@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.
@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?