@11039
"weakly solving is very poor terminology. It could mean just about anything."
++ It has a very precise meaning and it is the accepted terminology in the field of solving games
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
Not quite happy with that proof.
Despite a long list of axioms, I failed to make 100% clear that at any stage, the legal moves are to place a piece at ANY remaining location (although this could be inferred by later reasoning, where it was assumed).
Thus it covers hex and tictactoe, but not connect4 or your game.
In addition, my statement of the assumptions does not make it clear enough that the symmetry of the game swapping the players does not have to send every location to itself. For tictactoe a symmetry preserving locations will do, for hex, you need to flip the boat.
That's what comes of recklessly recreating a proof from scratch (simple as it is)!
Since I don't see it anywhere, let me explicitly point out that the diversion into strategy stealing - interesting as it is - is of no detectable relevance to the solution of chess because most of the assumptions fail. Most simply, every move removes a piece from some location. I am not suggesting that anyone thinks otherwise.
@11043
"strategy stealing is of no detectable relevance to the solution of chess"
++ Strategy stealing is a way to prove the game-theoretic value of the initial position cannot be a black win, as white can steal the strategy of any tentative black win.
Anyway it is obvious from other considerations e.g. the initiative that Chess cannot be a black win and observed results confirm that.
@11039
"weakly solving is very poor terminology. It could mean just about anything."
++ It has a very precise meaning and it is the accepted terminology in the field of solving games
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
I say again - 'weakly solving' could mean just about anything.
The fact that some organizations assign a particular meaning or meanings doesn't change that.
Its a very bad choice of words.
Better terminology could be used.
Stands.
--------------------
And persons such as tygxc will try to relate such terminology to promoting ridiculous concepts such as 'taking the square root' of gigantic numbers of possible positions to ridiculously reduce the number.
While persons such as Elroch and Dio and Marattigan patiently continue to constantly refute tygxc's 'weakly solving' claims.
If I remember correctly mpaetz has too. And I believe others have also.
While O will simply see the exchanges as trolling opportunities for him.
And will continue to deludedly see the forum as his property while it is actually flypaper he is stuck in. He is 'stuck' here.
"And will continue to deludedly see the forum as his property while it is actually flypaper he is stuck in. He is 'stuck' here"-playerafar
At a certain point some pepple have to stop yapping unless it is an actual problem you can solve and that does not include only optimissed you complain about others troll so much here if anything it is just as bad or worse than optimissed
But can't answer simple questions that even are not that personal (they don't reveil name,year you were born ,etc)
But eh whatever I guess some people yap on this forum more than optimiss
Ps:you can call me a hypocrite if you want but it is not going to change a thing
@11045
"taking the square root of gigantic numbers"
++ It should be obvious that weakly solving a game requires less than strongly solving.
Schaeffer weakly solved Checkers with a proof tree of 10^7 positions each representing a search of 10^7 positions, i.e. 10^14 positions. Checkers has 5*10^20 legal positions.
Take the initial position of Chess. White has 20 legal moves, black has 20 legal replies.
That gives 20 * 20 = 400 positions to start strongly solving.
Weakly solving only needs 1 black reply to each of the white moves, i.e. 20 * 1 = 20 = Sqrt (400) positions.
That explains where the square root comes from.
The solution of checkers required 1000 years of CPU time.
Note carefully that 10^14 is the ~(2/3) root of 5e20, not the square root. The square root idea comes from a very rough approximation for a game where effectively no position reachable on move N can be reached on a later move (I.e. the game is highly directional, and avoided positions can never be returned to). This assumption fails for both checkers (once kings are on the board) and even more for chess (where only pawn moves, captures, castling and loss of castling rights are irreversible, leaving all moves with B/N/Q not so, and the same for all moves with K and R that don't lose castling rights).
And no, there is no valid reason why chess is easier (because you GUESS that it probably won't matter if you fail to do most of the required analysis).
@11039
"weakly solving is very poor terminology. It could mean just about anything."
++ It has a very precise meaning and it is the accepted terminology in the field of solving games
'weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition'
I say again - 'weakly solving' could mean just about anything.
The fact that some organizations assign a particular meaning or meanings doesn't change that.
Its a very bad choice of words.
Better terminology could be used.
Stands.
And utterly irrelevant. As irrelevant as saying you hate the word elephant.
The purpose of words is to communicate, not to be aesthetically pleasing. They are labels only. And the best way to communicate about a technical topic is to use the established terminology, only extending this where necessary.
@11043
"strategy stealing is of no detectable relevance to the solution of chess"
++ Strategy stealing is a way to prove the game-theoretic value of the initial position cannot be a black win, as white can steal the strategy of any tentative black win.
This indicates ignorance of the rules of chess and/or the way they relate to the strategy-stealing argument.
The crucial point you miss is that whatever white's first move is, it offers new possibilities for black at some point in the game. In the strategy-stealing argument this is not so. No new possibilities are given to the other side, merely a subset of the possibilities without the additional first move.
Say for example, white chooses 1. a3 as his first move and then copies black's strategy. At some later time black plays b4 and then bxa3. White then has nothing to follow from the stolen black strategy, as without a3 having been played this could not have happened.
You would have done better to have read my helpful post where I explained why the strategy-stealing argument has no relevance to chess.
...
Take the initial position of Chess. White has 20 legal moves, ...
If you adhere to the FIDE laws, then strictly speaking White has 40 legal moves in the initial position.
Art 4. allows a player having the move to move only his own pieces.
4.3 Except as provided in Article 4.2, if the player having the move touches on the chessboard,with the intention of moving or capturing:
4.3.1 one or more of his own pieces, he must move the first piece touched that can be moved
4.3.2 one or more of his opponent’s pieces, he must capture the first piece touched that can be captured
because if he touches an opponent's piece he must capture it.
But that applies only to a player having the move.
In view of art. 1.3
1.3 A player is said to ‘have the move’ when his opponent’s move has been ‘made’.
That does not apply to White in the initial position when no moves have been made, therefore White can make any of 20 legal moves with the black pieces as well as 20 legal moves with the white pieces.
@11051
8 pawns * 2 moves + 2 knights * 2 moves = 16 + 4 = 20 moves
@11051
8 pawns * 2 moves + 2 knights * 2 moves = 16 + 4 = 20 moves
16 pawns * 2 moves + 4 knights * 2 moves = 32 + 8 = 40 moves
@11050
"for example, white chooses 1. a3 as his first move and then copies black's strategy"
++ That is no strategy stealing. 1 a3 has consequences.
However, if 1 e4 c5 were a black win, then 1 c3 e5 2 c4 would be a white win.
If 1 d4 Nf6 2 c4 g6 3 Nc3 d5 were a black win, then 1 Nf3 d5 2 g3 c5 3 d3 Nc6 4 d4 would be a white win.
White can lose a tempo by moving a pawn 1 square and then a 2nd square.
Black can also lose a tempo.
White can lose 2 tempi by moving a knight to and fro.
Black cannot copy that and still win because of 3-fold repetition.
White can lose tempi by moving a bishop or a queen multiple times along a diagonal.
Black cannot copy that and still win because of 3-fold repetition.
The hypothesis of a forced black win thus is inconsistent.
@11050
"for example, white chooses 1. a3 as his first move and then copies black's strategy"
++ That is no strategy stealing. 1 a3 has consequences
Correct. And the same is true of ALL the other 19 legal white first moves. Hence there is no strategy stealing for chess, refuting #11044
...
Take the initial position of Chess. White has 20 legal moves, ...
If you adhere to the FIDE laws, then strictly speaking White has 40 legal moves in the initial position.
Art 4. allows a player having the move to move only his own pieces.
4.3 Except as provided in Article 4.2, if the player having the move touches on the chessboard,with the intention of moving or capturing:
4.3.1 one or more of his own pieces, he must move the first piece touched that can be moved
4.3.2 one or more of his opponent’s pieces, he must capture the first piece touched that can be captured
because if he touches an opponent's piece he must capture it.
But that applies only to a player having the move.
In view of art. 1.3
1.3 A player is said to ‘have the move’ when his opponent’s move has been ‘made’.
That does not apply to White in the initial position when no moves have been made, therefore White can make any of 20 legal moves with the black pieces as well as 20 legal moves with the white pieces.
Im presuming this is ironic, but the rule States white moves first so it would bo 0 legal 1st moves for black 
@11048
"The solution of checkers required 1000 years of CPU time."
++ Mostly to generate the 10-men endgame table base: from 1989 to 2005.
The forward proof of Checkers lasted from 2005 to 2007 i.e. 2 years.
The 17 ICCF World Championship finalists used an estimated
17 finalists * 16 CPU / finalist * 2 years = 544 CPU years
A CPU anno 2024 is more powerful than a CPU anno 2007.
Chess engines are now more efficient than Chinook was for Checkers.
"10^14 is the ~(2/3) root of 5e20, not the square root" ++ Yes, a property of checkers.
"there is no valid reason why chess is easier"
++ Chess is harder: 10^17 instead of 10^14 is 1000 times harder.
Even Schaeffer used game knowledge: 'From the human literature, a single “best” line of play was identified and used to guide the initial foray of the manager into the depths of the search tree. Although not essential for the proof, this is an important performance enhancement'
@10981
"we have 4 cases and 3 definitions"
++ The generally accepted definitions from peer reviewed literature and by the authority in the field of games solving Prof. Van den Herik are:
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.
Games solved: Now and in the future
Some trolls try to confuse with their own personal definitions.
An example of ultra-weakly solved is Hex.
Examples of weakly solved are: Checkers (8*8) , Nine Men's Morris, Losing Chess.
Examples of strongly solved are: Chess for up to 7 men and lost castling rights, Connect Four, Draughts (10*10) with up to 7 men, Nim
That is very interesting but I think you run into a problem. Conect 4 has an huge amount of positions. And we can not prove we have a wining strategy for all of then
@mrhjornevik
No not ironic, just pointing out a law in the flaws.
White moves first but, according to the laws he is not defined as "having the move" when he makes the first move.
The only rules that specify a player should move only one of his own pieces are the art. 4 rules quoted and they specifically apply only to a player "having the move".
So on his first move White is allowed to move a black piece (g7-g5 might be worth exploring).
Anyway - nobody in the forum seems to be contesting for a position that chess would someday be Solved in the usual proper and thorough meaning of the word.
So therefore - since the opening post much of the conversation has revolved around pushing variations of something named with the unfortunate coined terms 'weakly solved' or 'weakly solving'.
I have zero complaints about this.
Pointing out the negatives of the terminology is not a complaint.
--------------------------------------------
If the forum had started with the topic name like this:
'What does 'weakly solved' mean in the context of 'solving' the game of chess and can the term be realistically applied to the entire game?'
then would the discussion have been different?
Somewhat.
Would a new forum be started with that or similiar title?
Unlikely.
Because nobody cares to any degree about same except people in relevant professional projects connected to such.
And those people aren't here.
-----------------
in a chess video i viewed yesterday about Kasparov playing a chess game against 'the rest of the world' the subject of the chess tablebases came up in the video because a 7 man position had been reached.
It was remarkable because apparently a move that Irina Krush had suggested was not received by email somehow and Kapasparov was then able to win the game.