@5250
"What I take as solving chess would entail solving all possible ridiculous and reasonable positions that could arise from the starting position."
++ That would be strongly solving chess: a 32-men table base with 10^44 legal positions.
Chess can be weakly solved in 5 years with 10^17 relevant positions.
Naaa. ^^
@5234
"So relying on the judgement of GMs to eliminate broad categories of games/positions from consideration, thereby making the task easier, isn't actually relying on the judgement of GMs?"
++ The bulk of the work is done by the engines calculating from the humanly prepared starting positions towards the endgame table base or a prior 3-fold repetition. The GMs initiate the calculation and also terminate it when there is no doubt at all like in the opposite colored bishop ending presented. The GMs use knowledge only, no judgement. They know when all other things are equal and thus when there is no compensation of any kind to a material deficit like 1 e4 e5 2 Ba6? They know when an opposite colored bishop ending is a draw and when not.
...
So ++no, it relies on GMs who fail to use their judgement. One could well understand their judgement might be severely impaired after five years with no sleep evaluating chess positions once every 17 seconds.
It is sad that @tygxc does not understand the definition of weak solution, as used in the peer-reviewed literature on solving games. The idea that the definition permits "proof by proclamation" is laughable.
For example, here is a @tygxc-style proof of the weak solution of chess.
1. the initial position is symmetrical, so white cannot be lost (waving hands deals with any possibility of zugzwang)
2. there are a lot more draws between strong players than white wins, so obviously that is the right result.
QED
[While that is a parody, it fails to be a weak solution to the same extent as what he suggests].
So can we be certain that 1. d4 doesn't lose by force, Elroch?
Of course we can, if we wish to be. We can also be sure that we will be alive in 24 hours time. In both cases, our belief is reasonable probably right, and may be confirmed by the facts in the future, but certainty cannot be justified right now.
I can see why it is difficult for a chess player without substantial familiarity with the general truths about all inductive knowledge not to understand this, and that is to be expected. What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.
Due to the difficulty, I have on several occasions attempted to lead people through the non-technical sequences of thoughts that make the result clear, but I am well aware that many people - especially when they are not young - have no real interest in replacing long-held erroneous ideas with correct ones.
For those with young, lively brains, one line of reasoning goes like this. We (an individual, the human race, the human race assisted by as many computers as you like, as long as they are inadequate to properly weakly solve chess) start from a position of total ignorance. We don't know whether 1. d4 wins or not. From there the meta-proof that the appropriate quantification of the belief state that 1. d4 wins is not one proceeds inductively.
At each step you start from a position of uncertainty, quantified by some probability p < 1, then you acquire one element of inductive evidence. The sort of thing is the generation of the legal moves from a position.
The question is what example of such a step could change the probability of 1. d4 being a win from a value p < 1 to a value p = 1.
If we assume that we have not reached a sufficient body of evidence to make a weak solution of chess than it should be clear that one single piece of evidence cannot turn uncertainty into certainty.
I would hope that everyone here would understand that if you have a sequence of values p_i <= 1 with p_0 < 1 and p_n = 1 then you need one of the steps to take a value p_i < 1 to p_(i+1) = 1.
Is that really too difficult to understand as an explanation of why uncertainty is epistemiologically correct?
@5259
"five years with no sleep evaluating chess positions once every 17 seconds"
++ No. The 3 engines work non stop 24/7 and exhaust 1 position per 17 second.
The 3 ICCF grand(master)s work 9 to 5, 5/7. They launch the calculations, preferably from a 26-men position. They exceptionally intervene to terminate a clear drawn endgame.
How long did you say it would take? Five million years?
Sorry but weakly solving chess in five million years is highly unlikely, doing it that way. The so-called weak solution is the only meaningful way to solve it, incidentally, because the so-called strong solution isn't solving chess but finding the correct moves after complete rubbish by the opponent, like giving up seven peices in the first 20 moves. So since the strong solution is nonsense, then the so-called weak solution is correct or meaningful, so don't call it weak. There's no need to fall in with game theorists who are wrongly trying to apply their strategies to chess. Chess cannot be solved by strategies since the only meaningful strategy in chess is to find good moves.
This conversation you are having with others is complete nonsense from both sides. And I still think five million years is impossible, doing it the way you propose, because there's a big grey area, where borderline moves that may be mistakes or "brilliancies" have to be checked and there will be billions of them, that GMs or present day Stockfish algorithms simply can't handle.
No-one ever listens to those who can see things very clearly! 
They always say "the experts must be right!" 
They aren't.
Well, the real ones will be right.
So can we be certain that 1. d4 doesn't lose by force, Elroch?
Of course we can, if we wish to be. We can also be sure that we will be alive in 24 hours time. In both cases, our belief is reasonable probably right, and may be confirmed by the facts in the future, but certainty cannot be justified right now.
I can see why it is difficult for a chess player without substantial familiarity with the general truths about all inductive knowledge not to understand this, and that is to be expected. What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.
Due to the difficulty, I have on several occasions attempted to lead people through the non-technical sequences of thoughts that make the result clear, but I am well aware that many people - especially when they are not young - have no real interest in replacing long-held erroneous ideas with correct ones.
For those with young, lively brains, one line of reasoning goes like this. We (an individual, the human race, the human race assisted by as many computers as you like, as long as they are inadequate to properly weakly solve chess) start from a position of total ignorance. We don't know whether 1. d4 wins or not. From there the meta-proof that the appropriate quantification of the belief state that 1. d4 wins is not one proceeds inductively.
At each step you start from a position of uncertainty, quantified by some probability p < 1, then you acquire one element of inductive evidence. The sort of thing is the generation of the legal moves from a position.
The question is what example of such a step could change the probability of 1. d4 being a win from a value p < 1 to a value p = 1.
If we assume that we have not reached a sufficient body of evidence to make a weak solution of chess than it should be clear that one single piece of evidence cannot turn uncertainty into certainty.
I would hope that everyone here would understand that if you have a sequence of values p_i <= 1 with p_0 < 1 and p_n = 1 then you need one of the steps to take a value p_i < 1 to p_(i+1) = 1.
Is that really too difficult to understand as an explanation of why uncertainty is epistemiologically correct?
Lol no. Your "reasoning" is complete nonsense. Let's start with the basics: you can't just assume that we don't have a sufficient body of evidence to make a weak solution of chess. That's a completely unsubstantiated claim. In fact, there's a lot of evidence that suggests we DO have a sufficient body of evidence to make a weak solution of chess. For starters, we have the fact that computers can now beat the best human chess players in the world. This is strong evidence that we have a sufficient body of evidence to make a weak solution of chess, since computers are able to solve chess problems that are far beyond the ability of humans. Furthermore, there have been multiple occasions where humans have come close to solving chess. In the 1970s, for instance, a team of Soviet researchers came up with a chess program that could beat almost any human player. And more recently, in 2013, a team of researchers from the University of Alberta came up with a chess program that they claimed could beat any human player. So your claim that we don't have a sufficient body of evidence to make a weak solution of chess is simply not supported by the evidence. But even if we assume, for the sake of argument, that we don't have a sufficient body of evidence to make a weak solution of chess, your argument still doesn't make any sense. You say that "one single piece of evidence cannot turn uncertainty into certainty." But that's not true. One single piece of evidence can, in fact, turn uncertainty into certainty. For example, let's say I'm trying to decide whether or not it's going to rain tomorrow. I might start out with a 50% chance of rain, based on the current forecast. But then if I see that the sky is clear and there's not a cloud in sight, that would be a piece of evidence that would turn my uncertainty into certainty: I would now be 100% certain that it's not going to rain tomorrow. 
So your claim that "one single piece of evidence cannot turn uncertainty into certainty" is simply false. In conclusion, your entire argument is based on flawed reasoning and unsubstantiated claims. There is no reason to believe that we can't solve chess, and plenty of evidence to suggest that we can. 
@5260
"@tygxc does not understand the definition of weak solution"
++ I do understand. I quote peer-reviewed literature on solving games:
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
calls for opposition, i.e. an act of opposing, of resisting against the game-theoretic value.
'the game-theoretic value of a game, i.e., the outcome when all participants play optimally"
calls for all participants to play optimally
't is often beneficial to incorporate knowledge-based methods in game-solving programs'
encourages to incorporate knowledge
"1. the initial position is symmetrical, so white cannot be lost"
++ Yes, that is correct. Moreover white has the advantage of 1 tempo.
1 tempo is worth less than 1 pawn, about 0.33 pawn.
You can queen a pawn but you cannot queen a tempo.
So black cannot be lost either. So the initial position is a draw.
"waving hands deals with any possibility of zugzwang"
++ There is no Zugzwang in the initial position.
"2. there are a lot more draws between strong players than white wins, so obviously that is the right result."
++ Yes, the stronger the players, the more draws. The longer the time, the more draws.
Over the years the draw rate goes up.
It is impossible to explain in a consistent way the results of the ICCF WC: 136 games = 127 draws + 6 white wins + 3 black wins assuming chess being a white or black win.
@5260
"@tygxc does not understand the definition of weak solution"
++ I do understand. I quote peer-reviewed literature on solving games:
You quote papers by people who do understand the definition, but you have never quoted a statement that supports your erroneous positions.
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
Yes "ANY" opposition. ALL LEGAL MOVES.
You don't even understand the meaning of "opposition" in the context!
@5266
1 e4 e5 2 Ba6? is neither opposition, nor optimal play from both sides.
'Any opposition' means all legal moves that oppose to the game-theoretic value,
otherwise they would write 'all legal moves'.
So can we be certain that 1. d4 doesn't lose by force, Elroch?
Of course we can, if we wish to be. We can also be sure that we will be alive in 24 hours time. In both cases, our belief is reasonable probably right, and may be confirmed by the facts in the future, but certainty cannot be justified right now.
I can see why it is difficult for a chess player without substantial familiarity with the general truths about all inductive knowledge not to understand this, and that is to be expected. What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.
Due to the difficulty, I have on several occasions attempted to lead people through the non-technical sequences of thoughts that make the result clear, but I am well aware that many people - especially when they are not young - have no real interest in replacing long-held erroneous ideas with correct ones.
For those with young, lively brains, one line of reasoning goes like this. We (an individual, the human race, the human race assisted by as many computers as you like, as long as they are inadequate to properly weakly solve chess) start from a position of total ignorance. We don't know whether 1. d4 wins or not. From there the meta-proof that the appropriate quantification of the belief state that 1. d4 wins is not one proceeds inductively.
At each step you start from a position of uncertainty, quantified by some probability p < 1, then you acquire one element of inductive evidence. The sort of thing is the generation of the legal moves from a position.
The question is what example of such a step could change the probability of 1. d4 being a win from a value p < 1 to a value p = 1.
If we assume that we have not reached a sufficient body of evidence to make a weak solution of chess than it should be clear that one single piece of evidence cannot turn uncertainty into certainty.
I would hope that everyone here would understand that if you have a sequence of values p_i <= 1 with p_0 < 1 and p_n = 1 then you need one of the steps to take a value p_i < 1 to p_(i+1) = 1.
Is that really too difficult to understand as an explanation of why uncertainty is epistemiologically correct?
I disagree with you. It isn't a case of understanding or not understanding you. In some things you're quite correct and in others you make mistakes which could be regarded as elementary.
I have devised a fundamentally correct basis for the entirety of philosophy, based on a form of dualistic indeterminism. "Correctness" or lack of it is only by comparison with agreed-with or accepted norms, which cannot be regarded as axioms. That's the fundamental basis of your error: to imagine that the principles you take for granted are axiomatic.
We are talking philosophy, or trying to do so. I would suggest that your ideas are a form of idealism which is incomplete. It only accounts for relativism in thought but relativism is always balanced by absolutism. Intuitively you understand that but your intuition will be unconscious and not matched by your rational mind. This is because you believe that you're right, without a shadow of doubt. That's an absolutist frame of mind but your mistake is not to question it. Relativism and absolutism are the two fundamental principles of thought. If anyone wants to question sources, I'm the source. It's my subject area, as I've tried to explain to you. You're a statistician. I'm something else and this relates to something else.
RemovedUserName was very much on the right track when she criticised you. She's intelligent and intuitive and she could smell that something was wrong.
'I have devised a fundamentally correct basis for the entirety of philosophy...' Messianic words here 😆
Thanks. You're too kind. I expected the first words on it to be the usual stuff that the kids here can't get past.
It was a case of developing Hegel's ideas properly. He did have the right idea, about thesis, antithesis and synthesis but he failed to follow it through properly. I imagine that was because he thought he'd become more famous if he jumped on the nationalistic bandwagon, which was springing up around then and so his contribution turned out to be extremely destructive. If you have a powerful message but you yourself completely misunderstand or misuse it, that's what can happen.
So can we be certain that 1. d4 doesn't lose by force, Elroch?
Of course we can, if we wish to be. We can also be sure that we will be alive in 24 hours time. In both cases, our belief is reasonable probably right, and may be confirmed by the facts in the future, but certainty cannot be justified right now.
I can see why it is difficult for a chess player without substantial familiarity with the general truths about all inductive knowledge not to understand this, and that is to be expected. What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.
Due to the difficulty, I have on several occasions attempted to lead people through the non-technical sequences of thoughts that make the result clear, but I am well aware that many people - especially when they are not young - have no real interest in replacing long-held erroneous ideas with correct ones.
We can dispense with the rest because it enlarges on the core mistake.
<<What it amounts to is a poor estimate of a probability in a way that is qualitatively extremely wrong, but pragmatically unlikely to matter.>>
Discussing 1. d4, you seem to see its results as probabilistic. We have the same difficulty in quantum mechanics, as I once tried to explain but you failed to grasp it at that time. We accept that probability plays a fundamental part in QM. Is a fundamental entity a particle or a wave? What does wave mean?
If we see an entity as existing in a place at a time, we can see probability regarding its position as a waveform. But is that waveform a conceptual idea of our minds or is it intrinsic to the entity when it manifests as a waveform? Could it even be both?
We can now leave that indeterminate, because it doesn't apply to 1.d4. The question is "can we be sure that 1. d4 isn't a forced loss for white?" You are suggesting that there's a probability attached to that in such a way that the optimal outcome is represented by a probability. But that is a function of the estimated possible error in the machine and algorithms which determine it, or are supposed to. Probability does not exist intrinsically in 1. d4 and its optimum outcome with best play by both sides. It is either one thing or another. A forced win, a forced loss or a draw.
And that is why your attempt at explaining your belief that we can never be entirely sure fails. It's like agnosticism in religion. Maybe YOU cannot be sure but others believe they can, one way or another. How? The use of reason. Reason used correctly and well. There is no intrinsic probability attached to either matter and so any attempt to use that as an explanatory device is doomed to failure. The probability (or lack of complete certainty) exists in your mind. And that is all.
So, in a nutshell, what you are doing is you are confusing the relative with the absolute. The absolute aspect is the optimal result of 1. d4, which, obviously, is a draw. Asked whether we can be absolutely sure that 1. d4 doesn't lose for white, you answer is that we cannot be absolutely certain of that. But that is the relative aspect, which is the inability of your mind; or of a very advanced chess engine; to be absolutely sure.
But the reality is not probabilisic, in the same way that the position of a quantum entity is probabilistic. It's real and definite but considered unknown by some people, perhaps because they have lost all faith in human understanding and they try to mirror computers in their minds.
Let's imagine what a solution of chess requires. First it requires a big tablebase (in all seriousness, one that is too big to be infeasible. Let's pretend not and say we have a puny 12-piece tablebase. This requires about 10^24 bytes. That's about 10000 times bigger than the total storage capacity of all computers on the planet. Ridiculous, but technologically plausible. If you have a few trillion dollars)
Next you need two strategies. The first forces a drawn position in the tablebase with white, the second forces a drawn position in the tablebase with black.
The problem is that it seem rather unlikely you could avoid needing to rely on drawn positions not in the tablebase, if the opponent fails to co-operate in exchanging pieces (eg he blocks the position and shuffles pieces).
But can you somehow get round the need to use a large state space by considering that only opposing moves that produce new positions matter. If the opponent against a drawing strategy moves to a position previously reached he has achieved nothing.
So you don't need the full state for the positions, rather you check whether new positions are already in your strategy.
Thus I think @tygxc is correct to believe that FEN states are adequate for a solution of chess, even if he is woefully wrong on the computing power needed to solve this rigourously, as achieved for checkers.
Any flaws in that reasoning?
Whether FEN states are adequate for a solution of chess depends on the proposed method. The tablebase construction methods don't use any attributes of a position other than those in a FEN, so FEN states are clearly adequate for a solution by those methods.
On the other hand you (and @tygxc) are considering a solution that involves forward rather than retrograde construction of a solution, in which case I think there are flaws in the reasoning.
I think one flaw is that you appear to assume that identical FENs have identical results. You don't define what you mean by "position", but your penultimate paragraph would suggest you're taking it as a FEN. Of course it's impossible to repeat a FEN in a game but is is possible in a process for a solution.
The FENs after move 34 in the mainline and the variation below are identical, but one situation (I would say position) is a draw and the other is mate in 16.
A possible second flaw, I would say, regarding @tygxc's solution, so far as it can be understood, is that it involves SF which routinely doesn't consider only opposing moves that produce new positions in his own sense of the word (i.e. the equivalence class corresponding to the attributes mentioned in the triple repetition rule art. 9.2.2). It will happily repeat such "positions" (whether it's evaluation of said "position" is positive, negative or zero.)
Indeed it would be folly for it to consider only opposing moves that produce new tygxc positions as White in a situation with this FEN for example.
Of course identical FENs with different evaluations as in the first example couldn't occur without repetition of tygxc positions beforehand in at least one of the paths, but the problem is you wouldn't know if such repetitions were necessary as in the second example. Simply avoiding repetition could produce invalid results.
In any case @tygxc appears to believe not only that FEN states are adequate, but states using only the board layout, side to move, en passant and castling rights (the attributes Tromp uses in his estimate of the number of basic rules positions) are also adequate.
@5266
1 e4 e5 2 Ba6? is neither opposition, nor optimal play from both sides.
'Any opposition' means all legal moves that oppose to the game-theoretic value,
otherwise they would write 'all legal moves'.
No they wouldn't. Not all games consist wholly of moves, chess in particular.
And exactly where in the paper you keep quoting does it say, "weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against anything tygxc considers opposition"?
And you haven't decided on a version of chess that has a game-theoretic value yet, or is even playable. You say
We are talking about solving chess, i.e. the game with all its Laws of Chess.
then you talk about ICCF and TCEC games. How do the TCEC engines accord with FIDE art 4.1 or claim an adjudication by 7 man tablebase under ICCF rules? When can the ICCF players claim a draw under the TCEC draw rule? How can you have both
8.1.1 In the course of play each player is required to record his own moves and those of his opponent in the correct manner, move after move, as clearly and legibly as possible, in one of the following ways: ...
and
A.2 Players do not need to record the moves, but do not lose their rights to claims normally based on a scoresheet. The player can, at any time, ask the arbiter to provide him with a scoresheet, in order to write the moves.
in effect?
What's the game-theoretic value if a player has resigned simultaneously with moving to a dead position?
@btickler went to the trouble of defining a theoretically solvable and playable version of chess before inviting people to discuss whether it could practically be solved on his thread. You offer to solve "it" without bothering.
What I take as solving chess would entail solving all possible ridiculous and reasonable positions that could arise from the starting position. It would be a 32-piece tablebase minus positions where any side has more than 8 pawns or any pawns on the most rear rank, illegal positions, and rules to do with the fact that pawns can't move past each other without taking anything (the limit to the number of pieces on the board would be lower if there are extra bishops, knights rooks or queens) and perhaps other impossibilities. However, I'd guess the number would not be reduced by much since the original number is so insanely high.
If some computer was ever to approach this it would have to start with the endgames first and build up to more pieces. For example, it would not be rigorous to start from the opening, calculating, and declaring a loss for white after 1. e4 e5 2. Ba6 after some negative evaluation that is not a checkmate or draw evaluation as much as common sense would have it. It would be rigorous to prove from the ground up that 1.e4 e5 2. Ba6 loses based on all of the previous analysis from more basic positions and showing that all positions will end up in previously solved positions, which you don't have to keep proving since you've proved it before. But before that, one would have to prove more and more basic things until the level of certainty is like of a 7-piece tablebase right now. The essence from starting more basic is that you would have more confidence that weaker engines will not differ from an imaginary perfect chess engine, and you'd upgrade your computer along with the complexity, instead of starting with more complex positions and having analysis wasted with new analysis.
This may make solving chess sound deceptively easy since we just keep upgrading technology, but infer from the first paragraph that the calculations step up massively each time a piece is added. But with technology that increases so quickly, who knows.