btw did you know that he got banned? ):
Chess will never be solved, here's why
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Oct 24, 2022
0
#4886
It's almost the same game if the purpose is to capture the king. The reason it's not is that stalemate would become a win.
@6488
"As chess players willing to take a good bet we could." ++ You do not understand the difference between probabilistic and deterministic. You can bet on probabilistic subjects, like if player A can win positions 1 Nh3 or 1 e4 e5 2 Ba6? against player B or not. As for 1 Nh3 or 1 e4 e5 2 Ba6? drawing, winning, or losing it is deterministic, either or, there is neither probability nor betting.
"game theorists trying to solve chess definitely cannot" ++ They definitely can and should. Incorporating game knowledge is beneficial in solving a game - van den Herik.
"These results are unproven" ++ It is proven that 1 Nh3 cannot be better than 1 Nf3, see above. It is proven that 1 e4 e5 2 Ba6? loses for white: a checkmate in 82, see above.
"it is unproven that chess is a draw"
++ It is proven that chess is a draw: there is evidence compelling the mind to accept the truth or fact. There is a deductive argument that a single tempo is not enough to win as well as inductive evidence from millions of human and engine games, especially from ICCF.
"it was unproven that checkers was a draw (until it was proved)."
++ The weak solution of Checkers uses only 19 of the 300 openings. That solution prunes away irrelevant lines, so a weak solution of Chess can prune away 1 Nh3, 1 a4, and 1 e4 e5 2 Ba6?
On one side you say 1 e4 e5 2 Ba6? wins for white despite being a whole bishop down.
On the other side you say the initial position wins for white because of a single tempo.
That makes no sense. In the initial position a bishop or a pawn is enough to win, a tempo is not.
Oct 25, 2022
0
#4888
Elroch wrote:
It's almost the same game if the purpose is to capture the king. The reason it's not is that stalemate would become a win.
Not always
(You cannot queen a tempo, but an extra pawn is enough to win. - Confucius.)
Oct 25, 2022
0
#4889
Yes, I was going to draw attention to that distinction, but edited it out.
But it was unforgiveable not to be precise in saying "most stalemates would become losses" or "all stalemates where the player has a move which would otherwise be legal but moves into check would become losses". So kudos for taking me to task for that. 
Oct 25, 2022
0
#4890
Optimissed wrote:
Elroch wrote:
It's almost the same game if the purpose is to capture the king. The reason it's not is that stalemate would become a win.
I never could understand this supposed difference. The game ends when the king is attacked and has no means of escape. Probably for historical reasons, the king is never removed from the board. The game ends when either king is attacked and has no means of escape.
Stalemate cannot be a win for either side because the rules state that each side makes alternate moves. In a stalemate, that's impossible so the game ends inconclusively because neither king is attacked and the game cannot progress. It really is quite simple. Like my mind. Clear and simple.
Yes. The presumption is to remove the rule that you are not allowed to be in check after a move (this is necessary to make it possible for the king to be captured) and to permit the capture of the king (not actually a new rule since the possibility cannot arise in normal chess).
After this all stalemates where the side to move has a move which would be legal but moves into check become losses (because the move can be made and the opponent then captures the king) but, as MARattigan correctly pointed out, stalemates where the side to move has no legal move, even one that would move into check, remain draws unless you add a further rule (that not having a legal moves loses. Or that this wins!).
Oct 25, 2022
0
#4891
Yes, I favour Putin being captured rather than merely checkmated. And then melted down and turned into something useful.
Summary
Weakly solved means that for the initial position a strategy has been determined
to achieve the game-theoretic value against any opposition. [1]
The game-theoretic value of a game is the outcome when all participants play optimally.[1]
Optimal play is play without errors.
An error (?) is a move that changes a game from drawn to lost, or from won to drawn.[2]
A blunder or double error (??) changes a game from won to lost.
A strategy can be moves like Checkers,[3] or rules like Connect Four,[4] or a combination.
It is beneficial to incorporate knowledge into game solving programs.[1]
Chess knowledge can be acquired from the Laws of Chess only. [5]
The objective of Chess is to checkmate the opponent.[6]
A direct attack on the king can succeed only if the opponent does not play optimally.
Queening a pawn is more feasible to achieve checkmate.
We know from gambits that 3 tempi in the initial position are worth 1 pawn.[7]
1 tempo in the initial position is not enough to win: a pawn can queen, a tempo not.
Millions of human & engine games confirm that Chess is a draw.
In the last 10 ICCF world championship finals: 1469 games = 1177 draws + 292 decisive.[8]
Of the 1177 draws 1140 are perfect games with optimal play from both sides.
Starting from the 10^44 legal positions [9] none of the 56011 legal positions in a sample of 1 million can result from optimal play by both sides. Gourion’s 10^37 [10] is a better estimate, but In a sample of 10000 [11] none can result from optimal play either. That leaves 10^37 / 10000 = 10^33 positions. Multiply by 10 to include positions with 3 or 4 queens: 10^33 * 10 = 10^34.
Weakly solving Chess calls for a strategy, i.e. one strategy only.[1]
On w white moves not w black responses each, but 1 black response only.
w * 1 = Sqrt (w * w)
Thus Sqrt (10^34) = 10^17 positions relevant to weakly solving Chess.
Checkers has been weakly solved with 10^14 positions [3] and Losing Chess with 10^9 positions.[12] Checkers has been solved with 19 of the 300 openings: 200 transpositions and 81 pruned.
Cloud engines calculate a billion nodes / s.[13] Thus 3 such engines calculate in 5 years:
10^9 nodes / s / engine * 3 engines * 3600 s / h * 24 h / d * 365.25 d / a * 5 a = 4.4 * 10^17 nodes
A diagram is the location of the men on the board.
A position is a diagram + side to move + castling rights + en passant flag.[6]
A node is a position + evaluation + history.[13]
Thus 3 engines exhaust in 5 years all 10^17 relevant positions and weakly solve Chess.
Chess can be weakly solved in 5 years, but needs 3 million $ to hire 3 grandmasters and rent 3 engines.
'Give me five years, good assistants and the latest computers
- I will bring all openings to technical endgames and "close" chess.' - GM Sveshnikov [14]
References:
[1] Van den Herik https://www.sciencedirect.com/science/article/pii/S0004370201001527
[2] Hübner, Twenty-five Annotated Games, Berlin, 1996, pp. 7–8.
[3] Schaeffer https://www.science.org/doi/10.1126/science.1144079
[4] Allis http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf
[5] McGrath et. al. https://arxiv.org/pdf/2111.09259.pdf
[6] FIDE Laws of Chess https://handbook.fide.com/chapter/E012018
[7] Capablanca A Primer of Chess https://archive.org/details/aprimerofchess/page/n47/mode/2up
[8] ICCF WC Finals https://www.iccf.com/tables
[9] Tromp Ranking of Chess positions https://github.com/tromp/ChessPositionRanking
[10] Gourion https://arxiv.org/pdf/2112.09386.pdf
[11] Tromp https://github.com/tromp/ChessPositionRanking/blob/noproms/sortedRnd10kFENs
[12] Watkins https://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf
[13] NPS - What are the "Nodes per Second" in Chess Engine Analysis
https://chessify.me/blog/nps-what-are-the-nodes-per-second-in-chess-engine-analysis
[14] Sveshnikov https://e3e5.com/article.php?id=1467
Oct 28, 2022
0
#4893
tygxc wrote:
Weakly solved means that for the initial position a strategy has been determined to achieve the game-theoretic value against any opposition.
(Correct emphasis).
Oct 28, 2022
0
#4895
Pre-selecting only a limited number of opening possibilities invalidates any claim to have "solved" chess. Certainly, should such an enterprise find a forced win for either side, that would be a valid starting point for a more thorough evaluation of that strategy, following all the lines that limiting the starting point to ICCF draws and looking at the lines that the committee of GMs decided to ignore along the way. Eliminating well over 1/2 the possibilities eliminates any claim to a definitive proof.
@6513
"should such an enterprise find a forced win for either side"
++ That is impossible. As explained Chess is a draw.
"Eliminating well over 1/2 the possibilities eliminates any claim to a definitive proof."
++ Eliminating possibilities that are proven worse is allowed.
1 a4 cannot be better than 1 e4 or 1 d4
1 Nh3 cannot be better than 1 Nf3
1 e4 e5 2 Ba6? loses to checkmate in 82 and does not need to be looked into
++ Let us assume I had 20 books for sale:
1) How to draw against 1 d4
2) How to draw against 1 e4
3) How to draw against 1 Nf3
4) How to draw against 1 c4
...
19) How to draw against 1 f3
20) How to win against 1 g4?
Books 1-4 may sell well, but nobody would buy books 17-20.
The same if I were to submit a paper to a scientific journal:
"Chess: 1. d4 black draws" would be accepted,
but "Chess: 1. g4? black wins" would be rejected for lack of relevance
Oct 29, 2022
0
#4897
Optimissed wrote:
Elroch wrote:
It's almost the same game if the purpose is to capture the king. The reason it's not is that stalemate would become a win.
Forgive me for pointing it out but in stalemate, the king isn't captured, Elroch. That's a logical error. In stalemate, the king is confined to one square only but the king is safe.
Chesskingloop is also wrong.
If the rule against playing a move that would permit the king to be captured were removed (essential in order to make capturing the king possible at all), the larger class of statemates would have a legal move which would then allow the capture of the king.
The smaller class of stalemates (I doubt one has ever been seen in competitive play) would still have no legal move.
Oct 29, 2022
0
#4898
As I said, to consider any variant of chess where the king can be captured, the essential first step is to change the rules so that it is possible to reach a position where the king can be captured. The natural way to do this is to remove the rule that moves doing this are illegal (this rule primarily protecting players against the most heinous of errors, to leave the king in mortal danger).
(Aside: it used to be traditional not only to say "check" to warn a player of a threat to their king, but also "gardez" warning of an attack on the queen. )
Oct 29, 2022
0
#4899
tygxc wrote:
@6513
"should such an enterprise find a forced win for either side"
++ That is impossible. As explained Chess is a draw.
"Eliminating well over 1/2 the possibilities eliminates any claim to a definitive proof."
++ Eliminating possibilities that are proven worse is allowed.
Exactly the kind of pre-judgements that I maintain makes any "solution" reached thereby entirely unconvincing. If the goal in "solving chess" is to discover whether the game can be won by force by either player from the starting position against all possible counterplay, your method is inadequate. Simply declaring that vast numbers of possible lines "are proven worse" without any attempt to prove that is nonsensical.
Yes, I can see. I suppose it makes the logic easier but I wonder if it's accurate.
I'm sorry, but your thinking doesn't make sense. A definition only needs to be valid, there is no notion of "accuracy".
Given the set S of legal states s in chess where white is to move, each s of which has a non-empty set of legal moves M(s), a deterministic strategy for white is a mapping f from S where f(s) is always a member of M(s).
That definition is valid because it determines whether something is a deterministic strategy for white or not.
I think I know what you're saying. It's a way of defining determinism itself. However, determinism isn't shown to define chess and so there seem to be double-standards at play here. You're saying that you can define something into existence. This may be acceptable to mathematicians but then that existence only holds for the specific paradigm and only works if it can be cancelled out at the other end. But here you're making a statement, regarding the nature of chess, which is similar in type to those you condemn from tygxc.
It's far from convincing. You would have to do much better than that.
No, you don't understand.
The definitions of deterministic strategy was made in order to be able to define the value of strategies and positions.
The definition of value of a position was made in order to be able to state a proposition like:
"The value of the position after 1. Nh3 is less than or equal to the value of the position after 1. Nf3".
This is the routine way in which mathematics (and very closely related subjects) are done. You can't shortcut it except if everyone is so familiar with the topics that it is obvious without being said. That is not true in this forum!