Thinking like a chess player not a game theorist. Strong guesses are fine for playing chess, just not good enough for game theory.
Chess will never be solved, here's why
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#3024
"Strong guesses are fine for playing chess, just not good enough for game theory."
++ Those are not guesses, that is knowledge.
Per game theorist van den Herik: "Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs." section 5.2 page 303.
https://reader.elsevier.com/reader/sd/pii/S0004370201001527?token=3AD53819FEF603D72358044D0591F98280DF6ECF036B0E0EC2522C4D0100A55938CB7420B4E331271A5B8D357C0E0DFC&originRegion=eu-west-1&originCreation=20220413122447
1 a4 being inferior to 1 d4 and 1 e4 is in figure 31 on page 55.
The title of that game-theoretic scientific paper has 'knowledge' in it, not 'guesses'.
https://arxiv.org/pdf/2111.09259.pdf
tygxc wrote:
There is not any doubt that 1 e4 e5 2 Ba6? is inferior, even loses for white.
There is not any doubt that 1 a4 is not superior to 1 e4 or 1 d4 [ . . . ]
You contradict yourself, because it's you (and only you actually) who distinguishes "known" from "proven". You stated that "proven" is 100% sure, thus "known" cannot be 100% sure. If you say "there is no doubt", then it's 100% sure and thus proven. But that's not. That's actually what you have to prove; if you use that as a premise, it's actually "begging the question".
Heuristics are not used the way you intend to. Your interpretation is as usual very different from the general consensus.
As for A0's knowledge, I can safely say that I know that most of the times being a rook up is enough to win, but that does not mean that being a rook up is always enough to win. A0 generalizes from a limited sample: that's in fact an overgeneralization not suited for a solution. What A0 knows are averages.
Apr 13, 2022
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#2485
tygxc wrote:
#3024
"Strong guesses are fine for playing chess, just not good enough for game theory."
++ Those are not guesses, that is knowledge.
No, they are guesses based on the experience of play that cannot be proven correct. Your confidence as a chessplayer does not strengthen the reasoning: it would not help you get such a claim peer-reviewed.
Per game theorist van den Herik: "Next to brute-force methods it is often beneficial to incorporate knowledge-based methods in game-solving programs." section 5.2 page 303.
https://reader.elsevier.com/reader/sd/pii/S0004370201001527?token=3AD53819FEF603D72358044D0591F98280DF6ECF036B0E0EC2522C4D0100A55938CB7420B4E331271A5B8D357C0E0DFC&originRegion=eu-west-1&originCreation=20220413122447
1 a4 being inferior to 1 d4 and 1 e4 is in figure 31 on page 55.
The title of that game-theoretic scientific paper has 'knowledge' in it, not 'guesses'.
https://arxiv.org/pdf/2111.09259.pdf
You really don't understand. I have access to the full text of your first link, and it has nothing in it that supports your amateur viewpoint that heuristic knowledge can form part of a solution of a game. It also excludes chess - a category 4 game - by pointing out that "knowledge-based methods" are suited to when the decision complexity is low. The decision complexity of chess is high, typically 40 options per move.
Your last post is about AlphaZero's "chess knowledge".
AlphaZero is a CHESS PLAYER. It plays chess based on the application of inductive learning and incomplete sampling of the analysis tree. Its knowledge is excellent for playing chess but it gets some tactics wrong and loses some games to Stockfish (more now to the NNUE version for sure). And you assume it is infallible and think its knowledge is 100% reliable!
AlphaZero's "knowledge" has no different status to that of a chess player and is not certain for reasons which are very similar.
Bear in mind I have many years of experience with machine learning, some of it very similar to that used in AlphaZero, and I am entirely aware of the character of such "knowledge". It is entirely distinct from the knowledge involved in solving a game.
#3026
"If you say "there is no doubt", then it's 100% sure and thus proven."
++ When something is known, then there is no doubt, it is 100% sure, but the proof may not be available.
We know 1 e4 e5 2 Ba6? loses for white, there is no doubt, but there is no proof that works out all possible variations to checkmate. Proving it poses no problem, but it is not worthwhile to burn computer time on it, precisely because the outcome is not in any doubt.
Likewise we know 1 a4 is not superior to 1 d4 or 1 e4. Capablanca said so: 1 e4 and 1 d4 accomplish more than 1 a4. AlphaZero concurs. There is no doubt about it. It is 100% sure, but there is no proof available. Proving it is problematic in practice and nearly as demanding as proving 1 d4 and 1 e4 draw. However, once 1 d4 and 1 e4 are proven draws, then by the same methodology 1 a4 can be proven to draw too.
Likewise we know the opposite color bishop endgame is a draw and the ICCF grandmasters were right to agree on a draw. There would be no point in playing it out till a 3-fold repetition or a table base draw. If one of both had thought he had even the smallest chance of winning, then he would not have offered or declined the draw and they would have continued for months until all doubt was removed for both.
Likewise we know the KRBPPPP vs. KRNPPPP endgame with symmetrical pawns on 1 wing is a draw and the ICCF grandmasters were right to agree on a draw. There would be no point in playing it out till a 3-fold repetition or a table base draw. If one of both had thought he had even the smallest chance of winning, then he would not have offered or declined the draw and they would have continued for months until all doubt was removed for both.
Apr 13, 2022
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#2487
tygxc wrote:
#3026
"If you say "there is no doubt", then it's 100% sure and thus proven."
++ When something is known, then there is no doubt, it is 100% sure, but the proof may not be available.
We know 1 e4 e5 2 Ba6? loses for white, there is no doubt, but there is no proof that works out all possible variations to checkmate. Proving it poses no problem, but it is not worthwhile to burn computer time on it, precisely because the outcome is not in any doubt.
Likewise we know 1 a4 is not superior to 1 d4 or 1 e4. Capablanca said so: 1 e4 and 1 d4 accomplish more than 1 a4. AlphaZero concurs.
No. AlphaZero outputs probabilities. It is uncertain about the outcome of every move (except where complete analysis to a result is possible). The move that it assesses to have a higher probability of a good result, it views as better. It is sometimes wrong (to the extent that its decisions lose).
And Capablanca is less reliable than AlphaZero.
#3027
"you assume it is infallible and think its knowledge is 100% reliable!"
++ No not at all, in fact I calculated its error rate at 60 h/move to be 1 error in 10^5 positions and thus concluded 4 white candidate moves are required to achieve 1 error in 10^20 positions.
"AlphaZero's "knowledge" has no different status to that of a chess player"
++ My point is that there are other sources of knowledge than computation. Chess knowledge by great human players and AlphaZero is valuable in its own right and per van den Herik is beneficial to incorporate in game solving. It is no match report of AlphaZero vs. Stockfish, it is a scientific paper that uses AlphaZero to acquire chess knowledge.
Likewise checkers was solved with the program Chinook.
Likewise humans have proven a lot about endgames. That is valuable knowledge and it is beneficial to incorporate that by truncating unnecessary calculations once a known drawn endgame >7 men is reached.
Weakly solving chess is a formidable task in itself. So all available help in reducing the calculation effort is needed. A purist attitude 'if it is not calculated by the computer then it is not true' is detrimental.
Apr 13, 2022
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#2489
#3029
"The move that it assesses to have a higher probability of a good result, it views as better."
++ Yes, that is correct, but the paper went further to evolve several versions of AlphaZero so as to acquire more and more dependable knowledge.
"It is sometimes wrong (to the extent that its decisions lose)."
++ Yes, at 60 h/move it errs in 1 out of 10^5 positions.
"And Capablanca is less reliable than AlphaZero."
++ No, that is like saying Euler is less reliable than Ramanujan.
Capablanca remarks that 1 e4 and 1 d4 occupy and control the center and open diagonals for the bishops and the queen and no other move accomplishes that much. All of that is true and verifyable and his conclusion is logical and true. AlphaZero independently came to the same conclusion and ranks 1 d4 and 1 e4 above all 18 other possibilities, just like Capablanca said. Personally I would consider chess weakly solved if 1 e4 and 1 d4 are proven draws. To be extra sure I would also include 1 c4 and 1 Nf3 (top 3 and top 4 per AlphaZero). The other 16 possibilities however do nothing but needlessly burn computer time. There is no doubt and it is 100% sure that none of them is any better than 1 e4 or 1 d4.
The best first heuristic was also used in solving Losing Chess: some lesser lines were added later.
#3031
"The more people question it, the surer you get."
++ It baffles me how you can question that. Are you a beginner who does not know that a piece down without any compensation loses the game?
Apr 13, 2022
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#2492
tygxc wrote:
#3031
"The more people question it, the surer you get."
++ It baffles me how you can question that. Are you a beginner who does not know that a piece down without any compensation loses the game?
I think I can honestly say I doubt if I'd win it as Black even against Stockfish. I'd put money on losing it against a 32 man tablebase if there were such a thing.
Apr 13, 2022
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#2493
tygxc wrote:
#3031
"The more people question it, the surer you get."
++ It baffles me how you can question that. Are you a beginner who does not know that a piece down without any compensation loses the game?
Lasker used to say its a rook. A rook down. Not a piece.
There is considerable rationale in not including Ba6 in 'weakly' solutions.
But knocking out 1) a4 ... or any of the 20 white first moves at all - is just too intensely suspect.
But don't worry ! As I said - you've been getting control of the forum.
And for 3000 posts now !
Simply by refusing to cave in ! 
#3034
"I think I can honestly say I doubt if I'd win it as Black even against Stockfish. I'd put money on losing it against a 32 man tablebase if there were such a thing. "
++ Yes, I guess that is true. However, we are not talking about practical play against Stockfish here with the inherent human errors, but rather about weakly solving chess. I.e. both entities commanding the white and the black pieces are presumed to play optimal moves.
Stockfish should win this against itself or against any present or future engine, or against the postulated 32-men table base. An ICCF grandmaster should win this against the postulated 32-men table base. In practice ICCF grandmasters resign when they lose a pawn without compensation. There is also no doubt at all that the postulated 32-men table base would list the entry 1 e4 e5 2 Ba6 as black checkmates in X moves, presumably with X < 50.
Apr 13, 2022
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#2495
"Stockfish should win this against itself"
Heyyyy !!! That's interesting !
What odds does a computer have to give itself ... to beat itself ??
A subject in itself !
But - tainted by Stockfish's pathetic findings of wins in obviously drawing situations.
#3035
"Lasker used to say its a rook."
++ Where did Lasker say that? A rook is enough to win, a piece is enough to win, a pawn is enough to win.
"The winning of a pawn among good players of even strength often means the winning of the game." - Capablanca
"An endgame with an extra pawn is won, the plan is to queen the pawn;
an endgame with an extra piece is won, the plan is to trade the piece for a pawn." - Capablanca
Apr 13, 2022
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#2497
A pawn is Very Often not enough to win.
And a knight or bishop up often fails to win.
A rook is somewhat different.
Part of the theory of that is that if everything else is exchanged - the rook triumphs. Its the Minimum Mating Material.
mmm Rook up !!!
Apr 13, 2022
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#2498
(could get a series of pingpong posts now where @tygxc actually knows what I'm talking about - but there's a kind of 'argument' about things we actually agree on. Even though he's likely to maintain otherwise.
I think he does that all the time.
But its okay)
Analogy: You're walking through a particular part of town - and you walk by some busy tennis courts with many people playing ...
and you hear those volleys of Bop-bop-bop ... not quite like popcorn ...
has its own 'tennis' quality 
Apr 13, 2022
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#2499
tygxc wrote:
#3029
"The move that it assesses to have a higher probability of a good result, it views as better."
++ Yes, that is correct, but the paper went further to evolve several versions of AlphaZero so as to acquire more and more dependable knowledge.
AlphaZero is only useful for acquiring knowledge with uncertainty. It could however be helpful to generate candidate moves for an optimal strategy, much as programs were used for this in the (correct and complete) solution of checkers, which is a good model for what needs to be achieved for chess. For example, to solve chess it is necessary to solve over 400 positions reached after 3 ply of moves(absolutely non-negotiable!), while for checkers the number was much smaller (but directly analogous).
"It is sometimes wrong (to the extent that its decisions lose)."
++ Yes, at 60 h/move it errs in 1 out of 10^5 positions.
"And Capablanca is less reliable than AlphaZero."
++ No, that is like saying Euler is less reliable than Ramanujan.
No it isn't, because they were both human and moreover there is no strong reason to believe Ramanujan had superior skills to Euler: both were superb mathematicians, with Euler living a lot earlier but being a lot broader in his work. By contrast, AlphaZero is so strong it would be capable of beating Capablanca in a large majority of games with both colours. That despite the fact that Capablanca was one of the best human chess players ever.
But note also that chess is not mathematics. When Euler made a conjecture, he knew it was uncertain. He did not lose by not knowing the correct answer - rather he merely didn't solve that particular problem (and knew he hadn't solved it). He was human and occasionally made mistakes, but his standards were extremely high and other mathematicians took things further.
Capablanca remarks that 1 e4 and 1 d4 occupy and control the center and open diagonals for the bishops and the queen and no other move accomplishes that much. All of that is true and verifyable and his conclusion is logical and true.
Jeez.
AlphaZero independently came to the same conclusion and ranks 1 d4 and 1 e4 above all 18 other possibilities, just like Capablanca said.
Such ranking can only relate to practical chess, not game theory. There is a set of first moves that win, a set that draw and a set that lose (these sets form a partition of the 20 legal moves).
Personally I would consider chess weakly solved if 1 e4 and 1 d4 are proven draws.
This is a statement about your lack of understanding of what solving means.
Jonathan Schaeffer did not claim checkers was solved when the "best" openings had been dealt with. He worked towards a complete solution and then announced it and published it when it was complete. You should learn from him. He knows what he is talking about.
This discussion consists mostly of you repeating the same mistakes over and over again and other people correcting you. Look to Jonathan Schaeffer to find out who is correct.
#3039
"A pawn is Very Often not enough to win."
++ Among weak players or if there is compensation yes, but generally a pawn is enough to win.
"A pawn is a pawn" - Fischer
One example is the King's Gambit 1 e4 e5 2 f4 exf4 3 Nf3.
"It loses by force" - Fischer
"I could not find a way for white to equalise" - Kramnik
This was confirmed by AlphaZero: see figure 4 (d) on page 10.
https://arxiv.org/pdf/2009.04374.pdf
That is also the reason why most gambits have vanished from top grandmaster play.
Grandmasters go though a lot of trouble and accept all kinds of cramped positions just to win a pawn. Here is an example: Carlsen gambits a pawn and almost loses.
https://www.chessgames.com/perl/chessgame?gid=2122755
In weakly solving chess I would not care to handle e.g. Danish Gambit.
#3022
"If you can provide a strategy that indeed excludes useless lines without any doubt before values are given through a TBH (or 3-fold repetition, etc.), we are all ears."
There is not any doubt that 1 e4 e5 2 Ba6? is inferior, even loses for white.
There is not any doubt that 1 a4 is not superior to 1 e4 or 1 d4.
Likewise there is not any doubt that the opposite color bishop's ending and the endgame KRB vs. KRB with equal pawns on one wing are indeed draws, like the ICCF grandmasters agreed on.
So human knowledge allows to exclude these lines.
The 'good assistants' should take care of this pruning in the opening and in the endgame.