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

@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.

@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.

@44

Proof of what?

@46

Proofs of what statements?
I already provided proof of 2 in post @40.

In the game of chess, perfect or accurate play by both sides leads to a draw. For one player to win, the other must blunder, at least once. Often, winning a game comes down to making fewer mistakes than your opponent.

So, to win, you must provoke your opponent to make a mistake through some sort of tactical play involving a trap or else a sacrifice. Alternatively, to win, you must not only be patient but also hope for your opponent to make a mistake. This is the solution to the game of chess. Thus, chess is solved.

Let me say more.

Letting a chess engine such as Stockfish play against itself, I have discovered that many chess openings and variations can be drawn. It stands to reason, if an engine playing against itself from an opening's start position will draw, that opening is ok to play.

I had thought openings such as the King's Indian Defence and the French Defence would be refuted in this day and age of AI-inspired pawn storms and strategies that trap pieces. It turns out, strong engine play leads to draws.

The Queen's Indian, which apparently cost Magnus Carlsen a game recently, is also drawable.

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

Even stuff like the King's Gambit Accepted, the Evan's Gambit and the Danish Gambit, despite being gambits, can be drawn.

Even the Two Knights Fried Liver can be drawn.

Also, the seemingly dubious Dutch Defence and Bird's Opening resulted in draws.

And of course, the likes of Giuoco Piano, Ruy Lopez, and Queen's Gambit Declined would all be draws too. But I did not test those.

The two openings so far that I have found to not result in a draw are:

1. The Grob's Attack (1. g4)

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).

I am sure there are others. But it will take a while to figure it all out.

To carry out these experiments, there is no need to use the strongest ELO engine. The only requirement is that the engine you use plays the same way all the time, playing the best move it finds from its evaluation whatever that may be.

If the engine plays both sides as best it can, then only an inferior starting position for one side will result in something other than a draw: only an unsound opening or variation would not be drawable.

Thus, an unsound opening or variation can be regarded as a refuted line, something that can no longer be played unless you would like to play at a disadvantage.

An engine playing the Grob's against itself is interesting because you can see it turning a small advantage into an ever larger one and eventually a win.

So, I say, chess is solved. This discovery of mine is the solution to chess.

What do you think? Discuss.