Chess will never be solved, here's why

@6553

"When you start bringing hypothetical or non-existent omnipotent beings"
++ If it hurts your religious feelings, then please read 32-men table base instead of god.

@6556 

"I can’t read through 328 pages of replies." ++ Here is a 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. This follows from fitting a Poisson distribution.

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. This is clear as e.g. the 3 random samples displayed have 3 or more rooks and/or bishops on both sides. Gourion’s 10^37 [10] is a better estimate, but In a sample of 10,000 [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, which we know from ICCF can occur in perfect games: 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 with 19 of the 300 openings: 200 transpositions and 81 pruned [3] and Losing Chess with 10^9 positions. [12]

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.

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

References:

[1] Van den Herik, Games solved: Now and in the future, https://www.sciencedirect.com/science/article/pii/S0004370201001527   

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

[3] Schaeffer, Checkers Is Solved, 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  

Chess is a forced win for white. The first move advantage is enough to force mate, although it will take longer than the 50 move rule allows. 

@6558
Nonsense. Chess is a draw as we know from ICCF. You cannot queen a tempo. The 50 moves rule plays no role as we know from ICCF.

No. The first move advantage is enough to force a win. But, as we know, some forced checkmates are many hundreds of moves long. Longer than what the 50 move rule allows. 

Guilty as charged. But I admit I cheated, I used some long division too. 

Presumably 23,401.5 since you say it's a win for White. (How many toes have you got?)

Re: Ba6?! is a win for black.

Is there a good reference for this? It's hard to search 329 pages.

As to other solved games reaffirming conventional wisdom about said games, sure, that's exactly what you would expect... most of the time.

But surely it is possible to conceive of (or perhaps even construct) a game where this does not hold true. One where a deep enough exhaustive search of a conventionally weak opening will reveal some tactical advantage to that opening that is not otherwise apparent and actually allows for player 1 to win when otherwise the game is a draw from all of the conventionally good openings with perfect play.

So the question is, do we know that chess is not such a game, or do we think that chess is not such a game? I would say we think it's not such a game, but that we do not actually know. As such a game wouldn't necessarily produce evidence that the optimal line was not reachable by gradient descent on some heuristic evaluation but involved very deep tactical play.

Ok but someone in this thread was saying there's a forced line of 52 moves. That bishop odds is a huge advantage is categorically different from saying we have proof that it's a win in however many moves at most.

This is an unfortunate example of ego inverting the correct comparison.

People who have a profound understanding of uncertainty, based on a large amount of experience of simpler examples where the probabilities are not so extreme can see that the nature of the evidence involved and the reasoning available means that we cannot justify CERTAINTY about this result. The epistemiologically correct state of belief is that of slight uncertainty.

The error that the proverbial "man in the street" would surely make is one that is pragmatically fine for all normal purposes. This is to treat all small probabilities as zero. It's perfectly reasonable to (literally) bet your life on something with very low probability not happening. But some of us understand that it is quantitatively enormously wrong (in a way that those familiar how to quantify how wrong a belief is can see).

To illustrate that last point, suppose someone takes the view that an event that happens 1 in a trillion times is literally impossible. This would imply that they would be willing to stake an unlimited amount against any return on this being so. And they would be willing to do this an unlimited number of times. That is what certainty means quantitatively.

Suppose in this case they happen to have the power to bet a trillion dollars on the event for a return of 1 cent when they are proven right. A great bet, to this person.

Unfortunately, there are plenty of examples of events more unlikely than this that happen all the time in the quantum world. It's just a matter of numbers. So this person would lose trillions after trillions by treating a low probability as zero.

I feel a non-lazy person should be able to understand the above.

I will separate the part of my attempt at enlightenment that deals explicitly with the specific chess example for clarity.

The key is to recognise the nature of the evidence for the belief and the reasoning that leads to it.

The nature of the evidence is examples of possible chess play from the position. But not an exhaustive calculation, like that necessary to verify a chess problem. It's the sort of thing Sveshnikov imagined - good old fashioned chess analysis, incomplete but enough for high confidence.   In addition, there is weaker evidence from a large number of not so closely related positions with real play, where a material advantage leads to a win.

All of the reasoning from this evidence to the specific question - does a specific lousy opening position lose? - is INDUCTIVE.  For example, suppose you find a line with what appears to be sensible moves by each player to a finish and one side wins, this is weak evidence the position is winning. It is not actually more certain in itself than a game from 1. d4 winning for black with moves we thought were sensible is to support the view that 1. d4 loses.

Every additional step of inductive reasoning increases confidence in the result. But the distance between probability p> 0 and probability 0 is infinite on a logarithmic scale, and this is related to the fact that inductive reasoning steps never turn uncertainty into certainty. All they can do is reduce the uncertainty by a finite amount.

It's a really good bet that a lousy position that we cannot exhaustively analyse is losing, but it is not IMPOSSIBLE that it is not, just very unlikely (a phrase which incorporates an infinite range of levels of confidence short of certainty.

It's only really the somewhat more intuitively difficult nature of quantifying belief that makes this non-trivial. It's really no more complicated than the idea that you can never get to infinity by a finite number of steps of multiplying finite numbers together. This is true even when the numbers are really very big!

Regarding @Optimissed's reference to engines, they are of no significance to the key point. The recognition that inductive reasoning does not lead to certainty, and the quantification of belief by Bayesian probability (and the proof that this is in a definable sense the only consistent way to quantify belief) predates chess computers. All chess computers can do is exploratory analysis - where this is exhaustive it has analogous significance as an exhaustive analysis by a human (or a proof engine for mathematical theorems), and where it is not exhaustive it has analogous significance to the same by a human, and is merely inductive evidence.

Please don't advertise here.

Forget about the ego bit, which merely obstructs your self-improvement.

Mathematics is what is used to represent quantitative knowledge about the real world. This is the case for all of the models of physics. It is also true for, say, informational theory and computer science, which are comfortably included in the broad subject of mathematics as they deal with abstractions that are perfect for dealing with the underlying nature of many applications. It is also true of the quantification of belief - this just happens to be less familiar to many people.

"it loses. It doesn't probably lose"

There are two senses a position can lose, empirically and analytically.

Empirically, Ba6 loses (or... probably loses? it's the same thing). You could run billions of high level engine games and you probably wouldn't even get one draw. The reason anyone wins or draws with Ba6 is if their opponent makes serious blunders. Mostly at very low ELO.

Analytically, we don't know. Nobody has convincingly solved chess for Ba6. No amount of empirical evidence will show that Ba6 is losing unless it constitutes an exhaustive search. In all likelihood it is losing. But we do not have certainty either way.

Given the title of the thread is about solving chess, the context here is that we are talking about whether a position is an analytical loss, and not an empirical one.

@6559

"The first move advantage is enough to force a win."
++ No, it is not. You cannot queen a tempo.
The first move advantage diminishes with each move made. Engine-wise it starts at +0.33 reflecting the extra tempo and then gradually evaporates to 0.00.
A tempo is not enough to win. A pawn is. A bishop is.
It is curious that some people refuse to accept that a tempo is not enough to win,
and some people refuse to accept that a pawn, or a bishop is enough to win.

"some forced checkmates are many hundreds of moves long"
++ Yes, but those positions where there is such a forced checkmate cannot be reached from the initial position by optimal play from both sides.
In ICCF players are allowed to claim a 7-men table base win that exceeds 50 moves without pawn move or capture. Such claims never occur. No 7-men table base win claims occur at all, all decided games are by resignation after a human error. 22% of draws are by 7-men endgame table base draw claims.
All ICCF games are over long before the 50-moves rule would be triggered, the longest game was a draw in 119 moves. 50-moves draw claims do not occur in ICCF.

@6581

"There are two senses a position can lose, empirically and analytically."
++ We are only concerned about analytically here in this context of game solving.
From the AlphaZero paper we know that 1 g4? is the worst of the 20 possible moves.
Empirically white wins 29%, draws 22% and loses 48%.
The late IM Basman played it with success at IM level.
Analytically 1 g4? loses by force.

Steinitz "knew" he could give God pawn and move and still win.