As I said, I (and anyone else dealing with the abstract game) couldn't care less about ridiculous things like someone resigning when they checkmate.
Game theory (and solving games) is only concerned with moves being alternately played on the board and results being reached. Hope that is clear enough.
As I said, I (and anyone else dealing with the abstract game) couldn't care less about ridiculous things like someone resigning when they checkmate.
Game theory (and solving games) is only concerned with moves being alternately played on the board and results being reached. Hope that is clear enough.
Yes, I'm more or less in perfect agreement with that. (More or less because I think game theory could also be concerned with Bridge for example.)
But you can't carry on to conclude, "Game theory unquestionably does apply to all the forms of chess we are discussing here ... ".
The result of some of the forms of chess being discussed can be affected by flags falling or arbiters throwing a wobbler. Before you start applying game theory I think you need to modify the rules to discount such possibilities and the things you call ridiculous (how do you define that?), at which point the game will not be a form of the game that we are discussing here, except in the posts that are discussing chess in the context of game theory.
(By the way you talk about moves being alternately played on the board. If you're taking "move" to mean a transition between consecutive game states as you implied in an earlier response, these needn't be effected by alternate players.)
I would say that none of the games described in the FIDE handbook has a solution. Full stop. They can be simply modified to admit of a solution and that would be a first requirement before any useful game theory could be applied.
To tone down the classic confusing depth of discussion
I have not seen anyone (except for in this discussion) refer to strong solutions of states. But it would be reasonable to define it as "strong solution of the game like chess but with specified starting state". I think we can agree on that.
A basic chess tablebase plus "ply to exit equivalence class" provides every winning strategy that avoids increasing the ply to exit equivalence class.
You can't have a (deterministic) winning strategy with a loop in basic chess. However, the above paragraph seems clearly not to be all winning strategies. I assert that there are some other winning basic chess strategies that in some positions unnecessarily increase the ply to exit the equivalence class but do so in a way that does not change the result (because the new position has a forced exit that never returns to the position where the ply was increased).
So I am not disagreeing with you (using the reasonable definition of strong solution of a state), but pointing out that the basic-chess-tablebase-with-ply-count-to-irreversible-move (for winning or losing moves) provides something which is very substantial for versions of chess with additional drawing rules, and shows they are very closely related games.
Question: is ply to mate good enough for this purpose instead of the apparently superior ply to irreversible move?
Well, I obviously failed to grasp the point of your original post. My apologies. I need to have another go at that, but I won't respond immediately; I think I need a little time to consider if it implies that a strong solution of competition rules chess would fit in 10^44 classical bits.
So far as my use of strong solution of game states is concerned, I have seen it stated that n-man (basic rules) chess is strongly solved by the Nalimov tablebases, which I take to mean each n-man position is strongly solved (under basic rules most people would identify "position" and "game state").
I spend probably more time on endgame problems than actually playing chess; they generally assume basic rules and they usually call for the solution (unqualified) of specific positions, by which they mean weak solution of the games starting with the positions, which is a similar use.
!) In my opinion, in chess the pieces speak louder than words. If someone says "I resign" when giving checkmate, the checkmate would carry the day, although I think an arbiter would be within his rights to cross examine the perpetrator and if it was deliberate the player could possibly be warned or even subject to sanctions.
My point is the laws don't say that.
They do say:
12.1 The arbiter shall see that the Laws of Chess are observed.
If the laws of chess are observed in that case, both players win.
5.1.1 The game is won by the player who has checkmated his opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7.
5.1.2 The game is won by the player whose opponent declares he resigns. This immediately ends the game.
[snip]
So far as my use of strong solution of game states is concerned, I have seen it stated that n-man (basic rules) chess is strongly solved by the Nalimov tablebases, which I take to mean each n-man position is strongly solved (under basic rules most people would identify "position" and "game state").
It does, in a very straightforward manner. For each position, if there is a winning move, play one with the lowest moves to mate. Otherwise if there is a drawing move play one. Otherwise any move satisfies the needs of a strong solution.
Of course this is only true for the positions in the tablebase...
I spend probably more time on endgame problems than actually playing chess; they generally assume basic rules and they usually call for the solution (unqualified) of specific positions, by which they mean weak solution of the games starting with the positions, which is a similar use.
Almost. But note that such problems generally don't accept slower solutions, so a weak solution may not suffice.
@Optimissed
I'm sure something of the sort would happen, but the arbiters would be violating 12.1.
The laws themselves say unequivocally that both players win.
"12.1 The arbiter shall see that the Laws of Chess are observed."
Not very honest are you? The laws do not state that at all. That is your interpretation.
I just copied it verbatim from the handbook. You'll have to write off to FIDE and tell them they're dishonest.
...
Almost. But note that such problems generally don't accept slower solutions, so a weak solution may not suffice.
Endgame problems don't generally specify the number of moves to mate, so slower solutions are normally acceptable.
In any case, article 12 covers conduct and 12.1 is the overview. What you wrote is specific and not an overview. Therefore what you are saying seems illogical.
Just look at the link. I believe it's the most up to date version.
The laws taking effect from January next say the same.
Again you'll have to write off to FIDE and tell them they're illogical. (You might be right.)
@5912
++ The same weak solution without the 50-moves rule also applies with the 50-moves rule.
"Is that what you mean by your above statement?"
++ No, a weak solution of chess is a strategy for the initial position to achieve the draw against any opposition. Your 5-men position is strongly solved in the 7-men endgame table base and cannot result from the initial position by optimal play from both sides.
++ The game as described in the Laws of Chess. https://handbook.fide.com/chapter/E012018
"There are at least five games described in your link." ++ No, there is one only.
"why then are you bringing ICCF and TCEC into it when they have different rules?"
++ Because they share the same weak solution.
"The games I posted are interest to me" ++ Not to me. All 7-men positions are strongly solved. Weakly solving chess is from 32 to 7 men. I await your drawn KRPP vs. KRP.
"What rules are you going to assume?" ++ The Laws of Chess.
"all of them?" ++ Yes.
@5917
"most people would identify "position" and "game state""
++ No.
Diagram = position of all pieces.
Position = diagram + side to move + castling rights + en passant possibility i.e. FEN without ply
Game state or node = position + evaluation + history
Actually, it depends on which ruleset you are using.
Even in chess with a repetition rule and a ply count without irreversible move rule, the game state only requires the history back to the last irreversible move.
Which brings to mind that there is a minor imperfection in the FIDE rules in that the repetition rule says:
This certainly looks like it refers to the possible IMMEDIATE moves of all of the pieces. As such it could fail detect a loss of castling rights that would make it a different state. The reason this is important is that loss of castling rights changes the possible future paths, sometimes crucially, and this could be an achievement by one player.
The rule could be improved by saying "the possible future moves..." instead of "the possible moves..."
@5932
"As such it could fail detect a loss of castling rights that would make it a different state."
++ No. This is the actual wording. 9.2.2.1 and 9.2.2.2 treat castling and en passant.
9.2.1
The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
9.2.1.1
is about to appear, if he first indicate his move by writing on the paper scoresheet or entering move on the electronic scoresheet, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move, or
9.2.1.2
has just appeared, and the player claiming the draw has the move.
9.2.2
Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:
9.2.2.1
at the start of the sequence a pawn could have been captured en passant
9.2.2.2
a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.
https://handbook.fide.com/chapter/E012018
Looks like I was referring to a version of the rules that was replaced in 2018.
12.2.2 concisely covers it, MAR; and that rule prohibits two people both winning the same game.
...
12.2.2
12.2 The arbiter shall:
...
12.2.2 act in the best interest of the competition,
doesn't prohibit two people winning the same game.
If the game is played under basic rules an arbiter has no jurisdiction and art.12.2.2 doesn't apply..
If the game is played under competition rules art.12.1 mandates that the arbiter must declare the game won by both players in the circumstance I mentioned. If you feel that is not consistent with art.12.2.2 in that circumstance then you feel the FIDE laws are inconsistent. That doesn't mean the rule prohibits both players from winning.
FIDE might feel that art 10.2
10.2 The total score of any game can never exceed the maximum score normally given for that game. ...
is enough to resolve the inconsistency in that case. Both players win and each scores 1/2 point in the tournament. (Or maybe it's scored 1-0 or 0-1 depending on the arbiter's mood.)
...
Even in chess with a repetition rule and a ply count without irreversible move rule, ...
FIDE, just to be inconsistent, don't have a ply count without irreversible move rule. You can castle into a 50 or 75 move rule draw.
@5938
"You can castle into a 50 or 75 move rule draw."
++ Yes, you can, but not in a perfect game with optimal play from both sides.
Both players can aimlessly hop around with knights for 75 moves to trigger a 75-move draw with all 4 castling rights intact, but that is sure not to be a perfect game with optimal play and it would not oppose to the draw.
https://www.iccf.com/game?id=1164365
Here is an example of a game > 99% certain to be a perfect game with optimal play by both participants. It is the most recently finished ICCF WC finals game. It is exceptionally long: 65 moves and it ends in a 7-men endgame table base draw. The 50-moves rule was never even close to being triggered. There was always compelling reason to move a pawn or capture a piece. Not moving a pawn or capturing would not be optimal play and could cause a loss.
@5938
"You can castle into a 50 or 75 move rule draw."
++ Yes, you can, but not in a perfect game with optimal play from both sides.
Both players can aimlessly hop around with knights for 75 moves to trigger a 75-move draw with all 4 castling rights intact, but that is sure not to be a perfect game with optimal play and it would not oppose to the draw.
You are certain that two tempi provides a win for black in the following position? LeelaZero gives black 70%, and Stockfish evaluates almost exactly 1 pawn advantage. No way is the result clear.
[Very amusing that you are now relying on samples of size 1 to "prove" results about chess in general]
@5940
"You are certain that two tempi provides a win for black in the following position?"
++ No, that is still a draw. White is up 1 tempo in the initial position, which is a draw.
If white loses 2 tempi, then white is 1 tempo down.
To win you need an advantage of 1 pawn or 3 tempi.
"No way is the result clear." ++ This is very clear: a draw.
"you are now relying on samples of size 1 to "prove" results about chess in general"
++ That is one example of 1104 perfect games with optimal play from both sides.
...
Bear in mind that only the order of the results (win > draw > loss) is relevant for the analysis of the value of positions with optimal play....
I am bearing that in mind.
The problem is that the possible results are not just win. draw, loss under FIDE rules.
If a player (a) checkmates and simultaneously resigns under FIDE laws he wins and so does his opponent. If he (b) checkmates and simultaneously accepts a draw offer he wins but the game is drawn. If he (c) checkmates and does neither, he wins (and presumably his opponent loses, though it doesn't explicitly say that - given the first two cases are allowed, it's not obvious).
Some players might feel (a)>(c), others (c)>(a). There's no order given in the FIDE laws. Indeed some players might find (a) <draw, so long as opponent doesn't win in the latter.
This is easy enough to resolve by a simple change in the rules (several possibilities, but none so far suggested in the thread), but the change needs to be made before game theory can be usefully applied I think.