I am sure we all feel there is far too little consideration of the relevance of the lack of unique simultaneity in relativistic space-time to the interpretation of the rules of chess.
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Chess will never be solved, here's why
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Mar 13, 2022
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#2163
@btickler I never talked about time. It was all about the unnecessity of talking about something that much, which is not useful or anything. Too much information is wasted between pages. And why don't you make something useful if you all have that much information on the topic. I said. You are just twisting my words. Like almost anyone who disagrees.
Mar 13, 2022
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#2164
tygxc wrote:
#2152
About your objectivity and honesty, then, maybe you want to comment this excerpt from the very paper on checkers you cited so much:
"With checkers done, the obvious question is whether chess is solvable. Checkers has roughly the square root of the number of positions in chess (somewhere in the 10⁴⁰ - 10⁵⁰ range). Given the effort required to solve checkers, chess will remain unsolved for a long time, barring the invention of new technology."
That was in 2007. The 10^40 - 10^50 range is no longer valid.
Schaeffer was talking about positions in the absence of the 50 move and triple repetition rules. The removal of these from FIDE's basic rules in 2017 serves only to make the figures correct for the basic game.
Nothing has happened in the meantime to invalidate that range as far as the basic rules game is concerned. Chess has not shrunk.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.
The figure 3 x 10^37 is for diagrams without excess promotions, and is not in any way relevant. It changes neither Schaeffer's range nor Tromp's estimate (circa 4 x 10^44), which also relates to the basic rules game.
The number of positions in your proposed game of basic rules + two and a Schrödinger's half fold repetition rule would be vastly greater, because then positions must be defined effectively by a pgn from a ply 0 position - different positions for different pgns leading to the same fen.
In those 15 years also computers have become faster and chess engines better, now 10^9 nodes/s.
Also progress has been made on the 7-men endgame table bases.
Most of the effort of Schaeffer was related to building his endgame table base.
Schaeffer himself also said:
”The one thing I’ve learned in all of this is to never underestimate the advances in technology”
https://webdocs.cs.ualberta.ca/~jonathan/publications/ai_publications/checksolved.pdf
final line
Interesting to note from the paper you quote that checkers has not in fact been weakly solved, nor even fully ultra weakly solved.
Mar 13, 2022
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#2165
I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.
Mar 13, 2022
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#2166
@MARattigan
Quote from your post:
"Strictly speaking you can't lose on the clock under FIDE laws."
That doesn't sound right to me At All.
You play in a FIDE rated tournament.
You make 'perfect' moves - or maybe you don't.
Your opponent calls 'Flag' in a loud clear voice.
Because you've 'overstepped' on time. On the clock.
You're Done. Lost. Defeated. Fried. Clobbered. Eliminated.
Flattened. Deprived. Sent packing. Dismissed. Eclipsed. Diminished.
Fricasseed. Broiled. Squashed. Eviscerated. Dissected. Vivisected.
Same result as Checkmate.
1c4Boom1-0 wrote:
@btickler I never talked about time. It was all about the unnecessity of talking about something that much, which is not useful or anything. Too much information is wasted between pages. And why don't you make something useful if you all have that much information on the topic. I said. You are just twisting my words. Like almost anyone who disagrees.
Ermm...you cannot really talk about the uselessness of anything unless you first consider it a waste of time. There's nothing useful to be done on actually solving chess at this time...the only useful outcome of this thread is to dispel that very notion.
Telling people to make better use of their time implies that you know better what somebody wants/needs from their life than they do. We already have enough posters that think their words are correct, but always twisted by everybody else that reads them, thanks anyway ...
Mar 13, 2022
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#2168
playerafar wrote:
By the way - consider Black's play in this game ...
and it doesn't even take fifteen seconds to consider it ...
g4 e5 f3 Qh4# checkmate.
Something 'imperfect' about black's play there?
Well, both Leela and Stockfish prefer 1. ... d5 there.
I just accidentally left Leela analysing 1. g4 for a couple of hours on a GPU and its evaluation was 69% for 1. ...d5 and only 59.5% for 1. ...e5, a surprisingly large difference.
Mar 13, 2022
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#2169
@Elroch
Interesting about that d5 preference there.
But that might be because d5 is simply a better move anyway.
Like d4 is arguably the best first move for white.
Solider than e4 for multiple reasons.
Mar 13, 2022
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#2170
@MARattigan
Quote from your post:
"Strictly speaking you can't lose on the clock under FIDE laws."
Maybe that's Martin just teasing player ?? 
See post #2191
#2210
"Chess has not shrunk."
++ Chess has not shrunk, but it is smaller than Schaeffer believed in 2007.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.
"It changes neither Schaeffer's range nor Tromp's estimate (circa 4 x 10^44)."
++ Tromp's estimate 10^44 has no relevance to solving chess, as none of his 538 randomly sampled positions found legal can result from the initial position by a game with more than 50% accuracy. All of his 538 positions found legal contain multiple underpromotions to pieces not previously captured.
"The figure 3 x 10^37 is for diagrams without excess promotions"
++ That makes it very relevant. Diagrams = positions, as for any diagram with white to move there is a position with black to move by up/down symmetry. Promotions to pieces not previously captured do happen in less than 1% of games, and mostly to queens, not underpromotions. Underpromotions may happen in less than 0.1% of games.
If you want you can multiply 10^37 by 10 to include positions with 3 or 4 queens.
That leaves 10^38.
Even this number is much too large, as a random sample of 10,000 positions without promotions to pieces not previously captured shows the positions cannot result from the initial position by a game with more than 50% accuracy. Tromp conjectured than only 1 in 10^6 might be sensible. That would leave 10^32 sensible positions including those with 3 or 4 queens.
So the range is rather 10^32 - 10^38 according to knowledge of 2021.
"The number of positions in your proposed game of basic rules + two and a Schrödinger's half fold repetition rule would be vastly greater, because then positions must be defined effectively by a pgn from a ply 0 position - different positions for different pgns leading to the same fen."
++ This is nonsense. The 50-moves rule is never invoked in practice before the 7-men endgame table base is reached. I challenged you to provide one single grandmaster or ICCF game under any rules where the 50-moves rule was or could be invoked in a position with 8 men or more. I bet no such game exists at all.
Mar 14, 2022
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#2172
Elroch wrote:
I think you mean that the paper says checkers has not been strongly solved. Strategies for optimal play from the opening position are complete. This only meant about 10^14 calculations (so certainly not the full 10^20 positions). The 10 piece endgame tablebase for the solution has 39 trillion positions, which is between 10^13 and 10^14 positions.
I was referring to the comments:
(a)
The fact that the game wasn’t solved for every possible position and then tucked away in a database doesn’t seem to bother him. ”Well, the checkers players would love it, because [then] you’ve got this oracle that can tell them everything—answer every single unanswered question in the game of checkers,” he says. ”But first of all, I don’t have the patience to do it. And second of all, I don’t have the technology to do it.” Even with the best data-compression techniques, Schaeffer says, the amount of storage required to solve all possible positions of checkers would exceed even the capacity of the world’s biggest supercomputers with tens of petabytes (1015) of storage by an order of magnitude. That puts it—at the earliest—at least a decade away.
and
(b)
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
or from https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
The checkers proof consisted of solving 19 three-move openings, leading to a determination of the starting position’s value: a draw. Although there are roughly 300 three-move openings, over 100 are duplicates (move transpositions). The rest can be proven [not have been proven] to be irrelevant by an Alpha Beta search.
(a) apparently means there is no algorithm provided that tells each player what moves to make from the opening, only that the moves have been checked by computer and shown to be a draw - so on the face of it an ultra weak solution. (OK it's actually talking about a strong solution database there - but is there a weak solution database?)
except
(b) suggests the ultra weak solution is at most 19/200ths. complete. (Transpositions removing 100 of the original 300 obviously valid.) For a solution of any kind all possible openings must be dealt with.
(When I try to see details of the proof using the https://webdocs.cs.ualberta.ca/~chinook/solution/ link given in the link above, the checkers solution times out.)
#2218
"Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws.
There are 300 total tournament openings"
That is what I say about chess all the time.
Of the 500 ECO codes A00 to E99 only 50 are necessary to weakly solve chess.
If 1 e4 e5 is proven a draw, then it is not necessary to determine if 1 e4 c5 draws as well or not.
If 1 e4 and 1 d4 are proven draws, then it is not necessary to verify that 1 a4 draws as well.
If 1 e4 e5 2 Nf3 is proven a draw, then it is not necessary to look at 1 e4 e5 2 Ba6.
Mar 14, 2022
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#2174
tygxc wrote:
#2218
"Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings"
That is what I say about chess all the time.
Of the 500 ECO codes A00 to E99 only 50 are necessary to weakly solve chess.
If 1 e4 e5 is proven a draw, then it is not necessary to determine if 1 e4 c5 draws as well or not.
If 1 e4 and 1 d4 are proven draws, then it is not necessary to verify that 1 a4 draws as well.
If 1 e4 e5 2 Nf3 is proven a draw, then it is not necessary to look at 1 e4 e5 2 Ba6.
Understood. But you're obviously wrong.
@Marattigan
To weakly solve a game it is enough to provide an optimal strategy in a reasonable time, so to save storage space, you can leave out some lines and provide them on demand, but you have to know, after tests, that they can be provided on demand.
MARattigan wrote:
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
For chess, If one sits at the board against SF and has weakly solved the game, s/he will make some moves using the proof tree, some others can be calculated by an engine, but it must hit an endgame tablebase or an already solved position in reasonable time. Instead, if s/he uses an engine just to evaluate the position as usual, they will likely draw against an equally strong silicon opponent, but the moves would be just the result of evaluations/guesses: if they use the same engine 10 years later against a much stronger opponent, they would lose most of the games. If chess was indeed weakly solved, on the other hand, they would replicate the same outcome with the very same silicon ally even 1000 years later.
haiaku wrote:
@Marattigan
To weakly solve a game it is enough to provide an optimal strategy in a reasonable time, so to save storage space, you can leave out some lines and provide them on demand, but you have to know, after tests, that they can be provided on demand.
MARattigan wrote:
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
For chess, If one sits at the board against SF and has weakly solved the game, s/he will make some moves using the proof tree, some others can be calculated by an engine, but it must hit an endgame tablebase or an already solved position in reasonable time. Instead, if s/he uses an engine just to evaluate the position as usual, they will likely draw against an equally strong silicon opponent, but the moves would be just the result of evaluations/guesses: if they use the same engine 10 years later against a much stronger opponent, they would lose most of the games. If chess was indeed weakly solved, on the other hand, they would replicate the same outcome with the very same silicon ally even 1000 years later.
No that isn't so because the entire thing is too wishy-washy and unproven. "Optimal strategy" can obviously alter because it's inferential, based on ideas we have at present. The whole idea of a weak solution which may be relied upon absolutely is nonsense.
Mar 14, 2022
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#2177
tygxc wrote:
#2210
"Chess has not shrunk."
++ Chess has not shrunk, but it is smaller than Schaeffer believed in 2007.
No it's not. Tromp's figure is in Schaeffer's range.
The papers by Tromp (10^44) and Gourion (10^37) are from 2021.
Whether a paper is valid doesn't depend on the publication date. Both papers are valid - your use of the second is not.
"It changes neither Schaeffer's range nor Tromp's estimate (circa 4 x 10^44)."
++ Tromp's estimate 10^44 has no relevance to solving chess, as none of his 538 randomly sampled positions found legal can result from the initial position by a game with more than 50% accuracy. All of his 538 positions found legal contain multiple underpromotions to pieces not previously captured.
Firstly you're not proposing to solve chess. As far as I am aware no game referred to as "chess" that excludes the 50 move rule but includes either a 2-fold or 3-fold repetition rule has ever been prevalent.
Secondly, if whatever you propose to solve turns out to be a draw, then, using your method will need to consider all Black responses and also show that its a draw for all alternative White moves at any stage. This will result in a majority of games that look rather different from those you see at your local chess club.
You're good at issuing challenges. I challenge you to prove (or even convincingly demonstrate) just a single one of Tromp's 538 positions cannot result from the initial position by a game with more than 50% accuracy.
But if you could, that wouldn't say anything about the positions you would encounter in your computation.
"The figure 3 x 10^37 is for diagrams without excess promotions"
++ That makes it very relevant. Diagrams = positions, as for any diagram with white to move there is a position with black to move by up/down symmetry.
Diagrams ≠ positions
These are the same diagrams
But in the competition rules game they're not the same position. The first position is winning for White, the second position is a draw.
You can't have the same position with different theoretical results.
In either a variant of competition rules chess that excludes the 50 move rule or a variant of competition rules chess that excludes the 3-fold repetition rule, the second position would also be winning for White. That wouldn't make the positions the same in the former case because the possible forward play in each would be different.
(In your basic rules + 2-fold repetition game both positions are illegal because the game has already terminated; in your basic rules + 3-fold repetition game the second position is a win.)
You seem to have extraordinary difficulty in grasping that the same diagram can belong to different positions in different games or the same games.
Promotions to pieces not previously captured do happen in less than 1% of games, and mostly to queens, not underpromotions. Underpromotions may happen in less than 0.1% of games.
You should be interested in the positions your proposed procedure needs to consider to complete, not what happens at your local chess club.
If you want you can multiply 10^37 by 10 to include positions with 3 or 4 queens.
That leaves 10^38.
I don't want.
If it were I investigating the feasibility of your approach, I would start off with Tromp's relevant estimate of positions under basic rules and then multiply by different factors depending on the game to be solved.
The necessary factors are complicated to work out when an n-fold repetition rule is included in the game. That is because a position specification is then a pgn as opposed to a fen.
The tablebase generation procedures neatly bypass the n-fold repetition problem by never producing positions with the same diagram and side to move with different distances to their respective objectives.
Your procedure doesn't detail how it is proposed to get around the problem. SF14 (your proposed vehicle) happily repeats positions up to twice whether it thinks it's winning or not. With your new two and a Schrödinger's half-fold repetition rule half of the SF14 vs. SF14 games here would be drawn under the 2-fold repetition rule when observed.
An upper bound on the number of positions in you search space would be
2.9 x 10^44 x (n^(2.9 x 10^44)) where n is either 2 or 3 depending on when it is observed. The upper bound is obviously far too high and could easily be reduced - I leave it to you to reduce it.
Even this number is much too large, as a random sample of 10,000 positions without promotions to pieces not previously captured shows the positions cannot result from the initial position by a game with more than 50% accuracy.
As I pointed out that's irrelevant - but I await the result of my challenge with interest.
Tromp conjectured than only 1 in 10^6 might be sensible.
Of his basic rules positions. That has no relevance to a solution along your proposed lines of even a solution to the basic rules game.
That would leave 10^32 sensible positions including those with 3 or 4 queens.
Actually 4 x 10^44 / 10^6 is 4 x 10^38 - I should check your calculator installation.
So the range is rather 10^32 - 10^38 according to knowledge of 2021.
Or not as the case may be.
"The number of positions in your proposed game of basic rules + two and a Schrödinger's half fold repetition rule would be vastly greater, because then positions must be defined effectively by a pgn from a ply 0 position - different positions for different pgns leading to the same fen."
++ This is nonsense. The 50-moves rule is never invoked in practice before the 7-men endgame table base is reached. I challenged you to provide one single grandmaster or ICCF game under any rules where the 50-moves rule was or could be invoked in a position with 8 men or more. I bet no such game exists at all.
I didn't mention the 50 move rule. The relevance of the ply count 0 position is that no positions as defined for the purposes of art. 9.2.1 that occurred previously can occur subsequently.
(Again, what happens at your chess club, whether or not they're playing the same game as you're trying to solve, is of no relevance.)
Mar 14, 2022
0
#2178
haiaku wrote:
@Marattigan
To weakly solve a game it is enough to provide an optimal strategy in a reasonable time, so to save storage space, you can leave out some lines and provide them on demand, but you have to know, after tests, that they can be provided on demand.
MARattigan wrote:
Schaeffer’s proof solved checkers for 19 different openings, all of which end in draws. There are 300 total tournament openings, but many of these were determined to either be mirrors of other positions or altogether irrelevant to the proof because they lead to positions common to other openings.
For chess, If one sits at the board against SF and has weakly solved the game, s/he will make some moves using the proof tree, some others can be calculated by an engine, but it must hit an endgame tablebase or an already solved position in reasonable time. Instead, if s/he uses an engine just to evaluate the position as usual, they will likely draw against an equally strong silicon opponent, but the moves would be just the result of evaluations/guesses: if they use the same engine 10 years later against a much stronger opponent, they would lose most of the games. If chess was indeed weakly solved, on the other hand, they would replicate the same outcome with the very same silicon ally even 1000 years later.
You need only provide one opening line (half tree) if you weakly solve a game as a win. You have to provide a full half tree for each side if you weakly solve it as a draw.
That was apparently not done.
Of 300 openings only 19 were shown to draw. A further 100 validly excluded as transposition of moves, but the remaining 181 dismissed by the assertion that it would be possible to prove them drawn by alpha-beta pruning (without details of how that could lead to a proof) but without actually performing the computations.
I may be reading it wrong, but it is at least difficult to find either further details or an available database of the results computed. No database - no weak solution. Most of the lines still to be computed - no ultra weak solution either.
Btw. you have a touching faith in the reliability of computer results obtained over decades on different machines involving large amounts of data.
Mar 14, 2022
0
#2179
A little intuition on how ridiculous positions may not be so ridiculous. Throw some reachable set of material on the board (<=32 pieces, with enough pieces and pawns missing to make the number of excess pieces possible by promotion) on the board until you get a position that is legal (a large proportion) and you will get a position where Stockfish will provide some material balance between say -200 and 200.
It is to be expected that the distribution of the evaluation is not thinner than average near the middle, so at least 0.5% of these positions will be in the range -1 to 1 evaluation and for it to be entirely plausible the positions are a draw to an oracle (some won't but these will be made up for by others that appear to have larger evaluations that are in truth more difficult draws).
That means a quite large fraction of random positions are perfectly reasonable ones for optimal play to go to (if chess is a draw), and this is true for all chains through such positions, which can certainly start from a normal position such as the initial position.
Taking one such random position with an unusually large number of knights for example, you can work backwards from that position to reach an exponentially growing number of other positions by optimal play. It may be only when you reach say 10^9 such positions that one of them involves the possibility of an underpromotion to a knight (this is excessively pessimistic - underpromotions comprise at least 1 in a 100,000 perceived best moves in high level chess games).
You can repeat this process for multiple promotions to find that it is indeed perfectly reasonable for optimal play to reach positions with large numbers of underpromotions.
Note that each step of this process - working back from a position with odd material balance to an underpromotion - traverses a tiny fraction of the set of legal positions, say N positions (I generously allocated N=10^9 but was well aware a lot fewer would probably be needed on average), so a position with M underpromotions can reasonably find a path back to a position with no underpromotions by retrogade analysis looking at N * M positions, a very tiny fraction of the whole.
An intuitive error would be to think this number would be N^M, which would become very large for large M.
Optimissed wrote:
"Optimal strategy" can obviously alter because it's inferential, based on ideas we have at present. The whole idea of a weak solution which may be relied upon absolutely is nonsense.
For the purpose of weakly solving chess, "strategy" is not what we commonly think, that is a set of rule of thumbs, ideas, principles we use during the game to deal with the complexity of chess with our brains; it means a proof tree: for any opponent's move from the beginning, you can prove there is a move that will lead to the game-theoretic value of the game. Leaving out, for simplicity now, the matter of the 50-moves rule or three-fold repetition, you can see the previous posts here and here.
so reading a novel and writing & reading forum posts about something are the same. good. people can talk about chess being solvable or unsolvable but this level.. is beyong the necessity. if you know too much this topic why dont you write a program, make a product instead of this. besides no one will read all of this.. thousands of pages will be lost here even if they had useful information. write a book, form a product.. so people can use. whats this?
Always gotta be someone to complain about wasted time with their own wasted time
. Shoo. Go live your life and don't worry about other people's time spent.