I was also going to explain why game theory cannot apply to the solving of chess... [snip]
Go on, give us a treat. Perhaps afterwards you can explain why number theory does not apply to the number 213276247234766621.
I think @Optimissed might be right this time.
Under FIDE laws possible yields include but are arguably not restricted to (win,loss), (loss,win), (draw,draw), (win+draw,loss+draw), (loss+draw,win+draw), (win,win), (win+draw,win+draw) and (arbiter determined) without any ordering specified. The objective is checkmate but that cannot be forced except from positions that are already checkmate.
What part of game theory would apply?
Still thinking about 213276247234766621; don't tell me. It's not prime but it has abnormally few factors.
While I understand that you are being light-hearted, you understand that "solving chess" refers unambiguously to the abstract game of chess (or, to be precise, a version of it defined by the relevant rule set), which has no time limits, nothing happening off the board, but may include well-defined rules such as the option (or obligation) to claim a draw in an n-times repeated position, or when the 50 move rule applies.
No arbiters ever the chance to get involved any more than they do in the solution of tic-tac-toe - the only laws involved are those that govern legal moving and results.
If I recall, the only appeal to game theory that has taken place in this forum was to a general theorem that applies to a class of games to which chess belongs. Given the definitions:
- A (pure) strategy for a side is defined as a procedure that generates a move for any legal position (note that a mixed strategy is one where it may vary the chosen move in a position, but we don't need these).
- The value of a strategy is the minimum of the values it achieves against all opposing strategies
- An optimal strategy for a side is a strategy that achieves the maximum of the values of all strategies for a side
then there exists an optimal strategy for each side and these strategies achieve the same result.
I'd like this theorem to be trivial, but when trying to show it was, I convinced myself it is not quite! The theorem seems to rely on the fact that every game is finite, for example.
My point is that "chess" generally refers to one of the games defined in the FIDE laws.
No, not when SOLVING chess. This is about the abstract game.
Because they allow for resignation and agreed draws
Both completely irrelevant to solving chess, just ways to save time in real, imperfect games before the rules decide the result.
which occur asynchronoulsy with the moves and the results are are not prioritised in terms of win draw or loss either beteen themselves or with the results of completed moves, the possible results have no defined order. Is (win,win) for White better or worse than (win,draw) or (win,loss)?
There are exactly three results of a game
WIN > DRAW > LOSS
ok?
You say:
"1. A (pure) strategy for a side is defined as a procedure that generates a move for any legal position ..."
Where do claims come in? Those are part of chess.
To solving chess, you can assume all claims occur by the player they favour. Equivalently, you can assume an automatic result. It's not about competitive play.
A good strategy should generate a draw claim under the 50 move rule at some point if the opponent has a frustrated win. (It should also accept a draw offer in a losing position, but that would be extending the meaning of "solution".)
No, that would simply be part of the solution. A side aiming for a draw claims the draw when it occurs (or equivalently for solution, it is automatic).
2. The value of a strategy is the minimum of the values it achieves against all opposing strategies.
There can only be a minimum if the results are ordered. They're not under FIDE rules.
I have no idea what you are thinking about. WIN > DRAW > LOSS.
Ergo game theory doesn't apply to chess.
A false conclusion based on erroneous thinking I can't fathom.
It could as you say be applied to abstract version of "chess" that differ only marginally from the FIDE games.
That's the chess that is relevant to solving chess. It ain't about imperfect tournament and match play (FIDE's preserve)
But you define only a solution. If you want to propose finding a solution using existing software (as does @tygxc) the software will implement a concrete version of chess which also differs marginally from FIDE.
What you really mean is that FIDE differs from chess.
. The strangeness in this thread comes from two sources, both of whom have delusions that drive them. One driven by the need to be above everyone around them to feel secure and safe, and the other driven to turn the offhand comments of his deceased hero into reality.
. The analogy is not quite there.
Oh yes, so you're contesting what is told on account of the language used to tell it? I don't think that quite works, sadly for your assumption.
"Old bean" and "old thing" are completely extraneous to the discussion and only serve to deflect from the fact that you had no answer for my previous post. It's a common tactic...more common among the general public than claiming mental superiority, actually
. Your use of "contesting what is told" is a contortion you chose to avoid saying "contesting my argument", because then this answer which I am giving now becomes blatantly obvious...it's not part of your argument.
Carry on.