfect players if they are able to determine that their opponent is a non-perfect (but near perfect) player and chose moves that are more likely to create positions in which the non-perfect player will make a mistake. So opponent modeling and playing to the opponents weakness is an important factor in increasing ones rating. It's not just what you know about chess, it's that plus what you know about your opponent.
http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=other;action=display;num=1217891261
Jan 11, 2015
0
#158
I believe computers have not yet reached a level where draws are steadily increasing. They just make deeper errors than they used to. Top human chess players, by contrast, choose lines that are safer or riskier based on factors that are irrelevant to computers. Some top professionals probably dislike losing more than they like winning: this is a utility function which is different to the points scored.
there are different definitions of perfect play
the bare minimum would be a computer who always draws or wins, winning when the opponent makes a mistake that loses. the computer will play any move that preserves a draw when its drawn, and wins when winning.
if the computer plays the worst move possible that still draws or wins, it might be 2700 against GMs with almost all draws since its unlikely the GM will ever lose. but by definition that is a form of perfect play.
if it plays the "best" move possible always (based on evaluatating the position even though 2 drawn positions lead to the same result), then all humans have to do is find 1 way to draw, and then the computer has no way to win since it will always pick the same move. it might win many games but eventually peter out to all draws and go back to 2700.
if the computer randomized its top evaluated moves as long as the evaluated positions don't differ by that much, it would most likely score big against humans. probably at least 3300.
let's take something hypothetical, a computer who knows which move you are going to make in any given position. it is also allowed to make losing moves. the funny thing is that it would score much higher than "perfect play" since it's win rate would be almost 100% against humans. probably 4000 rating.
Jan 11, 2015
0
#160
There is a definite theoretical meaning of perfect play. It is based on the tablebase of the entire game of chess, containing all positions with their result with best play by both players (recursively defined), i.e. each position has a value 1, 1/2 or 0, no other distinctions matter.
Given that basis, perfect play is where a player never plays a move that makes the value of the position worse, assuming perfect play by both players afterwards (could be recursively defined, if you don't assume the tablebase has already been generated).
There is a nicety, which is that perfect play in a winning can be considered to be playing the moves which lead to the quickest checkmate, assuming best defense by the opponent.
The positional evaluation that is necessary by real computers (and people) which can be represented as a number, primarily indicates uncertainty about the result.
3000