Chess will never be solved, here's why

ladies' purses?

Summary

Weakly solved means that for the initial position a strategy has been determined
to achieve the game-theoretic value against any opposition. [1]
The game-theoretic value of a game is the outcome when all participants play optimally.[1]

Optimal play is play without errors.
An error (?) is a move that changes a game from drawn to lost, or from won to drawn.[2]
A blunder or double error (??) changes a game from won to lost.

A strategy can be moves like Checkers,[3] or rules like Connect Four,[4] or a combination.
It is beneficial to incorporate knowledge into game solving programs.[1]
Chess knowledge can be acquired from the Laws of Chess only. [5]

The objective of Chess is to checkmate the opponent.[6]
A direct attack on the king can succeed only if the opponent does not play optimally.
Queening a pawn is more feasible to achieve checkmate.
We know from gambits that 3 tempi in the initial position are worth 1 pawn.[7]
1 tempo in the initial position is not enough to win: a pawn can queen, a tempo not.

Millions of human & engine games confirm that Chess is a draw.
In the last 10 ICCF world championship finals: 1469 games = 1177 draws + 292 decisive.[8]
Of the 1177 draws 1140 are perfect games with optimal play from both sides.

Starting from the 10^44 legal positions [9] none of the 56011 legal positions in a sample of 1 million can result from optimal play by both sides. Gourion’s 10^37 [10] is a better estimate, but In a sample of 10000 [11] none can result from optimal play either. That leaves 10^37 / 10000 = 10^33 positions. Multiply by 10 to include positions with 3 or 4 queens: 10^33 * 10 = 10^34.

Weakly solving Chess calls for a strategy, i.e. one strategy only.[1]
On w white moves not w black responses each, but 1 black response only.
w * 1 = Sqrt (w * w) 
Thus Sqrt (10^34) = 10^17 positions relevant to weakly solving Chess.

Checkers has been weakly solved with 10^14 positions [3] and Losing Chess with 10^9 positions.[12] Checkers has been solved with 19 of the 300 openings: 200 transpositions and 81 pruned.

Cloud engines calculate a billion nodes / s.[13] Thus 3 such engines calculate in 5 years:
10^9 nodes / s / engine * 3 engines * 3600 s / h * 24 h / d * 365.25 d / a * 5 a = 4.4 * 10^17 nodes
A diagram is the location of the men on the board.
A position is a diagram + side to move + castling rights + en passant flag.[6]
A node is a position + evaluation + history.[13]

Thus 3 engines exhaust in 5 years all 10^17 relevant positions and weakly solve Chess.
Chess can be weakly solved in 5 years, but needs 3 million $ to hire 3 grandmasters and rent 3 engines.

'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.' - GM Sveshnikov [14]

References:

[1] Van den Herik https://www.sciencedirect.com/science/article/pii/S0004370201001527  

[2] Hübner, Twenty-five Annotated Games, Berlin, 1996, pp. 7–8.

[3] Schaeffer https://www.science.org/doi/10.1126/science.1144079  

[4] Allis http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf  

[5] McGrath et. al. https://arxiv.org/pdf/2111.09259.pdf  

[6] FIDE Laws of Chess https://handbook.fide.com/chapter/E012018  

[7] Capablanca A Primer of Chess https://archive.org/details/aprimerofchess/page/n47/mode/2up  

[8] ICCF WC Finals https://www.iccf.com/tables  

[9] Tromp Ranking of Chess positions https://github.com/tromp/ChessPositionRanking  

[10] Gourion https://arxiv.org/pdf/2112.09386.pdf  

[11] Tromp https://github.com/tromp/ChessPositionRanking/blob/noproms/sortedRnd10kFENs  

[12] Watkins https://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf 

[13] NPS - What are the "Nodes per Second" in Chess Engine Analysis
https://chessify.me/blog/nps-what-are-the-nodes-per-second-in-chess-engine-analysis  

[14] Sveshnikov https://e3e5.com/article.php?id=1467 

(Correct emphasis).

Sveshnikov's is a glib comment, not one arrived at quantitatively.

     Pre-selecting only a limited number of opening possibilities invalidates any claim to have "solved" chess. Certainly, should such an enterprise find a forced win for either side, that would be a valid starting point for a more thorough evaluation of that strategy, following all the lines that limiting the starting point to ICCF draws and looking at the lines that the committee of GMs decided to ignore along the way. Eliminating well over 1/2 the possibilities eliminates any claim to a definitive proof.

Tbh it probably leaves a pragmatic one but pragmatism also accomodates the word "probably".

@6513

"should such an enterprise find a forced win for either side"
++ That is impossible. As explained Chess is a draw.

"Eliminating well over 1/2 the possibilities eliminates any claim to a definitive proof."
++ Eliminating possibilities that are proven worse is allowed.
1 a4 cannot be better than 1 e4 or 1 d4
1 Nh3 cannot be better than 1 Nf3
1 e4 e5 2 Ba6? loses to checkmate in 82 and does not need to be looked into

++ Let us assume I had 20 books for sale:
1) How to draw against 1 d4
2) How to draw against 1 e4
3) How to draw against 1 Nf3
4) How to draw against 1 c4
...

19) How to draw against 1 f3
20) How to win against 1 g4?

Books 1-4 may sell well, but nobody would buy books 17-20.

The same if I were to submit a paper to a scientific journal:
"Chess: 1. d4 black draws" would be accepted,
but "Chess: 1. g4? black wins" would be rejected for lack of relevance

Forgive me for pointing it out but in stalemate, the king isn't captured, Elroch. That's a logical error. In stalemate, the king is confined to one square only but the king is safe.

Chesskingloop is also wrong.

This is complete nonsense. You should answer my points because I focus and you could learn how to. However, you would have to drop your pretension that you're aways right. You're occasionally right in some points only and, often, not in others. The same as most people.

If the rule against playing a move that would permit the king to be captured were removed (essential in order to make capturing the king possible at all), the larger class of statemates would have a legal move which would then allow the capture of the king.

The smaller class of stalemates (I doubt one has ever been seen in competitive play) would still have no legal move.

You mentioned that before but you can't move into check, which is different from someone putting you in check. I'm sure the rules have historical, moral significance.

Some people seem not to like stalemate and they think it shouldn't exist. I think that would make the game less interesting and less complex.

As I said, to consider any variant of chess where the king can be captured, the essential first step is to change the rules so that it is possible to reach a position where the king can be captured. The natural way to do this is to remove the rule that moves doing this are illegal (this rule primarily protecting players against the most heinous of errors, to leave the king in mortal danger).

(Aside: it used to be traditional not only to say "check" to warn a player of a threat to their king, but also "gardez" warning of an attack on the queen. )

     Exactly the kind of pre-judgements that I maintain makes any "solution" reached thereby entirely unconvincing. If the goal in "solving chess" is to discover whether the game can be won by force by either player from the starting position against all possible counterplay, your method is inadequate. Simply declaring that vast numbers of possible lines "are proven worse" without any attempt to prove that is nonsensical.

But to get a variant where the K can be captured, it's only necessary to extend the game by one move so that if a check can't be escaped from, you make another move and your K is captured next move. To get rid of most cases of stalemate, you have to allow the K to move into check. Why, if it removes an interesting dimension from the game. In what way is it desirable?

As a non-mathematical aside, I have always considered checkmate, as it is defined, an elegant way for the game to end. 

It's not. 

But a second way would be to say that making a move is mandatory unless you don't have a legal move. That way the king doesn't have to move into check.

Not altogether on topic. It's been discussed on other threads.

Wow. The first post of this forum has 41 downvotes. Must be nearly a record.

Well I would think that could be because they disagree or because it's been over-discussed. If it's the first reason, I think they're wrong. I can imagine ty might have, because he downvotes things. Never replies to me since I explained why I hold the opinions I hold but downvotes my comments.

Anyway, if this discussion has achieved one thing, it's that it's made me 100% certain that chess will never be solved, ever.