Chess will never be solved, here's why

@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.

@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.

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.

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.

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.

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.

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.

Working backwards from odd-but-balanced random positions (which on each step includes exponentially more) until you reach a "normal" position is a nice... what to call it... thought experiment I guess.

Yes, the strategies involved are quickly calculable, deterministic, and comprehensive.

Note I edited the start to better explain the range of material balance that is being dealt with - everything that is legally possible.

Note also that the intuitive idea is that typically there will be multiple predecessor positions with optimal play. There will be some positions with no predecessor, but it seems likely that these will not greatly reduce the log of the number of positions reachable by optimal play.

I guess we have to trust them they actually performed the computations . They would make a fool of themselves if they were demanded to provide the optimal strategy in reasonable time and the game didn't end in a draw.

He! that's a crucial point Schaeffer himself addressed. The solution of the four colour theorem aroused a similar controversy, you know.

Define exactly "full" and "semi-strong" solution and "performing" a solution. In this case it's better not to identify the process to obtain the solution with the solution itself (the result of the process), imo.

Yes. Optimissed seems not be clear that "weak solution" is an established label for a precisely defined entity. Referring to a "very weak solution" as he does is unhelpful, as this is an undefined term.

Likewise, no-one (probably including him) knows what he means by "semi-strong solution", since it has not been defined.

The "authorities" (researchers with peer-reviewed research) can be very safely assumed to understand such issues better.

In addition, the 50 move rule cannot be ignored. A basic rules tables is different to a tablebase for chess with a 50-move rule - obviously when some positions are drawn in one that would be won in the other, this changes things. The basic rules tablebase has a strict superset of winning positions. The Syzygy tablebase is the first 7 piece tablebase with DTZ - indicating the number of moves before an irreversible move that is not a blunder - this guides a defender to play a path that achieves a 50-move draw by, for example, choosing maximal DTZ move (like an attacker in a winning position avoids interminable wandering by picking a minimum DTM (distance to mate) move.

#2212
"the 50 move rule cannot be ignored"
The 50 moves rule can be ignored for all positions with 8 men or more.
It never gets invoked in grandmaster or ICCF games before the table base is reached.
It is just a practical rule to ensure that games and tournaments finish in a reasonable time,
even if some player does not know her 5 basic checkmates.
Whoever disagrees, please do present one grandmaster or ICCF game where the 50 moves rule was or could be invoked before the 7-men endgame table base was reached.

The 50 move rule can be addressed as a side issue.
Something like the clocks in chess and somebody's flag is down and do they have mating material.
So in addressing a position - a supercomputer can assign findings:

1)  Forced draw available to one player because there is forced free-of-checkmate play available to compell a 50 move draw.
2)  Such forced play available to Either player.

3) Comments as to whether a player could decline that option of such forced play and play/risk for the win instead.
4) Comments as to whether there's a win available to one player in over 50 moves.  
5) Comments as to whether 'greater than 50' was not addressed in the position because it was quickly found to exceed default computer time allotments -
and therefore referred to another Tablebase computer and Project ! 

To make any comprehensive attempt to define solving -
it seems logical to set out the categories of possible results and findings.

Tempting:  either a position has a checkmate available by force in a known or upper-bounded number of moves - or it does not.

Digital A or B again.  Usually a mistake in so many many situations.