No, I am referring to the situation where a win is beyond your horizon but you know you have a practical advantage, and it turns out that as both players play apparently accurately, the advantage grows eventually into a winning one. This phenomenon happens with both strong players and computers.
The practical chance for an advantage to have time to "grow" into a win is more limited the more towards the endgame you are.
Interesting idea, I see what you mean now.
yeh really, from time to time i study the board hoping to find the solution.
There is generally a trade-off between computing time and storage capacity in computation. For example, the tablebase of chess is a hypothetical database (impractical on account of its astronomical size) which allows instant determination of the evaluation of all possible moves in a position.
At the other extreme it is possible (easy, in fact) to write a tiny program that uses a small amount of memory which could evaluate all the possible moves in any position, with the only problem being that the calculation for a position usually takes longer than the age of the Universe.
The history of the (moves of) a game is irrelevant in adjudicating any given position.
Chess is clearly a two-person zero sum game, so it has an optimum strategy--I think Von Neumann proved this with an analogy to spherical geometry.
Nobody knows if it is optimally a win for white or for black, or a draw, and I don't think players' consensus matters on this point. For example, when the tables for a crertain set of endgames was actually computed some years ago, there were found endings previously universally considered draws that, in fact, were wins--though the winning sequence was tactically incomprehensible to any human.
By the way, someone upstream gave the wrong number of opening moves in tic-tac-toe. Because of the symmetries, there are only three: corner, middle, or side. (I think the earlier poster mistakenly said that there were six!)
The history of the (moves of) a game is irrelevant in adjudicating any given position.
While the rest of your post was correct, this is an error. The value of a position in competition rules chess (eg FIDE, USCF) can depend crucially on:
To understand the latter, consider the case where there is a single path to a win, but that path goes through a position that has been visited twice.
@107
"The history of the (moves of) a game is irrelevant in adjudicating any given position.
this is definitely an error." ++ No, it is not an error.
"The value of a position in competition rules chess (eg FIDE, USCF) can depend crucially on:
the ply count since the last irreversible move and which positions have been previously visited twice" ++ Visiting the same position twice can always be avoided. The 50-moves rule is never triggered with perfect strategy i.e. optimal play from the initial position.
@107
"The history of the (moves of) a game is irrelevant in adjudicating any given position.
this is definitely an error." ++ No, it is not an error.
"The value of a position in competition rules chess (eg FIDE, USCF) can depend crucially on:
the ply count since the last irreversible move and which positions have been previously visited twice" ++ Visiting the same position twice can always be avoided. The 50-moves rule is never triggered with perfect strategy i.e. optimal play from the initial position.
Now you are just making yourself look foolish.
Adjudication only occcurs in real games between real players and definitely can depend on the history of the play. If it could not, certain rules would be unnecessary! [It is mostly a historical curiosity, as rapid finishes have become the norm].
As a specific example, in a real game if a position has been repeated twice and one player loses if they don't repeat the position a third time on the next move, the position has to be adjudicated a draw. By contrast the same basic chess position is a win for the other side.
Perhaps you got confused and thought the post was about the abstract game?
@109
"Perhaps you got confused and thought the post was about the abstract game?"
++ The title of the thread is: Game Theory - Perfect Strategy?
If one player can win a position, then the perfect strategy is not to repeat positions twice.
There is no "adjudication" in solving chess, there is a tablebase (with the usual hypothetical approach). Indeed, there are no games - rather a tree.
Chess doesn't have perfect symmetry, the position of the king and queen are switched for black and white, which is why if you both castle kingside you are both on the same side of the board, instead of opposite.
As far as the pieces, the board has horizontal symmetry in the initial position.
In any case, symmetry itself means nothing... as a premise I'm using the observation that positions like these are equal:
So even if you find a definition of symmetry for which the statement is not true, it's only an argument against my terminology.