#1526
"SF or another engine can only "guide the search" if its evaluations are perfect, so you are relying on it for perfect evaluations."
++ No, I do not rely on the Stockfish evaluation. I could even do without any evaluation function at all and just use Stockfish to generate moves and positions that result from a given positions and select between the moves at random. It would take more time but it would reach the same result. There are 2 peer reviewed papers where AlphaZero does it at random.
"Otherwise you cannot guarantee an accurate solution, which this us all about."
++ Yes, I can. If the result is a table base draw then all black moves are retroactively validated as optimal. That all white moves are optimal follows from exhaustively exploring all resonable white alternative moves.
"what if 1. e4 ...a5 wins for black?"
++ It goes contrary to experience from centuries and millions of games that A) black would win and B) it would be by 1 e4 a5. If there is such a thing as a strategy in chess then the center, not the wings, develop pieces, make no weaknesses is part of it. 1 e4 a5 goes against every knowledge humans and engines have gathered independently over centuries.
"what if the object of a weak solution is to determine whether white can win against any possible reply by black to 1. e4?"
++ Well it is. White tries to win, black tries to draw. If the ideal game with optimal moves leads to a draw then black succeeds to draw and white fails to win.
"artificially constraning the weak solution to one drawing reply by black isn't sufficient."
++ If 1 e4 e5 draws, then the same method with more time and money could be used to see if 1 e4 c5, 1 e4 e6, 1 e4 c6,... 1 e4 a5, 1 e4 b5, 1 e4 f5 draw as well or not.
"It's exactly equivalent to solving a chess puzzle and claiming that chess is solved."
++ No, it is not. Chess is weakly solved when for every reasonable white move there is at least one black move that leads to a table base draw.
#1487
"knocking 10^44 down to 10^17"
++ Can we please agree that the 10^44 is too high? Tromp exactly counted the number of possible chess positions. Then he randomly sampled 10000 of these. He found 543 of these legal. Thus he arrived at 10^44 legal positions. However all of his 543 randomly sampled positions found legal contain multiple excess underpromotions. Such positions can never occur in a reasonable game with reasonable moves and hence not in an ideal game with optimal moves. I gave a proof game for one of his randomly sampled positions. An ideal game with optimal moves would have an accuracy close to 100% and an average centipawn loss close to 0. The proof game for the randomly sampled position has an accuracy near 0% and an average centipawn loss close to 500. So none of the 543 positions play any role in weakly solving chess and the 10^44 is too high.
"Relying on Stockfish for perfect evaluations to bridge to the actually perfect evaluations of tablebases"
++ No, I do not rely on Stockfish for perfect evaluations. I rely on the 7-men endgame table base for perfect evaluations draw / win / loss. I use Stockfish only to generate the candidate ideal game i.e. to guide the search towards the 7-men endgame table base. The proof that all black moves are optimal comes retroactively from the 7-men endgame table base giving a draw. The proof that all white moves are optimal comes from exhaustively investigating all reasonable white move alternatives.
"Removing all promotions"
++ The Gourion count 10^37 excludes all excess promotions, i.e. all promotions to a piece not yet captured or i.e. all promotions needing to borrow the promoted piece from another box of 32 chess men, not all promotions. I agree that some positions with e.g. 4 queens do occur in reasonable games with reasonable moves and thus can occur in an ideal game with optimal moves. Thus in that respect the Gourion count is too low. Thus the number of legal and sensible positions would lie between 10^44 (Tromp) and 10^37 (Gourion).
"Casting aside dozens of orders of magnitude for "nonsensical" positions (also an assumption) based on sampling a small set set of positions"
++ Tromp randomly sampled 10,000 positions without excess promotions. I presented 4 above. Inspection shows that these positions are not reasonable: cannot be reached by a reasonable game with reasonable moves and thus cannot occur in an ideal game with optimal moves. Tromp conjectured that only 1 in 10^6 legal positions without excess promotions is sensible: can occur in a reasonable game with reasonable moves.
"that limits your reduction to 6 orders of magnitude"
++ That is right: if Tromp's conjecture on 10^6 is right, then the figure of legal and sensible positions would not lie between 10^37 and 10^44, but between 10^31 and 10^38. We do not know if Tromp's conjecture is right. We do not have the number of legal and sensible positions with reasonable excess promotions. It should lie between 10^31 and 10^38, I assume 10^36 to stay at the safe side.
"Assuming Sveshnikov knew anything about solving chess vs. just analyzing openings when there's no demonstration that his statement is anything more than an offhand boast at a dinner party."
++ Sveshnikov knew something about chess. Unlike all here he was a grandmaster. Even if he had not become a grandmaster in 1977, he would have become a grandmaster in 2017 by becoming 65+ Senior World Champion. Sveshnikov was ridiculed for his statements that the Sveshnikov Variation (oh no, the hole at d5), the French Advance (oh no, white loses a tempo), the Alapin Variation (oh no, white gets an isolated queen's pawn) were correct. He was vindicated by Carlsen playing the Sveshnikov at his World Championship Match with Caruana. Maybe it was an offhand boast at a dinner party. Maybe it was a profound prophesy based on years of chess analysis without and with engines.
Sveshnikov claimed he could in 5 years with modern computers and good assistants analyse from the opening to the 7-men endgame table base. So his claim is about analysing openings. That is what he did for a job. Unlike all here he was a recognised world top expert at analysing openings.
"If Tygxc had the money and achieved his 5 year analysis goal, he would be able to produce an engine that plays exceptionally well, perhaps...but it would not be a solution for chess at all."
++ No, I would not produce any engine, I would use an engine that exists to analyse from the opening to the 7-men endgame table base. It would be a weak solution for chess as it would produce an ideal game with proof that all moves are optimal.
"You can weakly solve chess with brute force even without any further pruning" ++ I agree.
"just not within our lifetimes by any foreseeable technology."
++ I respectfully disagree. It depends on the speed of the engine and on the number of positions needing to visit.
Cloud engines have reached 10^9 nodes / second, that is 1000 times faster than a desktop.
The number of legal and sensible positions lies as said above between 10^31 and 10^38 I assume 10^36. That would be the number of positions needed to visit for strongly solving chess i.e. a 32-men table base. The time and the storage are prohibitive.
Weakly solving chess requires to visit less positions than strongly solving chess. Each pawn move and each capture make huge numbers of positions unreachable and thus irrelevant. How many positions are relevant? We do not know until it is done. We may have a better estimate after one opening say C67 is analysed, that would take about 3 months of cloud engine time.
Checkers was solved using the square root of the number of legal and sensible positions. Checkers is no chess, but is a draw as well as chess is conjectured to be.
Losing Chess was solved using the 4th root of the number of legal and sensible positions. Losing Chess is no chess, but it is close in its rules.
It is thus plausible to assume that for chess it is about the square root too. That leaves 10^18 relevant positions i.e. 10^9 seconds for the whole of chess i.e. all 500 ECO codes.
To weakly solve chess it is not necessary to look at all ECO codes.
If 1 e4 e5 draws, then it is not necessary to establish if 1 e4 c5 draws as well or not.
Instead of 200 ECO codes B00 to C99 only 19 of these are enough.
That is another reduction by a factor 10 i.e. 10^17 positions or 10^8 seconds for the relevant ECO codes.
Concentrating on multiple, excess underpromotions is a flea-bite in the percentage of riduculous positions that are legal. Possibly only approximately zero positions out of every 10,000 are both legal and non-ridiculous, meaning that they are legal and relevant; not containing random moves and gross blunders. Approx. zero out of 10,000 still would lead to a very high number of relevant positions overall. So the first part of your argument is correct.
However, you do fall into error very soon. <<<++ No, I do not rely on Stockfish for perfect evaluations. I rely on the 7-men endgame table base for perfect evaluations draw / win / loss. I use Stockfish only to generate the candidate ideal game i.e. to guide the search towards the 7-men endgame table base.>>>
SF or another engine can only "guide the search" if its evaluations are perfect, so you are relying on it for perfect evaluations. There's no escape from that. There's no argument you can effectively make, to the contary, since an algorithm is the only thing between a guided solution and a so-called strong solution. A strong solution is meaningless in competitive chess terms and so each game has to be assessed and SF is not up to the task. There's no question about that. It is not debateable and you should accept it. Otherwise you cannot guarantee an accurate solution, which this is all about.
I wish some of the others were capable of arguing coherently and decisively and yet any argument is only as good as the readers' perceptions of it. No-one can be forced into understanding, if indeed they are capable.
<<To weakly solve chess it is not necessary to look at all ECO codes. If 1 e4 e5 draws, then it is not necessary to establish if 1 e4 c5 draws as well or not.>>
Yes, that's obviously correct if the only form of the idea of a "weak solution" is to determine if black can actually draw. But as Elroch correctly asked, what if 1. e4 ...a5 wins for black? I think the idea is ridiculous ,so do you and so does Elroch but he is correct to enquire. What if it does? Or, differently, what if the object of a weak solution is to determine whether white can win against any possible reply by black to 1. e4? That doesn't mean "against all black replies". It means "against any single one of them or more". Then, all black first moves become relevant. The point is that artificially constraining the "weak" solution to one drawing reply by black isn't sufficient. It's exactly equivalent to solving a chess puzzle and claiming that chess is solved.
Isn't it?