@4893
"He claims it is achieved by ignoring all moves that have an evaluation below some number."
++ No, that is not what I said. The evaluation plays no role.
First it is obvious that weakly solving requires far less positions than strongly solving.
Losing Chess has been solved with 10^9 positions only, not 10^44.
"Next to brute-force methods it is often beneficial to incorporate knowledge-based
methods in game-solving programs."
https://www.sciencedirect.com/science/article/pii/S0004370201001527
Knowledge:
1 a4 opposes less to the draw than 1 e4 or 1 d4
1 Nh3 opposes less to the draw than 1 Nf3
1 c3 opposes less to the draw than 1 c4
1 e4 e4 2 Ba6? loses by force and does not oppose to the draw
1 e4 e5 2 Nf3 Nc6 3 Nd4?, 3 Nxe5?, 3 Ng5?, 3 Nh4? do not oppose to the draw
1 e4 e5 2 Nf3 Nc6 3 Ng1 does not oppose to the draw: 3...Nb8 draws
Chess will never be solved, here's why
my gooooooooddddddddddddddddddrd
Says the 1 day old sockpuppet.
It's a little bit like a gnat commenting on a picnic. Do you really deserve to complain?
The state space of the version of chess with a repetition rule (traditionally 3-fold) is enormous whether there is or is not a rule like the 50 move rule.
The reason is that what has happened matters, not just the current position. Indeed, you need to keep a visit count for all positions that have been visited and that could be reached again by a legal sequence of moves. So the state space consists of objects that consist of a position (a la FEN) plus a list of other positions that have the property that the current position can be reached from them and they can be reached from the current position (another way to put this is that they are all in the same equivalence class as the current position, according to the partial order that is defined as the existence of a legal path between two positions).
Another way to define this state space is as a set of equivalence classes of partial games. The equivalence relation is that the current position is the same and the set of counts for all previous positions that could be reached again in the future of the game is the same.
Anyhow, this state space is mindbogglingly enormous. I have never even seen an estimate of it, but its size clearly has thousands of digits in base 10, compared with the mere 45 digits for the size of the state space of basic chess.
There is a simplification that helps to get around the size of the state space. I assert that if there is a strategy that can reach a decisive result from a position, there is a strategy that can reach this result without ever repeating a position or allowing the opponent the opportunity to repeat the position. If this claim is true, solving the game becomes equivalent to solving a version of chess where any repetition of position is illegal (and if there are no legal moves it is a draw).
Actually that doesn't help much - we still need the list of previous positions that are reachable.
I do think that you and I agree that solving chess is more/less impossible. My view is that is so unless, by means of Real AI being developed some time in the future, it is found possible to write a set of algorithms that can reduce chess to mathematic equations which can then be solved. And that's a bit too pie-in-the-sky.
my gooooooooddddddddddddddddddrd
Says the 1 day old sockpuppet.
It's a little bit like a gnat commenting on a picnic. Do you really deserve to complain?
Me boring? Good grief, the man is a duffer.
Think I know who that is too.
If I might interject, I think that perhaps you are thinking that without the 50 move rule, endless repetitions can occur and so chess is therefore infinite and could not be solved...but in terms of solving, an endless repetition is simply a draw, and the calculations move onward.
THANK YOU! Someone finally addressed my question in a meaningful and helpful way. Your response sounds reasonable and my first inclination is that it's likely correct.....but I'm gonna think about it some more.
I do think that you and I agree that solving chess is more/less impossible. My view is that is so unless, by means of Real AI being developed some time in the future, it is found possible to write a set of algorithms that can reduce chess to mathematic equations which can then be solved. And that's a bit too pie-in-the-sky.
I think we need to be careful here. I'm not comfortable with "more/less impossible". There's a big difference between something actually being impossible and being beyond human capability, and it appears we're conflating the two.
There's a theorem that states that it's impossible to create a map such that more than 4 colors would be required to assure that no area on the map would share a boundary with another of the same color. It's pretty simple to see that this is true, but no proof has ever been found, so we can't say it's impossible. It's just a theorem, not a proven fact....as intuitive as it may be. Proofs are tricky. You may think you know something and it may in fact be true, but unless there is an agreed on proof, claiming it as true is risky. That's why I'm so reluctant to accept the solvability of chess. stickler got me over one major hurdle a few posts ago....but I'm still a bit wary.
No, you missed my point entirely. As long as we understand that infinity is a notional idea, it is also possible to use that idea metaphorically.
It obvously isn't claptrap, since it's a point of view, which is completely valid in a World that is not dominated by one ideational paradigm at the expense of all others.
No, some things are large enough to be "close enough" to infinite to be considered so for practical purposes, or infinitesimally small enough to be indistinguishable by human standards. Others literally have no end, ever. Your concept conflates the two.
As the point being discussed was whether or not chess is a finite game, the difference is material. There is indeed a limited number of positions in which the pieces can be placed on the board. (Many would be impossible to reach following the rules of play, further limiting the number of actual positions needing to be considered in a solution to the game.) Chess is a finite game as far as the calculations posters here are proposing.
If I might interject, I think that perhaps you are thinking that without the 50 move rule, endless repetitions can occur and so chess is therefore infinite and could not be solved...but in terms of solving, an endless repetition is simply a draw, and the calculations move onward.
THANK YOU! Someone finally addressed my question in a meaningful and helpful way. Your response sounds reasonable and my first inclination is that it's likely correct.....but I'm gonna think about it some more.
Sorry, I for one didn't realise it was a question.
He's right ... a repetition is only a repetition if the same position occurs with the same person to move, same castling rights etc. Therefore, as he points out, it cannot affect the end result. If neither have nothing better than repetition then it's a draw with or without the repetition rule. Trying to flag someone in a drawn position is clearly wrong;.
That also illustrates very clearly that FIDE's interpretation of the "insufficient material rule" is deeply mistaken, on the same premises as not flagging someone in a drawn position. Evidently, both sides may have mating material. The sooner FIDE is kicked into touch or otherwise got rid of, the better.
i wonder how good the world would be if elroch and optimissed didnt waste their time and energy arguing over pointless topics
Oh go away, we're vacuuming.
cope
also applies to you.
It's always funny to watch people complain about threads they have the ability to skip by. Do you habitually punish yourself? It takes a certain lack of self awareness.
Provide some meaningful content of your own...bonus points if it is actually chess related.
You know chess will be solved.
It definitely will be.
We see all these movies about cyber technology.
Maybe, we'll develop super computer intellects and actually solve chess.
Losing Chess has been solved with 10^9 positions only, not 10^44.
What does this have to do with the solvability of chess? Different rules, fewer possible moves.
i wonder how good the world would be if elroch and optimissed didnt waste their time and energy arguing over pointless topics
I half agree!
[snip]
chess is a finite game
Can you support this?
If I might interject, I think that perhaps you are thinking that without the 50 move rule, endless repetitions can occur and so chess is therefore infinite and could not be solved...but in terms of solving, an endless repetition is simply a draw, and the calculations move onward.
In the case of tablebases, they are built going backwards from checkmate. So, you cannot ever logically reach an endless repetition in a regression like this. We're at 7 man tablebases right now, so for 7 pieces or less, if the position is *not* forced mate and not in the tablebase, it is therefore a draw. Draws are inferred by exclusion.
When thinking about the logic of generating tablebases I came to the conclusion that at each pass of the algorithm, as you add the evaluation of more positions further from mate, at some point you have a step when no more are added. At this stage all the unevaluated positions must be draws. (The reason being that every mate in N leads to at least one mate in N-1 on the next move, so if there are no mate in N, there can be no mate in more than N). Is this convincing?
I also thought along the lines of btickler for a version of chess with no repetition/50 move rules, that for mathematical purposes alone you can extend to infinite games and say an infinite game is a draw. This could be made finite without changing anything significant about the value of starting positions (I assert) by adding either a very large N-move rule or a repetition rule.
@4891
"I have never even seen an estimate of it"
I have shown one: The number of possible chess games lies between 10^29241 and 10^34082
https://wismuth.com/chess/longest-game.html
However, all of that is irrelevant. The 50-moves rule plays no role at all in solving chess.
Solve chess without the 50-moves rule. The same solution applies with the 50-moves rule.
We have over 1000 perfect games with optimal play from both sides: ICCF WC draws.
In none of these was the 50-move rule invoked.
Average game length was 39 moves with standard deviation 14, minimum 16, maximum 102.
7-men endgame table base wins were allowed including those that exceed 50 moves without capture or pawn move, but no 7-men endgame table base wins were claimed.
7-men endgame table base draws were commonly claimed in 10% of games.
All this is copy-pasted, isn't it. Therefore you never readjust your views, even when mistakes are pointed out.