44 is fine. ...
In the example below the position after move 34 in the mainline is a theoretical draw under competition rules.
The position after move 34 in the variation is a theoretical mate in 16 under competition rules.
Are you saying that the two positions are the same under competition rules?
44 is fine. ...
The position after move 34 in the mainline in the example below is a theoretical draw under competition rules.
The position after move 34 in the variation is a theoretical mate in 17 under competition rules.
Are you saying that the positions are the same under competition rules.?
No.
Just for clarity, I am also not saying that the Earth is hollow, or a list of 10^1000 other false statements independent of what I wrote. What I did say is what I wrote.
I would suggest you take a glance at the positions in real chess games after 36 moves and see what proportion of them have as few as, say, 12 pieces on the board.
@5065
"losing chess has far more legally forced moves"
++ In Checkers capture is compulsory too. In Checkers pieces cannot retreat, in Losing Chess they can. Losing Chess is more like Chess than Checkers: same 64 squares, same 32 men, same 6 kinds of men. Losing Chess is a white win, while Checkers and Chess are draws.
"The exponent 14 for the genuine weak solution of checkers is 0.7 times the exponent 20 for the state space. The reason it is this large is that the job was done properly."
++ No, the reason is that in Chess there are more nonsense moves than in Checkers.
"Even with a tiny factor of 3 times more positions after each move (after allowing for transposition), 10^17 would be exceeded after a tiny 36 moves"
++ 36 moves is not tiny. The average of an ICCF WC game is 39. The average length post novelty in the 2022 Sinquefield cup was 33. With full transpositions width 4 gives e^4 = 54. With no transposition width 4 and depth 36 gives
(4^37 - 1) / (4 - 1) = 10^21. Chess is full of transpositions. Thus 10^17 makes sense.
"what reason do you have for believing that sloppy solution"
++ I do not advocate a sloppy solution, but a smart solution.
"none of those involved in the solution of checkers" ++ In Checkers there are less possibilities for stupid moves. You cannot retreat pieces or aimlessly hop around with pieces.
"the many years that doing the job properly required?"
++ Most years for Checkers were to build the table base and develop the Chinook engine.
For chess the table base already has been built and Stockfish already exists. Computers are more powerful now.
"It does not permit guessing"
++ Not guessing, but using knowledge. That is permitted and beneficial see this paper.
https://www.sciencedirect.com/science/article/pii/S0004370201001527
@5067
"The very large majority of positions:
have no symmetry
have pawns
don't have castling rights"
++ Yes, that is correct.
"I believe there are roughly twice as many positions as sets of symmetric positions."
++ Every non-symmetric Tromp position with pawns and without castling rights corresponds to 4 positions with the same game-theoretic value and a symmetric strategy to achieve it.
Every non-symmetric Gourion diagram with pawns and without castling rights corresponds to 2 positions with the same game-theoretic value and a symmetric strategy to achieve it.
You are correct about the number 4. I was not including black-white symmetry.
@5065
"losing chess has far more legally forced moves"
++ In Checkers capture is compulsory too. In Checkers pieces cannot retreat, in Losing Chess they can. Losing Chess is more like Chess than Checkers: same 64 squares, same 32 men, same 6 kinds of men.
Losing chess is very different to both checkers and chess, since its solution is dominated by forcing moves. This is why it is so small. An error in the comparison with checkers is that losing material is desirable in Losing Chess and typically undesirable in checkers.
Losing Chess is a white win, while Checkers and Chess are draws. Another signficant (if partially unproven) difference.
"The exponent 14 for the genuine weak solution of checkers is 0.7 times the exponent 20 for the state space. The reason it is this large is that the job was done properly."
++ No, the reason is that in Chess there are more nonsense moves than in Checkers.
Nonsense is a sloppy term. You will not find anything akin to this is the entire peer-reviewed literature.
"Even with a tiny factor of 3 times more positions after each move (after allowing for transposition), 10^17 would be exceeded after a tiny 36 moves"
++ 36 moves is not tiny. The average of an ICCF WC game is 39. The average length post novelty in the 2022 Sinquefield cup was 33.
Very few of those games are fully resolved. These are human decisions.
With full transpositions width 4 gives e^4 = 54. With no transposition width 4 and depth 36 gives
(4^37 - 1) / (4 - 1) = 10^21. Chess is full of transpositions. Thus 10^17 makes sense.
"what reason do you have for believing that sloppy solution"
++ I do not advocate a sloppy solution, but a smart solution.
No, you advocate calling a non-solution a solution. The sloppiness is yours.
Refer to the entire peer-reviewed literature on weakly solving games to learn about this.
"none of those involved in the solution of checkers" ++ In Checkers there are less possibilities for stupid moves. You cannot retreat pieces or aimlessly hop around with pieces.
Irrelevant opinion to weak solution. Check the literature. (Eg for the weak solution of checkers or Losing Chess).
[snip]
"It does not permit guessing"
++ Not guessing, but using knowledge. That is permitted and beneficial see this paper.
https://www.sciencedirect.com/science/article/pii/S0004370201001527
This paper nowhere supports ignoring a legal opposing move to a strategy based on heuristics. If you believe otherwise, point it out. Otherwise you need to accept you are wrong.
...
there is a pawnless position with 8-fold symmetry
...
OK, I'll fall for it. Post one.
Let's just put this one to bed. Ignoring all the pieces, the kings do not permit that degree of symmetry. Two fold geometric symmetry is maximal. Geometrically, since the two kings are preserved under a symmetry, so is the line between them, and that leaves at most one flip available.
@5073
"Losing chess is very different to both checkers and chess, since its solution is dominated by forcing moves."
++ In Checkers it is the same. In Chess there are practically forcing moves, not legally forcing moves. If I capture your queen you are most often practically forced to recapture, though there may be other legal moves to play on a queen down. So in Chess there are more moves that are legal, but obviously not optimal.
"This is why it is so small" ++ No, Losing chess is only 10^9 because it is a forced win.
"Nonsense is a sloppy term." ++ Semantics... call it moves that are clearly not optimal.
"Very few of those games are fully resolved"
++ 16% are by 3-fold repetition, 10% by reaching a table base draw, 74% by agreement.
"These are human decisions."
++ Yes, they agree on a draw, when neither side has any hope to win, e.g. in some opposite colored bishop ending. Likewise all decisive games are by resignation and none by checkmate.
It is pointless to continue for months until a 3-fold repetition is reached.
Likewise it is pointless to let the cloud engines calculate further in such positions.
That is another task for the good assistants: adjudicate clear draws.
"you advocate calling a non-solution a solution."
++ No, a solution is a solution, nothing more and nothing less. It is however stupid to spend time on obviously irrelevant positions. That is not sloppy, that is clever.
"Check the literature. (Eg for the weak solution of checkers or Losing Chess)."
++ For Checkers and Losing Chess humans also guided the computer.
"This paper nowhere supports ignoring a legal opposing move to a strategy based on heuristics"
++ As long as the move opposes to achieving the game theoretic value it should not be ignored. However, if it does not oppose to achieving the game theoretic value or if it opposes less, then it can safely be ignored.
1 a4 opposes less than 1 d4 or 1 e4, can be ignored
1 e4 e5 2 Ba6? does not oppose, can be ignored
Do not confuse rigor and stupidity.
"Positions may be irrelevant because they are unreachable or are not required for the proof."
"The rest can be proven to be irrelevant by an Alpha-Beta search"
https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
"A similar task could be to avoid dominated lines."
"the above search procedure was augmented by human input"
"there is still a considerable art (or lack of science) involved in the harder ones"
"our heuristics used in automation could be much improved"
https://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf
Two possibilities: either the entire peer-reviewed literature about weak solution of games is wrong, and they could have used hand-waving to ignore the large majority of the computation necessary, or @tygxc needs to learn something.
Heuristics are perfectly acceptably used TO SELECT MOVES FOR THE PROPONENT OF A STRATEGY. NEVER TO IGNORE LEGAL MOVES BY THE OPPONENT OF A STRATEGY.
Capitals to deal with deafness.
@5073
"Losing chess is very different to both checkers and chess, since its solution is dominated by forcing moves."
++ In Checkers it is the same. In Chess there are practically forcing moves, not legally forcing moves. If I capture your queen you are most often practically forced to recapture, though there may be other legal moves to play on a queen down. So in Chess there are more moves that are legal, but obviously not optimal.
"This is why it is so small" ++ No, Losing chess is only 10^9 because it is a forced win.
"Nonsense is a sloppy term." ++ Semantics... call it moves that are clearly not optimal.
"clearly" is a sloppy term, as used by you here. It has no literally no place in a rigorous weak solution.
"Very few of those games are fully resolved"
++ 16% are by 3-fold repetition, 10% by reaching a table base draw, 74% by agreement.
Right, so only 26% of these games are fully resolved (including the 16% that are generally effectively by agreement, by a choice to permit repetition (as in one of my fairly recent daily chess games on move 10. Neither of us were actually looking for a draw, we just wandered into a position where it was the prudent choice for both!
"These are human decisions."
++ Yes, they agree on a draw, when neither side has any hope to win, e.g. in some opposite colored bishop ending. Likewise all decisive games are by resignation and none by checkmate.
It is pointless to continue for months until a 3-fold repetition is reached.
Likewise it is pointless to let the cloud engines calculate further in such positions.
That is another reason why the good assistants are needed: to adjudicate clear draws.
"you advocate calling a non-solution a solution."
++ No, a solution is a solution, nothing more and nothing less. It is however stupid to spend time on obviously irrelevant positions. That is not sloppy, that is clever.
No, the entire peer-reviewed literature disagrees. That's the difference between rigour and hand-waving.
"Check the literature. (Eg for the weak solution of checkers or Losing Chess)."
++ For Checkers and Losing Chess humans also guided the computer.
So?
"This paper nowhere supports ignoring a legal opposing move to a strategy based on heuristics"
++ As long as the move opposes to achieving the game theoretic value it should not be ignored. However, if it does not oppose to achieving the game theoretic value or if it opposes less, then it can safely be ignored.
1 a4 opposes less than 1 d4 or 1 e4, can be ignored
1 e4 e5 2 Ba6? does not oppose, can be ignored
Do not confuse rigor and stupidity.
You have failed to find any basis to disagree with the point that I made: This paper nowhere supports ignoring a legal opposing move to a strategy based on heuristics
"Positions may be irrelevant because they are unreachable or are not required for the proof."
Neither of these EVER permit you to ignore a move by the opponent of a strategy. NEVER.
"The rest can be proven to be irrelevant by an Alpha-Beta search"
https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
SAME.
"A similar task could be to avoid dominated lines."
"the above search procedure was augmented by human input"
"there is still a considerable art (or lack of science) involved in the harder ones"
"our heuristics used in automation could be much improved"
https://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf
Not the slightest support for the erroneous idea that heuristics can be used to ignore legal moves by the opponent without destroying rigour.
You failed to find any support for the validity of "sloppy solution" (this term refers to something that is claimed to be a weak solution but patently isn't because it ignores legal opponent moves).
@5077
"clearly is a sloppy term, as used by you here.
++ Some moves require extensive calculations to determine if they are optimal or not.
Some moves are 'clearly' or 'obviously' not optimal. They can be dismissed immediately.
Giving up material with no compensation at all is clearly or obviously not optimal.
1 e4 e5 2 Ba6? is clearly or obviously not optimal.
I have shown it is a forced checkmate in 82, but that is not really necessary.
"Only 26% of these games are fully resolved"
++ Even 0% of the decisive games are fully resolved to checkmate.
Most draws are agreed because of a forced transition to a table base draw, or a forced 3-fold repetition e.g. perpetual check, or a known draw like opposite colored bishop endgame.
"one of my fairly recent daily chess games on move 10"
++ I am not taking about a daily game of @Elroch, but about the Finals of the World Championship 5 days/move, engines allowed, between 2 ICCF GM, SIM, IM who have qualified. They usually play on too long rather than not long enough.
...
there is a pawnless position with 8-fold symmetry
...
OK, I'll fall for it. Post one.
Let's just put this one to bed. Ignoring all the pieces, the kings do not permit that degree of symmetry. Two fold geometric symmetry is maximal. Geometrically, since the two kings are preserved under a symmetry, so is the line between them, and that leaves at most one flip available.
Spoilsport! He was probably still trying.
@5076
"NEVER TO IGNORE LEGAL MOVES BY THE OPPONENT OF A STRATEGY."
++ The definition says:
"weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
It does not say against all legal moves.
It implies an act of opposing against achieving the game-theoretic value.
"From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop.
Therefore, theoretically one of these two moves must be the best,
as no other first move accomplishes so much" - Capablanca
AlphaZero ranked the 20 possible first moves: Figures 5 & 31
https://arxiv.org/abs/2111.09259
If the 4 best moves cannot win for white, then the 16 worse moves cannot win either.
That is logic.
Thus 1 a4 can be dismissed and it is enough to consider 1 e4, 1 d4, 1 c4, and 1 Nf3.
"Should the opponent offer any material, even a Pawn, which in your estimation you may capture without danger, it is advisable to take the offered piece, even if as a result full development is retarded for one or two moves." - Capablanca
"Other things being equal, any material gain, no matter how small, means success" - Capablanca
1 e4 e5 2 Ba6? loses material. All other things are equal. White loses.
The move 2 Ba6? cannot be optimal and thus can be dismissed.
In the last 8 posts....not a word about chess.
And it wont get better.
But at least it got butter
Actually batter if you come from Wigan. They eat at the chippie.
But they're into bitter too.
@5076
"NEVER TO IGNORE LEGAL MOVES BY THE OPPONENT OF A STRATEGY."
++ The definition says:
"weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
It does not say against all legal moves.
It implies an act of opposing against achieving the game-theoretic value.
"From the outset two moves, 1.e4 or 1.d4, open up lines for the Queen and a Bishop.
Therefore, theoretically one of these two moves must be the best,
as no other first move accomplishes so much" - Capablanca
AlphaZero ranked the 20 possible first moves: Figures 5 & 31
https://arxiv.org/abs/2111.09259
If the 4 best moves cannot win for white, then the 16 worse moves cannot win either.
That is logic.
Thus 1 a4 can be dismissed and it is enough to consider 1 e4, 1 d4, 1 c4, and 1 Nf3.
"Should the opponent offer any material, even a Pawn, which in your estimation you may capture without danger, it is advisable to take the offered piece, even if as a result full development is retarded for one or two moves." - Capablanca
"Other things being equal, any material gain, no matter how small, means success" - Capablanca
1 e4 e5 2 Ba6? loses material. All other things are equal. White loses.
The move 2 Ba6? cannot be optimal and thus can be dismissed.
All those who have been involved in the peer-reviewed research in this field understand that "all opposition" includes all legal moves. That is why their many years of work are based on this notion, not on your second-rate alternative. They would be rightly contemptuous of sloppy reasoning with unreliable, vague heuristics that can have exceptions (and in some cases are known to have exceptions!) . Eg the solution of checkers was not completed by assuming all positions where one side was two pieces up was decided. 
@5077
"clearly is a sloppy term, as used by you here.
++ Some moves require extensive calculations to determine if they are optimal or not.
Some moves are 'clearly' or 'obviously' not optimal. They can be dismissed immediately.
Giving up material with no compensation at all is clearly or obviously not optimal.
1 e4 e5 2 Ba6? is clearly or obviously not optimal.
I have shown it is a forced checkmate in 82, but that is not really necessary.
You have not proved this.
"one of my fairly recent daily chess games on move 10"
++ I am not taking about a daily game of @Elroch, but about the Finals of the World Championship 5 days/move, engines allowed, between 2 ICCF GM, SIM, IM who have qualified. They usually play on too long rather than not long enough.
The class of situation is identical, and it is likely that specific game was perfect to an oracle.
The general situtaion is that two players reach a position where both believe not repeating moves may be inferior, so they do so and accept a draw. Their belief is of course not certainty and may be wrong.
It is a given that in time a powerful enough computer will be created that can solve chess, literally finding a path to a win from every possible position. And really, who cares? Unless you are Hans Nieman {just kidding, maybe} you don't use an engine when you are playing chess against an opponent. You have not solved chess, and never will, which for most of us is why we play. Not for the mathematics, but the art and beauty that can be found in the game. It is an addiction, our joy and pain simultaneously. Most of this thread is pointless argument in my opinion, but feel free to differ. Some people just get off on contention.
...
there is a pawnless position with 8-fold symmetry
...
OK, I'll fall for it. Post one.
The very large majority of positions:
As a consequence, I believe there are roughly twice as many positions as sets of symmetric positions.