Forums

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

Sort:
harry_the_gamer
tygxc wrote:

@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.

1) not just 7 men endgames, even if there are 9, 10, 11 pieces or more left on the board, the top engine moves may well be much more related than you think.

2) i am not going to answer this, since there is no way to determine what is "reasonable" without knowing the position. I simply pointed out the fact that you cannot determine probability by multiplying when the inputs are not independant.

3) ok, fair

4) Yes, most players will expect a post with the arguably clickbaity title "Chess has been SOLVED!!" as an indication of chess being strongly solved.

 

Also where are the links to the proofs?

harry_the_gamer
tygxc wrote:

@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.

where are the proofs? it has been 14 days since i sent my last message.

tygxc

@44

Proof of what?

harry_the_gamer
tygxc wrote:

@44

Proof of what?

LINKS to the proofs you stated that there were in post #40.

tygxc

@46

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

harry_the_gamer
tygxc wrote:

@46

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

then what about #1?

Maxx_2010

Chess it 's the best game ever i love chess

tygxc

@48

What exactly do you require proof of?

Maxx_2010

I don 't understund I am not good at english

harry_the_gamer

"[...] For all practical purpose this has already been done: Chess is a draw. [...]"
in #36

tygxc

@52

"Chess is a draw"

Proof:
Take any sufficiently large and sufficiently strong chess tournament.
You can e.g. take Tata Steel Masters 2023, or Zürich 1953, but let us look at the last 11 World Championship Finals of the International Correspondence Chess Federation. This is the strongest chess we know: 50 days per 10 moves, engines allowed. https://www.iccf.com/tables
Of 1469 games there were 1177 draws and 292 decisive games.
Assume a Poisson distribution of the errors per game.
That is a plausible assumption, also used for e.g. radioactive decay, or phone calls.

First assume Chess being no draw, i.e. being either a white win, or a black win.
Each draw then must contain an odd number of errors.
Thus the probability of an odd number of errors must be 1177 / 1469.
Thus 1177 / 1469 = Poisson (1, lambda, 0) + Poisson (3, lambda, 0) + Poisson (5, lambda, 0) + ...
There is no lambda that satisfies this equation.
Thus Chess cannot be a white win, or a black win.
Thus Chess is a draw.

Verification:
Now assume Chess a draw.
Each decisive game must contain an odd number of errors.
Thus the probability of an odd number of errors must be 292 / 1469.
Thus 292 / 1469 = Poisson (1, lambda, 0) + Poisson (3, lambda, 0) + Poisson (5, lambda, 0) + ...
There is a lambda that satisfies this equation: lambda = 0.25 errors / game average

Thus:
Games with 0 errors: perfect games with optimal play from both sides, draws: 1140
Games with 1 error: decisive games: 289
Games with 2 errors: draws with 2 errors that undo each other: 37
Games with 3 errors: decisive games with either 3 x ?, or 1 x ? and 1 x ??: 3
Games with 4 or more errors: 0

Thus of the 1177 draws 1140 are perfect games with optimal play from both sides.

Example:
https://www.iccf.com/game?id=1164344  
This perfect game reaches a 7 men endgame table base draw in 57 moves.

 

harry_the_gamer

"First assume Chess being no draw, i.e. being either a white win, or a black win.
Each draw then must contain an odd number of errors."

This is contradictory as it states that there are no draws then refers to draws in the next sentence.

"There is no lambda that satisfies this equation." why not?

"Each decisive game must contain an odd number of errors" Not quite. Some errors are naturally bigger than others and will more than "cancel out" the previous. And there are different errors such as a material error or a structure error. How do you compare them?

"Thus of the 1177 draws 1140 are perfect games with optimal play from both sides."

What does this prove?
This only results in a 97% confidence that chess is a draw.

TheSummoner82

Stockfish 16.1 against Dragon 3.3 on a fast computer without using an opening book will always be a perfect game resulting in draw. The only gains they’re making at this point with Stockfish and Torch for example are in unbalanced positions where one side makes a slight inaccuracy. To play the best move in EVERY situation would mean solving chess. We are not there yet but chess is getting slowly drained. The best computers are damn near the edge of perfection. And perfect chess between Stockfish and Dragon looks surprisingly straightforward and natural. AlphaZero’s weirdness as exciting as it may be would backfire against Stockfish or even Dragon now.

tygxc

We are now there: all perfect games without errors, all draws.
https://www.iccf.com/event?id=100104

sadam04
tygxc wrote:

We are now there: all perfect games without errors, all draws.

Thats it 10 minutes in the time out chair