After considering the evidence, I don't think chess can be "solved". Too many permutations.
Chess will never be solved, here's why
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And in some cases, we might all agree. For example, "Yes, we all agree that it's certain. Smoking causes lung cancer". Hasn't been "proven", but in this case, close enough. There's no point whatsoever in further debate.
But some would say solving chess is not the same, and we are pursuing an absolute, mathematical proof, not one that we can all agree is "close enough" or "for all practical purposes".
Oct 18, 2022
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#6184
Like so often, this reveals that a large fraction of this debate is semantic. While several of the people here understand the accepted academic viewpoint about logical propositions and the reasoning that can prove them (eg the solution of checkers, the proof of the 4-colour theorem), those who "debate" against the consensus are using several of the same terms but incorrectly in crucial cases.
A "proof" to @tygxc is not a proof according to the standard meaning of the word. It's not that he is knowingly applying a different paradigm (including confusing different uses of the same terminology). Rather he gets confused and thinks he is advocating something of equal status to a rigorously proved result.
mikekalish wrote:
And in some cases, we might all agree. For example, "Yes, we all agree that it's certain. Smoking causes lung cancer". Hasn't been "proven", but in this case, close enough. There's no point whatsoever in further debate.
But some would say solving chess is not the same, and we are pursuing an absolute, mathematical proof, not one that we can all agree is "close enough" or "for all practical purposes".
If chess can't be represented mathematically, then those who say that it can would appear to be wrong.
@6310
https://www.iccf.com/event?id=85042
136 games = 119 draws + 17 decisive games.
Assume chess a win.
Fit a Poisson distribution with 119 / 136 probability of an odd number of errors / game.
It is impossible, thus Chess is a draw.
Fit a Poisson distribution with 17 / 136 probability of an odd number of errors / game.
It is possible with average 0.143 error / game.
Games with 0 errors: 118
Games with 1 error: 17
Games with 2 errors: 1
Notice there is an anomaly in the games of SIM Bock, Steffen.
Strike the 16 games of SIM Bock Steffen.
120 games = 116 draws + 4 decisive games
Assume Chess a win, it is impossible to fit a Poisson distribution of errors / game with 116 / 120 probability of an odd number of errors / game. Thus Chess is a draw.
Fit a Poisson distribution with 4 / 120 probability of an odd number of errors / game.
It is possible with average 0.0345 error / game, i.e. 1 error / 29 games
Games with 0 errors: 116
Games with 1 error: 4
The above game is 96.6% certain to be an optimal game without any error by either side.
@6311
"more specific around the term error"
++ An error (?) is a move that changes a drawn position a loss, or a win to a draw.
a blunder or double error (??) is a move that changes the game state from a win to a loss.
Intuitively, I think chess can be solved. My belief has nothing to do with human ability, the power of computers, present or future, or the time it might take.....or if it will ever be done. The question to me is simply, "Does a solution exist?".... not "Will we ever find the solution?". I think those are two very different questions...both interesting.
It's hard for me to understand how there would not exist an algorithm that would guarantee at least a draw....just my thinking. I think it's unlikely that humans will ever devote the necessary resources to getting it done, but seems to my crude mind that the solution is out there waiting to be found......and again, that's just an opinion.
Aside....I know (from experience) what an "error" is. But I don't think that's helpful if you can't pin down in every position which moves are errors and why. And the simple fact that "this move leads to defeat 98% of the time" isn't persuasive to me, although it might be to some.
Oct 18, 2022
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#6189
tygxc wrote:
@6310
https://www.iccf.com/event?id=85042
136 games = 119 draws + 17 decisive games.
Assume chess a win.
Fit a Poisson distribution with 119 / 136 probability of an odd number of errors / game.
It is impossible, thus Chess is a draw.
Fit a Poisson distribution with 17 / 136 probability of an odd number of errors / game.
It is possible with average 0.143 error / game.
Games with 0 errors: 118
Games with 1 error: 17
Games with 2 errors: 1
Notice there is an anomaly in the games of SIM Bock, Steffen.
Strike the 16 games of SIM Bock Steffen.
120 games = 116 draws + 4 decisive games
Assume Chess a win, it is impossible to fit a Poisson distribution of errors / game with 116 / 120 probability of an odd number of errors / game. Thus Chess is a draw.
Fit a Poisson distribution with 4 / 120 probability of an odd number of errors / game.
It is possible with average 0.0345 error / game, i.e. 1 error / 29 games
Games with 0 errors: 116
Games with 1 error: 4
The above game is 96.6% certain to be an optimal game without any error by either side.
im not sure if i understood right, but what i understood is if there are no mistakes, the game is a draw, but we are humans, and not even chess engines are sure about the game, for example, chess engines give ana advantage to white between 0.3 and 0.6(for playing e4 at least), which is an indication of a draw, but that advantage could grow exponentially as the game goes on, but we don’t know if it does, as not even chess engines can calculate the best of the best moves, maybe some trash opening that appears for the engine calculating 30 moves as a trash opening, but if it saw the actually most optimal moves, it would be some forced mate in 200 moves and each non-optimal move makes it faster, but that’s the problem, that’s too much moves to calculate, we can’t prove that there’s a forced mate in 200 moves because nothing can calculate move orders that far! it’s simply too much!
Oct 18, 2022
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#6190
tygxc wrote:
@6311
"more specific around the term error"
++ An error (?) is a move that changes a drawn position a loss, or a win to a draw.
a blunder or double error (??) is a move that changes the game state from a win to a loss.
Obfuscating, non-standard terminology.
Both are blunders. One is a whole point blunder, the other a half point blunder.
If chess can't be represented mathematically, then those who say that it can would appear to be wrong. Thus, a proof in the mathematical sense would be impossible. It would still be down to a belief that all the possible lines of chess had been looked at and seen to lead to an optimum result. Otherwise, we have a result dependent on the assumption that all the possible lines had been followed through correctly by a brute force search, although one that is possibly led by algorithms that have been shown to have a 100% true predictive power. This assumptive proof is inductive, of course and is therefore not the rigorous, mathematical proof that is assumed to be the requirement of those interested in a theoretical proof of the rectitude of a solution for chess, rather than a practical or pragmatic one.
@6314
"there would be more than a 100 million move orders"
++ There are 10^44 legal positions, of which 10^17 are relevant to weakly solving chess.
"you have to know the best move against every move played"
++ Not the best move, but one of the good moves that are no errors
"even the best chess engine can’t play perfectly" ++ But when it runs for 17 s on a 10^9 nodes/s cloud engine, then a table base exact move is among the top 4 engine moves
"costs a fortune to use" ++ I estimate 3 million $ during 5 years
"would force mate in 279 moves" ++ No, Chess is a draw
"you could get to the same positions with dozens upon dozens of move orders"
++ That is why positions are key, not move orders
"yes, chess can be solved" ++ indeed
"nothing we have or can have, will be able to solve it"
++ 3 cloud engines of a billion nodes/s and 3 grandmasters can do it in 5 years.
tygxc wrote:
@6311
"more specific around the term error"
++ An error (?) is a move that changes a drawn position a loss, or a win to a draw.
a blunder or double error (??) is a move that changes the game state from a win to a loss.
This is not the kind of specificity I was thinking of. I realize this is clear in your mind, but it's not clear in mine. I don't disagree with these "definitions" but they don't help with the fundamental questions I have.
Oct 18, 2022
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#6194
There is no doubt that chess with a choice of drawing rules is simple to represent mathematically. Technically, chess with a drawing rule that prevents infinite games falls into a different class of games to basic chess, but maths has no problem with either.
(The added definition that a theoretically drawn basic chess position is one where neither side can force a win brings it closer to finite versions of chess. Note also that, unlike for many key notions in computer science, there is a terminating algorithm that determines the values of all basic chess positions with this added definition).
Elroch wrote:
@Optimissed, I know Contact has pi in it, but this was way too late and not consistent with my memory! It has to be a novel published by the mid-1970s.
I read virtually nothing published after 1966 except part one of the Foundation Trilogy, which may have been later than that. My dad continued to read sci-fi whenever and wherever he could get hold of it and at least twice I gave him job lots of a hundred or two books, because I was a part-time book dealer for a few years.
Since the 30 digits of pi is piquing my memory cells but without a positive feedback, maybe it was pre 1964, since I probably read most sci-fi published before then except a few authors maybe like James Blish.
@6322
"if there are no mistakes, the game is a draw" ++ Yes, correct.
"between 0.3 and 0.6(for playing e4 at least), which is an indication of a draw" ++ Yes
"that advantage could grow exponentially as the game goes on" ++ As one side errs
"not even chess engines can calculate the best of the best moves"
++ There are only good moves, errors (?), and blunders (??)
"some trash opening" ++ There is knowledge. 1 a4 cannot be better than 1 e4 or 1 d4, 1 Nh3 cannot be better than 1 Nf3
"it would be some forced mate in 200 moves" ++ No, Chess is a draw
"we can’t prove that there’s a forced mate in 200 moves" ++ There is no such #200
"nothing can calculate move orders that far" ++ Yes, 10^9 nodes/s cloud engines can calculate from the initial position to a 7-men endgame table base draw or a prior 3-fod repetition draw.
Just had a thought. It wasn't Algernon the mouse was it? You probably read that classic .... about a man who was mentally retarded and received a treatment that gave him an IQ of 200 or something.
To me, solving chess is purely mathematical with zero consideration of such things as confidence levels or statistical treatments.
If someone "solves" chess to the point of being 99.99% confident, I'll bet on him every time, but I would not consider his solution a true solution. In most cases, 99.99% is plenty good. In solving chess, it's "close but no cigar".
But the reason I'm following is because I'm open to hearing arguments on both sides.....which I'm definitely hearing.
@6324
"non-standard terminology"
'I have attached question marks to the moves which change a winning position into a drawn game, or a drawn position into a losing one, according to my judgment;
a move which changes a winning game into a losing one deserves two question marks
There are no exclamation marks, as they serve no useful purpose. The best move should be mentioned in the analysis in any case; an exclamation mark can only serve to indicate the personal excitement of the commentator.' - GM Dr. Hübner
Oct 18, 2022
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#6200
A move which can be seen to change the result by half a point deserves "??" for a sufficiently strong player. Check with any GM.
The eccentric view that blunders only occur from winning positions rather than drawing ones is a random obfuscation by you.
Huebner points out that from a detached viewpoint there are no brilliant moves, merely correct ones, since no move positively changes the theoretical result.
By contrast, blunders do exist.
haha! it's funny that you assume chess can never be solved. i've come close to it, i'm a mathematician graduate student in harvard university.
my thesis dissertation will be on solving the problem of chess. i'm close to solving it so it will be solved soon
chess can be solved, but the problem is, even with the first 10 moves, there would be more than a 100 million move orders, and you have to know the best move against every move played, which even chess engines aren’t always sure about, even the best chess engine, stockfish15/AlphaZero (im on alphazero’s side) can’t play perfectly, to solve chess, you have to know the best move, in every single position whatever it was, and not even the best chess engine with the best computer it runs on, which costs a fortune to use, can truly calculate a position in depth enough for that, for example, maybe starting with a budapest rook lift would force mate in 279 moves, no engine, not even with some super mega quantum computer or something like that can calculate that far! as you not only have to know every single possible position, but every move order! you could get to the same positions with dozens upon dozens of move orders!
the conclusion of this is yes, chess can be solved, but nothing we have or can have, will be able to solve it