Chess will never be solved, here's why

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.

@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

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.

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.

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.

@6531

"chess can be solved" ++ Yes

"it will take a very long time and dedication" ++ 5 years

"it would be far too difficult for a human to ever memorize all the right moves"
++ A human can memorize 10,000 perfect games with optimal play from both sides.
The solution might also be condensed into a set of rules that are easier to remember.

@6525

"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"

++ No. The goal of ultra-weakly solving chess is to determine the game-theoretic value of Chess i.e. the outcome if both players play optimally. For all practical purpose Chess is already ultra-weakly solved and we know the game-theoretic value is a draw.

The goal of weakly solving Chess is to determine how black can draw.

"vast numbers of possible lines are proven worse"
++ It is proven that 1 e4 e5 2 Ba6? is worse than 2 Nf3.
It is proven that 1 a4 is no better than 1 e4 or 1 d4.
It is proven that 1 Nh3 is no better than 1 Nf3.
Here is a paper that proves it with no other input but the Laws of Chess:
https://arxiv.org/pdf/2111.09259.pdf 

@6516

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

Sveshnikov probably arrived at it quantitatively. He held a MSc and almost a PhD in engineering.
I have arrived at it quantitatively. I try to explain in a different way.

Let us assume we calculate all w legal white moves, all w legal black responses and so on all the way up to checkmate or a draw. Then we calculate all 10^44 legal positions and we strongly solve chess to a 32-men table base. That would take 10^27 years.

Let us now restrict ourselves to weakly solving chess: finding a strategy i.e. one strategy for black to draw: against all possible w white moves 1 black response that draws. w*1 = Sqrt (w*w). Thus that would need to calculate Sqrt (10^44) = 10^22 positions and take 300,000 years.

Now observe that the vast majority of the 10^44 legal positions contain multiple underpromotions to pieces not previously captured. Underpromoting instead of queening is like blundering a piece. Let us first restrict all promotions to pieces already previously captured. There are 10^37 such positions.
Now note that positions with 3 or 4 queens do occur in perfect games with optimal play from both sides. So multiply by 10 to include such positions with 3 or 4 queens. 10 * 10^37 = 10^38.
Now the same reasoning as above: Sqrt (10^38) = 10^19. That would take 316 years.

Now note that black tries to achieve the draw. So white tries to oppose to the draw.
Moves that lose for white like 1 e4 e5 2 Ba6? do not even try to oppose to the draw.
Thus such moves can be pruned away. That has to be done judiciously, hence grandmasters are needed. Some losses of a piece might be sacrifices. Grandmasters must decide if there is any compensation of any kind. If yes, then calculate. If no, then prune.
Likewise some endgames e.g. with opposite colored bishops are known draws. The computer can calculate a long time until a 3-fold repetition, while the humans see it is not possible to win in any way. Also here some opposite colored bishop endgames can be won. Here the grandmasters judge. If there is any chance to win, then calculate. If there is no chance to win, then adjudicate a draw so as to save calculation time.
So this human incorporation of knowledge reduces another 2 orders of magnitude to 10^17 relevant positions, solvable in 5 years.

I only see 24. Not that it matters, but if I'm right and you're wrong..... THAT would definitely be a record....or at least a first.

  I am sure we are both right about our observations. That is a very odd discrepancy.

Upon reflection, I was looking at reactions rather than downvotes, so I think you were being quite gentlemanly not to point that out. 

I'm sure it would do better if it weren't borderline unintelligible.

Imagine a paradigm of 100 Kasparovs, solving two Ruy Lopezes each, blah blah blah, chess will never be solved QED.