bob wrote:
The only thing I don't buy is the "some max elo".
Max ELO can be broadly theoretically derived.
Chess is finite. Q.E.D.
From a mathematical point of view there is no difference between chess and tic-tac-toe.
(I realise now that Kai attempts to derive an upper bound on max Elo. That is of course more work than a simple proof of existence.)
Again, my point. The upper bound he proposed is impossible to understand for humans. Can a 60,000 Elo computer lose a knight odds game against a 2800 human? Who knows, but I would bet on the computer. What is the max material needed as an advantage for a 2800 player to beat a 60,000 player? Absolutely no idea for me. But I suspect a knight won't even be close.
And his 60,000 Elo is probably well off the real mark. For example, who says that (a) perfect chess will only require 100 moves to win the game? Suppose perfect = 300 moves min? Who says that EVERY move in that game is singular? So the number could be way lower, or way higher.
bob wrote:If you look back through this thread, the claim has been made that "GMs play perfectly with a knight advantage." If that were true, then they would, in fact, score 100%. Since 100% would be the definition of perfect play.
I looked at the very first post and there is no claim that the GM would score 100%.
Some posts may have simplified the argument to "GMs play perfectly with a knight advantage". But the point of this thread is not to deny that GMs are human.
The claim is that top GMs in good health on normal days and at reasonable time controls should be able to outscore current and future top engines when given a knight advantage. The argument to support this claim is that in order to win a particular game it is sufficient for the GM to play that particular game perfectly. If the GM can do that in a particular game, no amount of processing power will help the engine. Zillions of nps in a lost position only help the engine to see more quickly that it is dead lost.
The definition of perfect play is not "scoring 100%" at all. For starters, 100% against a fallible opponent does not imply perfect play.
The definition of perfect play is very simple: play winning moves in a theoretically won position, play drawing moves in a theoretically drawn position.
Finding a "perfect" move can be difficult in a position that is still undecided from a human point of view. It is considerably easier in a position where one side has a clear winning advantage.
Given the lack of hard evidence, the question whether knight odds is already sufficient may still be largely a matter of opinion. But it seems rather reasonable that a top GM will be able to use the extra knight to control the game to such a degree that he can avoid taking risks and calmly but steadily increase his advantage.
perfect: No mistakes. If the game is winnable, the GM would have to win it or his play would not be "perfect". Unless you assume that some knight-odds games must be draws, there is no other way to think about it. 100% is required here.
Is a knight enough? Who knows. It is certainly closer to the truth than 1 pawn. But computers have a LONG way to go before they play perfect chess, and they are already winning pawn odds games. I "assume" a queen would always win, but I am not even sure of that. If there is a long singular path, can the human follow it precisely? I'm not sure. I would find it no harder to play perfectly in a normal game than in an odds game. You still can't make a single mistake if you are going to have to play perfectly. Humans will never do that until reaching simple endgames. So the question is, how near to perfect do they have to play to win a knight odds game? I don't know enough about that nearly infinite tree to be able to answer that. And then there is the question of can they play that near to perfect?
bob wrote:
The only thing I don't buy is the "some max elo".
Max ELO can be broadly theoretically derived.
Chess is finite. Q.E.D.
From a mathematical point of view there is no difference between chess and tic-tac-toe.
(I realise now that Kai attempts to derive an upper bound on max Elo. That is of course more work than a simple proof of existence.)
And his 60,000 Elo is probably well off the real mark. For example, who says that (a) perfect chess will only require 100 moves to win the game? Suppose perfect = 300 moves min? Who says that EVERY move in that game is singular? So the number could be way lower, or way higher.
That was the upper bound for Max Elo. First there IS finite a Max ELO (you denied even that), second in fact it can be shown to be even lower than 60,000 ELO points, I was simply being generous. There is a rigorous calculation that there are about 10^120 possible different chess games. Therefore the Max ELO is BELOW 400*120=48,000 ELO points. 48,000 is the upper bound for Max ELO. What's so hard? I will rephrase for you: the ELO of the Perfect Engine cannot be higher by more than 48,000 ELO points than the ELO of the random engine. Therefore cannot be "way lower, or way higher" (as you wrongly said) than 48,000 and 60,000, can be only lower than 48,000 and lower than 60,000.
bob wrote:
The only thing I don't buy is the "some max elo".
Max ELO can be broadly theoretically derived.
Chess is finite. Q.E.D.
From a mathematical point of view there is no difference between chess and tic-tac-toe.
(I realise now that Kai attempts to derive an upper bound on max Elo. That is of course more work than a simple proof of existence.)
And his 60,000 Elo is probably well off the real mark. For example, who says that (a) perfect chess will only require 100 moves to win the game? Suppose perfect = 300 moves min? Who says that EVERY move in that game is singular? So the number could be way lower, or way higher.
That was the upper bound for Max Elo. First there IS finite a Max ELO (you denied even that), second in fact it can be shown to be even lower than 60,000 ELO points, I was simply generous. There is a rigorous calculation that there are about 10^120 possible different chess games. Therefore the Max ELO is BELOW 400*120=48,000 ELO points. 48,000 is the upper bound for Max ELO. What's so hard?
That seems to come from the calculation of the number of possible positions. I believe that comes from the smallest compression algorithm that will store 64 squares with max legal pieces of each type, which seems to be roughly 2^168 or so.The longest possible game has been pretty well ironed out, playing within the 50 move rule. 96 pawn pushes + 30 captures gives a max length of 136 * 50 moves. For one game. A pretty big number. How many such games are there, plus all the shorter ones? 5500 has been a common estimate, and whether it is 5500 moves or 136*50 moves is not worth quibbling over. But that dwarfs your 100 move estimate.
And for me, 48,000 would be an acceptable estimate, because it is only 45,000 Elo above the best humans. Would that be enough to win a knight odds game from the weaker side? Every time? I'd suspect so, not that we will ever see that sort of perfect play from a computer. But max elo = 48000 is much more acceptable than the "knight odds will always be too much to give a human." I don't see any rigorous proof to support that at all.
bob wrote:But max elo = 48000 is much more acceptable than the "knight odds will always be too much to give a human." I don't see any rigorous proof to support that at all.
I don't know what rigorous proof can exist for that. Larry, me and Ronald gave you many possible plausible, common sense educated guesses, and often an educated guess (sometimes a "model") is much more than just lamenting that "there is no proof so we are completely ignorant on the issue". To have a measure of the value of the "models" we proposed, I can put my money on the future human world champion rated above FIDE 2700 winning a match of 10 games against 32 men tablebases at Knight odds.
bob wrote:perfect: No mistakes. If the game is winnable, the GM would have to win it or his play would not be "perfect". Unless you assume that some knight-odds games must be draws, there is no other way to think about it. 100% is required here.
As I said, to score better than the computer, he does not need 100%. The claim is that he can outscore the computer, i.e. score > 50%.
As I said, to win a particular game, it is sufficient to play THAT game perfectly. (Strictly speaking it may not always be necessary to play the full game perfectly, but against future top engines it is rather unlikely that an imperfect move will go unnoticed.)
The "perfect play" argument is only used to explain why even a zillion-fold increase in computer speed is not going to help.
bob wrote:But max elo = 48000 is much more acceptable than the "knight odds will always be too much to give a human." I don't see any rigorous proof to support that at all.
I don't know what rigorous proof can exist for that. Larry, me and Ronald gave you many possible plausible, common sense educated guesses, and often an educated guess (sometimes a "model") is much more than just lamenting that "there is no proof so we are completely ignorant on the issue". To have a measure of the value of the "models" we proposed, I can put my money on the future human world champion rated above FIDE 2700 winning a match of 10 games against 32 men tablebases at Knight odds.
I'd be happy to take the bet, but since that won't ever happen, it would be pointless...
Laskos wrote:I don't know what rigorous proof can exist for that. Larry, me and Ronald gave you many possible plausible, common sense educated guesses, and often an educated guess (sometimes a "model") is much more than just lamenting that "there is no proof so we are completely ignorant on the issue". To have a measure of the value of the "models" we proposed, I can put my money on the future human world champion rated above FIDE 2700 winning a match of 10 games against 32 men tablebases at Knight odds.
I'd be happy to take the bet, but since that won't ever happen, it would be pointless...
Not only won't it happen, it wouldn't prove anything, anyhow. There a many ways to play with a 32 man tablebase that wouldn't optimize the winning chances.
Laskos wrote:I don't know what rigorous proof can exist for that. Larry, me and Ronald gave you many possible plausible, common sense educated guesses, and often an educated guess (sometimes a "model") is much more than just lamenting that "there is no proof so we are completely ignorant on the issue". To have a measure of the value of the "models" we proposed, I can put my money on the future human world champion rated above FIDE 2700 winning a match of 10 games against 32 men tablebases at Knight odds.
I'd be happy to take the bet, but since that won't ever happen, it would be pointless...
Not only won't it happen, it wouldn't prove anything, anyhow. There a many ways to play with a 32 man tablebase that wouldn't optimize the winning chances.
Only if the initial position is lost at best. Then you can finagle which move you play to try to choose the one that is hardest to defend against. But if it is drawn, it is drawn. I'd likely assume that knight odds is lost with perfect play as a fairly reasonable assumption but I am not 100%, because of cases like KNK being a draw, or even KRNKR being a draw. So it is not certain the extra knight would win... But it seems reasonable. The problem is, the human, who would not have access to this perfect information. How imperfectly would he play when facing what Ken Thompson called "God"... That is the issue and I suspect he would not play well enough. Maybe we will reach the point where the knight advantage is not enough, even without endgame tables. I can only track my own progress, but in 1968 I was searching about one node per second on a machine that could execute 80K instructions per second (IBM /360 model G40). By 1983 that was 10K, by today it is 100M on inexpensive hardware and I have seen 250M+ on exotica... so 45 years, 1N to 250M, quite a jump. What will the next 45 years bring? And that completely ignores search/evaluation improvements which will also come along.
Laskos wrote:I don't know what rigorous proof can exist for that. Larry, me and Ronald gave you many possible plausible, common sense educated guesses, and often an educated guess (sometimes a "model") is much more than just lamenting that "there is no proof so we are completely ignorant on the issue". To have a measure of the value of the "models" we proposed, I can put my money on the future human world champion rated above FIDE 2700 winning a match of 10 games against 32 men tablebases at Knight odds.
I'd be happy to take the bet, but since that won't ever happen, it would be pointless...
Not only won't it happen, it wouldn't prove anything, anyhow. There a many ways to play with a 32 man tablebase that wouldn't optimize the winning chances.
The reason I am insisting on tablebases is that a far from perfect engine, maybe not much stronger than present day top engines, may perform better against human GM than the perfect engine if some special routines are implemented to play such a chess as to fool, confuse and trap humans.
I can reformulate the bet: no engine in 30 years from now, playing the chess it considers the best against itself, will beat at Knight odds a good GM in 10 games match at tournament time control. Here "30 years" are just to have a deadline.
