Chess has been SOLVED! I think the following is the solution to the game of chess.

If white and black are playing at different ELO strengths, then which side wins does not only depend on the start position but also on playing strength. In other words, the weaker side is weaker because he, she or it is making mistakes. The hypothesis is that optimal play by both white and black leads to a draw. How else to simulate optimal or perfect play by both sides if not by using two instances of Stockfish?

The point is, if you can only simulate perfect play, you can't say you've solved anything.

Tic Tac Toe isn't solved based on an approximation of "best play." It's solved because we can prove what perfect play looks like, exhaustively. That's what "solved" means.

With chess we can only do that with a handful of pieces on the board in the endgame. Tons of endgames are solved, but the game is much more complicated than that.

Everyone agrees that you can't have a better approximation of perfect play with current technology than a very strong engine. But it doesn't follow from that that Stockfish is truly optimal. Stockfish right now is superior to Stockfish last year.

Yes, but absolute perfect play is actually not necessary to figure out chess. I covered this. Both Stockfish and the weaker ELO Rybka will win against 1.g4. The engine only needs to be strong enough to understand the advantage in the opening in question and gain further from it.

Right now, I can say 1.g4 is refuted. It should not be played. A superior engine in the future will not be able to un-refute 1.g4.

Only openings and variations that the self-playing engine draws are playable.

All of this information is part of the SOLUTION to chess. This is my point!

It is like putting an X in the corner of tic-tac-toe is part of the solution to tic-tac-toe. After that first move, if your opponent makes a mistake, you win.

To be sure, in the future, a stronger engine might refute an opening that is currently drawable. Thus, what is now playable might not be playable in the future.

GMs have been doing this sort of thing for a while. Sound lines, dubious lines, etc. Chess theory is also a part of the "solution" to chess.

The central problem is that you keep using language with specific technical definitions when you mean something other than what those words technically mean.

If you're talking about game theory, "solved" is an important word. And it doesn't mean what you think it means.

Also, we can't know that some hypothetical future engine couldn't un-refute the Grob. We can reasonably think it's unlikely, but personally I'd bet on more openings being draws rather than fewer. But Stockfish has not published a specific tree of variations that must always lead to a win for Black against the Grob. It's played it's best guess at the best moves and won as Black. You're asserting that no future engine can ever do better there, but you haven't actually posted any reasoning to support that argument. You just keep asserting it.

"Playable" and "dubious" are loaded terms that have nothing to do with game theory, but as an aside, as long as you aren't playing against Stockfish, Stockfish's results are at best tangentially related to what is "playable."

Well maybe you are right. A future engine might see the Grob differently.

I just thought there was something to both Stockfish and the weaker Rybka scoring a win regarding the Grob.

Regarding draws, right now it seems almost every opening is drawable. I have only found 2 so far that are not draws.

Anyway, that's enough of this experiment.

Moving on.

@1

"openings such as the King's Indian Defence and the French Defence would be refuted"
++ They probably are. That is why they now are shunned in top human and ICCF play.

"The Queen's Indian is also drawable." ++ Yes.

"To my surprise, so too is the very open and structurally unusual Sicilian Najdorf." ++ Yes.

"King's Gambit Accepted, the Evan's Gambit and the Danish Gambit can be drawn."
++ Probably not. See Figure 4d of https://arxiv.org/pdf/2009.04374.pdf 
'King's Gambit loses by force' - Fischer
'I could find no way for white to equalize' - Kramnik

"the Two Knights Fried Liver can be drawn." ++ Doubt that. Show your drawing line.

"Dutch Defence and Bird's Opening resulted in draws." ++ Doubt that for Dutch, see Figure 4a.

"the likes of Giuoco Piano, Ruy Lopez, and Queen's Gambit Declined would all be draws" ++ Yes.

"1. The Grob's Attack (1. g4)" ++ Yes, 1 g4? is the only move that loses for white. A human can still play it. IM Basman won many games with 1 g4? as his opponents failed to refute it.

"2. The Nakhmanson Gambit, a variation of either the Italian or Scotch Game (1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Nf6 5.0-0 Nxe4 6.Nc3 dxc3)." ++ Almost all gambits lose by force.

"there is no need to use the strongest ELO engine"
++ No, you need a strong engine and much time per move.

"only an unsound opening or variation would not be drawable" ++ Yes, that is correct.

"turning a small advantage into an ever larger one and eventually a win"
++ There are no small or large advantages, a position is either a draw, a win, or a loss.
1 g4? is a loss for white and the only first move that loses for white.

^^^

Not an authority on any of this.  More like Tom Cruise commenting on world affairs...

@30

2106 > 1559

For this discussion, systems development career > chess rating.  Stockfish cannot evaluate perfect play at ~3500, so 2100, 1800, or 1550 makes little difference at all.  You will fail to prove anything here as you do in every thread you post your 10^17 nonsense in.  

The thing is stockfish isn't perfect, so using it as a theoretical "perfect engine" doesn't make

sense. "Solving" a game requires showing that from the starting position WITH OPTIMAL PLAY that one side will win. Stockfish is not yet the "optimal play" that we look for.

@32

"one side will win" ++ No, black draws.

"Stockfish is not yet the optimal play"
++ With enough time per move it approaches zero errors.

I said I was moving on but then I stumbled on something else interesting.

Apparently, a variation of chess on a 5x5 board with 5 pawns and 5 pieces (K, Q, R, B, N) called "Gardner Mini Chess" was formally "solved" by computer scientists in 2013. For that game, perfect or optimal play by both sides leads to a draw.

This is my hypothesis for standard chess. To be sure, mine is a thought experiment but the logic is sound.

Also, I think, even when chess is formally solved and it is proven that perfect play results in a draw, precisely because so many openings are playable or drawable, the game will continue to be played, casually and professionally.

Concerning the Grob 1.g4, apparently Stockfish playing white can still beat Rybka. So if you are better than your opponent, go for it.

For me, the biggest surprise of this experiment was that various opening gambits are drawable.

And yes, I have found when an engine is given more time to think, it will play different moves, presumably better ones.

1) you cannot assume that black draws without analysing every position from start with a perfect engine

2) True, however the problem is it APPROACHES 0 errors, to hit absolutely 0 errors will take at least on the orders of 10⁸⁰ years, which is obviously not feasible. Even if you do analyze all the positions, there is a chance that stockfish will miss a tactic / something else since the piece / position evaluation in stockfish is not perfect.

@35

"assume that black draws without analysing every position from start with a perfect engine"
++ To establish that Chess is a draw,
there is no need neither to analyse every position, nor for a perfect engine.
Analysing every position with a perfect engine would be strongly solving chess to a 32-men data base of all 10^44 legal positions and that would take 10^27 years with present technology.

Just establishing that black draws is ultra-weakly solving Chess. For all practical purpose this has already been done: Chess is a draw. That is clear from statistics on millions of human and engine games, especially ICCF WC Finals draws: engines allowed, 50 days per 10 moves.

It is also logical.
To win you need an advantage of 1 pawn. As we know from gambits 3 tempi are worth a pawn.
A tempo is less than a pawn and thus insufficient to win. A pawn can queen, a tempo cannot.

"it APPROACHES 0 errors, to hit absolutely 0 errors will take at least on the orders of 10⁸⁰ years"
++ At 17 seconds/move on a billion nodes/second cloud engine (or 4.7 hours/move on a million nodes/second desktop) the table base correct move will always be among the top 4 engine moves except for 1 error in 10^20 positions. Weakly solving Chess needs only 10^17 relevant positions and thus 0.001 error will be made i.e. none.

"the piece / position evaluation in stockfish is not perfect"
++ A weak solution does not depend on the Stockfish evaluation, but depends on calculation depth to reach the 7-men endgame table base with its perfect evaluation.

@34

"Concerning the Grob 1.g4"
++ Here is the refutation of 1 g4?

Weird. When I play against myself I always seem to have one side that I favour more than the other.

1) Is there a proof of this? as far as we know this could still just be a fluke.

2) Same as previous question. Is there a proof that it is impossible to win with less than 1 pawn advantage?

3) How do you deduce that 3 tempos is worth 1 pawn?

4) Where does the 10^17 come from? "1 error in 10^20 positions" where do you get this statistic?

5) Here's the problem: we can't calculate with enough depth to reach the "perfect play" that is demonstrated by the tablebase: Ignoring the fact that we do not even know how many plies it will take with optimal play to reach a position with 7 man, the cost of calculating to 50 plies is around a few billion nodes. The node count increases exponentially¹ relative to the plies calculated, so 140 plies (my guess for how long on average it takes for two theoretical "Perfect-Players" to reach a position with less than 8 pieces on the board) would then take around 9 quadrillion nodes. At 1 million nodes per second, that's going to take 285 years, so unless somebody is gonna setup a generation long stockfish spree, it is very doubtful that we will actually generate the 9 quadrillion nodes needed.

¹: Actually, slightly sub-exponential, around 10^(1.31*sqrt(x)) for x plies

@39

"1) Is there a proof of this?" ++ Yes.

"2) Is there a proof that it is impossible to win with less than 1 pawn advantage?" ++ Yes.
Each further move dilutes the 1 tempo initial white advantage.
A pawn can queen, a tempo cannot.
Millions of human and engine games confirm that, especially ICCF

"3) How do you deduce that 3 tempos is worth 1 pawn?" ++ From study of gambits.
'Should the opponent offer any material, even a Pawn, which in your estimation you may capture without danger, it is advisable to take the offered piece, even if as a result full development is retarded for one or two moves. If as a result of the capture full development will be retarded more than two moves, then it is doubtful whether the capture should be made. It might be risked with the White pieces but never with the Black' - Capablanca

"4) Where does the 10^17 come from?"
++ There are 10^44 legal positions as shown by Tromp, but the 3 random samples with > 3 bishops or rooks per side show these can never result from optimal play by both sides.
A better estimate is 10^37 by Gourion, but multiply by 10 to accept 3 or 4 queens: 10^38.
Inspection of a random sample of 10,000 Gourion positions shows none can result from optimal play by both sides. Try to construct a reasonable game for any of the 10,000 FEN. Leaves 10^34.
Weakly solving only needs 1 black move, not all black moves. Thus a square root leaving 10^17.

"1 error in 10^20 positions where do you get this statistic?"
++ By extrapolation from Table 2 of this paper
1 s/move 11.8% decisive games
1 min/move 2.1% decisive games
1 h/move 2.1%*2.1/11.8 = 0.37% decisive games
60 h/move 0.37%*2.1/11.8 = 0.075% decisive games
Thus 1 error of top 1 move in 100,000 positions.
Thus exact move not among top 4 engine moves 1 case in 10^20 positions.

"we can't calculate with enough depth"
++ With enough time we can. 5 years on 3 cloud engines of 1 billion nodes/s (or 3000 desktops of 1 million nodes/s) is enough to exhaust the 10^17 relevant positions.

"we do not even know how many plies it will take with optimal play"
++ We know: in ICCF 42 moves on average, i.e. 84 ply

"At 1 million nodes per second, that's going to take 285 years"
++ It takes 3 cloud engines of 1 billion nodes/s each during 5 years.

1) and 2) link the proofs

3) ok

4) "Thus 1 error of top 1 move in 100,000 positions.
Thus exact move not among top 4 engine moves 1 case in 10^20 positions." i feel like this bit is slightly erroneous because the best moves are not always completely unrelated, especially in the endgames, so it is unreasonable to assume that the chance of a move not among the top 4 engine moves is equal to the fourth power of the chance of a move not being the top engine move.

"[...] By extrapolation [...]" are you sure that it is possible to extrapolate the data in a reasonable way in this context?

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Aside from the technical discussion, I think we have differing opinions of what "solved" is supposed to represent. I would expect most chess.com users to think that "solved" means that for every possible position we can deduce the absolute best move. Thus this lengthy discussion resulted from a typo or clickbait in the title.

@46

"the best moves are not always completely unrelated, especially in the endgames"
++ Once a 7 men endgame reached, the result is looked up in the 7-men endgame table base.

"it is unreasonable to assume that the chance of a move not among the top 4 engine moves is equal to the fourth power of the chance of a move not being the top engine move."
++ It is reasonable. What else should it be?

"are you sure that it is possible to extrapolate the data in a reasonable way in this context?"
++ At least it provides a reasonable estimate from data we have.

"I think we have differing opinions of what solved is supposed to represent."

There are 3 different kinds of solved:

Ultra-weakly solved means that the game-theoretic value of the initial position has been
determined,
weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition, and
strongly solved is being used for a game for which such a strategy has been determined for all legal positions.
A strategy can be a set of moves, a set of rules, or a combination.
The game-theoretic value of a game is the outcome when all participants play optimally.
Optimal play is play without errors.
An error (?) is a move that turns a draw into a loss, or a win into a draw.
A blunder or double error (??) is a move that turns a win into a loss.