Chess will never be solved, here's why

I found it.

You should be aware that you are engaged in a semantic disagreement. You are using the word "blunder" for an imprecise notion relating to practical chess while, in the post replied to, the word "blunder" was used for the precise theoretical concept of a move that changes the final result with optimal play thereafter.

On a very general (and very important) point, it is remarkable how often people are not fully aware whether they are debating about the truth of an objective fact or having a disagreement about the use of a label (such as "blunder" here). I am not asserting that you are not in this case.

No personal interpretation involved. I have explained how the valid forms of reasoning available do not justify certainty. Some here understand this, but not all. It is a philosophically important difference but, for the man in the street, inappropriate certainty is generally pragmatically fine.

I think @Optimissed might be right this time.

Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.

What part of game theory would apply?

Still thinking about 213276247234766621; don't tell me. It's not prime nor (I think) a recognisable Carmichael number, but it has fewer factors than you'd expect. 

I think, rather, he will assume you're still learning (at age 71) but don't yet know what you're talking about.

While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.

No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe  - the only laws involved are those that govern legal moving and results.

If I recall, the only appeal to game theory that has taken place in this forum was to a general theorem that applies to a class of games to which chess belongs. Given the definitions:

1. A (pure) strategy for a side is defined as a procedure that generates a move for any legal position (note that a mixed strategy is one where it may vary the chosen move in a position, but we don't need these).
2. The value of a strategy is the minimum of the values it achieves against all opposing strategies
3. An optimal strategy for a side is a strategy that achieves the maximum of the values of all strategies for a side

then there exists an optimal strategy for each side and these strategies achieve the same result.

I'd like this theorem to be trivial, but when trying to show it was, I convinced myself it is not quite! The theorem seems to rely on the fact that every game is finite, for example.

Game theory does not deal with probabilistic outcomes in games like chess (deterministic, perfect information).

Tablebase results are discrete.

Perfect play can be clearly defined in a tablebase.

This is true for a (hypothetical) 32-piece tablebase.

(The only place probabilities have arisen here is as states of belief for unresolved propositions).

Yes and no. What are the abstract rules? The complexity of solving one set of abstract rules may be very different from another, so it seems to me that question needs to be addressed before commenting on OP's question.

It could be that an abstract game based on basic rules will eventually be solved by human ingenuity while an abstract game based on  competition rules proves too difficult.

And if you plan to use a GUI/Stockfish combination in solving, you do have an arbiter; it's the GUI. You also have a concrete set of rules.

And now I will enjoy my run...

@5344
"a relatively simple version of chess which has a 50 move rule and no 3-fold repetition rule"
++ This is all besides the question.

The 3-fold repetition rule is vital. Chess might even be a win for white if repetition were forbidden like in Stratego or Go. The repetition rule is a major drawing mechanism and occurs in 16% of perfect games in ICCF WC draws.

The 50-moves rule plays no role. It is never invoked in perfect games in ICCF WC draws.
The same solution of chess without 50-moves rule also applies to chess with 50-moves rule.
If chess is solved with 50-moves rule, then that solution does not need the 50-moves rule, so that same solution also applies to chess without 50-moves rule.

Ermm, no.  First, you can't use Stockfish in solving anyway, because it is incapable of evaluating perfect play.  Second, a GUI, that is, the user interface, would certainly not be an arbiter of any kind .

The rules of competition/tournament chess are an adjunct set of rules added on to handle pairings, avoid days or weeks long games, etc.  Solving chess is solving the basic game and its ruleset.  If you want to solve it by retrograde analysis (tablebase), then the 50 move rule or 3-fold repetition is not required.  If you want to solve it going forwards, you have to handle repetitions/circular positions, and need some criteria for moving on with analysis, ergo the 3-fold repetition rule is as good as any, but the mechanism is also not required to follow any particular rule which is external to chess.  

I wouldn't consider chess fully solved if the 50 move rule is applied, and given the processing power already required, I don't see that throwing it in the mix gives much benefit.  The choice of 50 moves is not scientific, it is arbitrarily chosen to give a human impression of exhaustion of possibilities.  In a situation where the 50 move rule could come into play for solving, you probably have one piece that either needs to reach a particular square, or a piece that needs to be forced to a particular square, so right there a 32 or 64 move rule already fits better .

My point is that "chess" generally refers to one of the games defined in the FIDE laws. Because they allow for resignation and agreed draws which occur asynchronoulsy with the moves and the results are are not prioritised in terms of win draw or loss either between themselves or with the results of completed moves, the possible results have no defined order. Is (win,win) for White better or worse than (win,draw) or (win,loss)?

You say:

"1. A (pure) strategy for a side is defined as a procedure that generates a move for any legal position ..."

Where do claims come in? Those are part of chess. A good strategy should generate a draw claim under the 50 move rule at some point if the opponent has a frustrated win. (It should also accept a draw offer in a losing position, but that would be extending the meaning of "solution".)

2. The value of a strategy is the minimum of the values it achieves against all opposing strategies.

There can only be a minimum if the results are ordered. They're not under FIDE rules.

Ergo game theory doesn't apply to chess. It could as you say be applied to abstract version of "chess" that differ only marginally from the FIDE games. 

But you define only a solution. If you want to propose finding a solution using existing software (as does @tygxc) the software will implement a concrete version of chess which also differs marginally from FIDE.

_______________________________________________________________________________________________________________________

Correct. We have discussed the difference in this problem for various rule sets.

Where in the thread has there been an explicit definition of any ruleset other than the FIDE laws? 

The first point is true. I have referred to a relatively simple version of chess which has a 50 move rule and no 3-fold repetition rule. 

But the 50 move rule by itself hardly constitutes a game. What are the rest of the rules?

And how many people would call it chess? It could, maybe, fall under USCF basic rules where the 50 move rule and triple repetition rules can individually be optionally chosen from the tournament rules where they occur but you're still left without a solvable game.

I have also discussed the huge state space of chess with a repetition rule but argued that this can be sidestepped for the purpose of solution as optimal strategies with basic chess rules only repeat positions when they are not trying to win).

The question is not about the nature of a solution but about solving. In a solution along the lines of the checkers solution the engine doesn't know whether it's trying to win or not. I guesses and if it guesses wrong it can draw positions it could have won or lose positions it could have drawn. Would not avoiding repetition simply give wrong results?

This is slightly less complex as the half-move count can be omitted from the state space.

Try practising positions like this against Syzygy both ways and then tell me it's slightly less complex.

8/8/5N2/p7/8/k1K5/8/1N6 b - - 0 1 (for some reason the setup's decided to misbehave)

This position flakes out SF which assumes both rules.

 [FEN "7k/8/8/8/8/8/1R6/1K6 w - - 0 1"]

1. Ka1 Kh7 2. Kb1 Kg7 3. Ka1 Kf7 4. Kb1 Ke7 5. Ka1 Kd7 6. Kb1 Kd6 7. Ka1 Ke6 8.
Kb1 Kf6 9. Ka1 Kg6 10. Kb1 Kh6 11. Ka1 Kh5 12. Kb1 Kg5 13. Ka1 Kf5 14. Kb1 Ke5
15. Ka1 Kd4 16. Ka2 Kc3 17. Rh2 Kd4 18. Rb2 Kd3 19. Kb1 Kc3 20. Rh2 Kd4 21. Rb2
Kc3 22. Rh2 Kd4 23. Rb2 Kc3 24. Rg2 Kd3 25. Ka1 Kd4 26. Ra2 Kc3 27. Rg2 Kd4 28.
Ra2 Kc3 29. Rf2 Kd3 30. Rf1 Kd4 31. Rb1 Kc3 32. Rf1 Kd4 33. Rf2 Kc4 34. Rb2 Kd4
{Stockfish 15-martin} 35. Rb5 Kc4 36. Rh5 Kd4 37. Kb2 Kc4 38. Ra5 Kd4 39. Kb3
Ke3 40. Ra4 Kd3 41. Rb4 Kd2 42. Rd4+ Ke2 43. Kc3 Ke3 44. Kb4 Kxd4 

Of course, the lack of a 50 move rule may change the optimality of strategies, but I confidently believe (without proof) there are single strategies that are optimal for this version and the two others.

That's sounds hardly different from @tygxc's assertions that his ICCF games are perfect. I strongly doubt it. Do you have any basis for your confidence?

There's a difference between game theory and combinatorial game theory, as I pointed out long ago.  The entire reason that combinatorial game theory came to be is because of the distinction between the two directions each travels in.

Elroch said:

Game theory does not deal with probabilistic outcomes in games like chess (deterministic, perfect information).

I fail to see how that means he is championing game theory as the key to solving chess.  What I do see is that deciding that chess is *not* a game of perfect information is an attempt to turn the solving of chess into a religious belief.  It's objectively a game of perfect information.  The capability of human beings to absorb that perfect information does not factor in.

But it's not a zero sum game without some changes to the FIDE rules.

FIDE derives from Chess, not the other way around.  It's an illusion that FIDE controls the rules of the game.  It merely makes pronouncements and attempts to push chess players in one direction or another.  When they do not follow, FIDE is the entity that must amend itself .

The history of Chess is relatively FIDE-free when you look at it in total.

And it's had an awful lot of different versions each with its own solution.

I agree FIDE needs to get its act together regarding the rules. It can't be that difficult.

But have you ever come across any set of chess rules that defines a zero sum game?

Your argument boils down to "it's hard to know things we don't know yet even when all the pieces are right in front of us".  Which is a statement, and it is true (literally, in the case of the pieces being right in front of us)...but it doesn't have much bearing on the discussion.  

You always give the point up when you try to inject dismissive humor.  It's like a tell in Poker.

     You can't find such a quote because it never existed. I did say I believe that  1.e4  e5  2.Ba6  is losing for white, but certainty is by definition "established beyond dispute", and I repeatedly admitted that it is possible I might be wrong. Unarguable proof is still lacking.