Chess will never be solved, here's why

chess is good  and fun

At this point I'm joining @Optimissed in failing to understand what you mean by uniqueness. I thought it referred to diagram/side to move pairs where there are positions having different possible forward play. 

Perhaps you could explain again.

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e4 e5 e6 e7 e8 Re5 Hf3 Kn f3 are good moves 

There are several interesting partial orders on the set of positions.  These are based on 3 different properties of moves:

(1) legality

(2) non-blunder (i.e. keep the value the same)

(3) efficient optimality (i.e. non-blunder that wins fastest against most resilient defense if winning or loses slowest against optimal play if losing). This condition only differs from (2) when the result is not a draw.

A chosen one of these properties can be required for the moves of each of the two players in a sequence of moves (9 possibilities in total, of varying interest), and each of these 9 choices gives a partial order on the positions where:

P >=Q means there is a sequence of moves between the positions that satisfies the two chosen conditions for the two sides.

Thus each of those 9 choices leads to an equivalence relation on positions where

P == Q  if and only if P >= Q and Q >= P (i.e. there are sequences of moves in both directions with the chosen properties.

As an example, if the condition for white is efficient optimality and the condition for black is legality, you have the right criteria for seeking an efficient optimal strategy for white.

Such a strategy behaves very differently in winning positions to drawing ones. In the former, every move by either player moves between equivalence classes of positions (based on the distance to the objective). In the latter moves can dither around in an equivalence class indefinitely, but can also move irreversibly between equivalence classes. It is impossible, by definition, ever to return to an equivalence class even when drawing.

Of course when at least one player is not blundering, the repetititions of positions occur during the wandering within an equivalence class.

Don't repeat the same thing over and over, as if we don't read your posts or we were stupid, just answer the questions, please.

You have stated that countless time, no need to repeat yourself. You stated that you expect to search only 10¹⁷ positions out of 10³⁷ and in order to do that, you want to search only 4 candidates for White and one for Black at any move. Now, how do you determine those 4 top candidates and be sure the optimal move is among them? You invoked best-first algorithms as if they were some sort of magical tools. They are not. You stated that to be sure the optimal move is among those candidates, you would just leave SF calculate 60 hours per move. If I understand you well, it should do that at any increment of depth; otherwise, you cannot be sure that the top 4 candidates generated in leaf positions before the endgame tablebase are the best, since the engine did not calculate for 60 hours those positions, right? The closer the endgame, the less reliable would be those 4 candidates. So how many hours to select those 4 best options at any increment of depth? 1 position = 1 nanosecond is not the right answer, and neither 1 nanosecond per candidate move.

#2016

"So all you need to do now is decide whether you're going to have a 2 or 3 fold repetition rule."
++ It does not matter. I would use 2-fold for simplicity, but 3-fold is basically the same.

"That is rather like saying you can take the size of the state space to be 1, just check if there's a mate."
++ No, checking for checkmate, stalemate or 3-fold repetition is fast.
Generating daughter FEN from the mother FEN takes more time.

"If you're looking for a solution you need to provide an algorithm for perfect play."
++ Yes, the algorithm is brutal force calculation towards the table base.

"the moves the algorithm provides may necessarily be different" ++ No, it is the same.

"Are you saying that in all possible chess games there are almost no games that reach 50 moves without the capture of a piece or a pawn move, or are you saying that in practice players (who are invariably out of their depth in frustrated mates with more than 5 men on the board if tablebase access is not available) almost never invoke it."
++ Both: most GM and ICCF games are over before move 50. Even in those games that go beyond move 50 the 50-moves rule is almost never invoked as there is some compelling reason to capture or move a pawn. Even in those cases where the 50-move rule is invoked, it is nearly always while already within the 7-men endgame table base. I do not know any GM or ICCF game drawn by the 50-moves rule with 8 or more men. Do you know of any?

"If the latter what possible relevance is there to solving chess?"
++ The relevance is that GM and ICCF games at least look like ideal games with optimal moves. Some GM and ICCF games may in fact be ideal games that form part of the solution of chess.

"The Troitzky line concept is meaningless with the 50 move rule in effect."
++ The Troitzky line is very useful even in practice: when the blocked pawn is too far, there is no win.

"It makes a vast difference to the size of the state space and results in different solution algorithms for all three cases." ++ No, the state space stays the same.

"Well take it up with D.S.Nau and the other people producing papers on the subject."
++ It goes against all logic.
If you can do a task in x time, then you can do the same task in x+1 time.
If you can do a task in x+1 time, then you may be unable to do the same in x time.
The problem here is dependence on an evaluation function. KNN vs. KP is essentially +5. When the engine sees a way to win the pawn, it will evaluate that +6, though KNN vs. K is a draw. An engine will also prefer a +3 fortress draw over a +1 win. That highlights the inadequacy of an evaluation function: only brute force calculation to the end does it.

"Bully for the human! What's the relevance?"
++ The relevance is that if an unaided human can calculate 20-30 moves in a few hours, then it is plausible that a cloud engine in 5 years can calculate all the way to the end.

"There are 557914624 basic rules KNNKP positions"
++ So that is 0.557914624 seconds.

"Are you saying that SF14 checks whether it's exhausted all positions when it's evaluating and comes back with a message saying, "not going to do any more evaluating I've run out of positions"?"
++ You cannot check more positions than there are positions, unless you check the same position a billion times, which would be a waste. It is easy to compare a new FEN to the previously considered FEN.

"A solution is something theoretical."
++ The solutions to Losing Chess, Checkers, Nine Men's Morris, Connect Four are practical.

"Grandmaster games or ICCF games do not give you one."
++ GM and ICCF games are the closest we have to ideal games with optimal moves.
Some GM and ICCF games may be ideal games and thus part of the solution of chess.

It is a joke that you can prove anything by ignoring the moves that don't superficially appear to be in the top 4 candidates to a weak player.

Anyone who believes that does not know what "solving chess" means.

There are people who refuse to have particular things proven to them ...
but there's a converse too it seems.
People who insist that some things are proven - that are Not proven.

#2024

"Don't repeat the same thing over and over, as if we don't read your posts or we were stupid, just answer the questions, please." ++ The answer is yes. The explanation is for those who did not read or could not understand my previous wording.

"You have stated that countless time, no need to repeat yourself."
++ OK, but that is the answer to your question.

"You stated that you expect to search only 10¹⁷ positions out of 10³⁷ and in order to do that, you want to search only 4 candidates for White and one for Black at any move."
++ Yes, that is correct.

"how do you determine those 4 top candidates and be sure the optimal move is among them?"
++ I determine the 4 top candidates with the Stockfish evaluation function or a simplified version of it. I reckon the optimal move is among them by extrapolation: 1 error in 10^5 positions for the top 1 move, 1 error in 10^10 positions for the top 2 moves, 1 error in 10^15 moves for the top 3 moves, 1 error in 10^20 moves for the top 4 moves. That should do as I plan to consider only 10^17 moves.

"You invoked best-first algorithms as if they were some sort of magical tools."
++ Best first is a heuristic used in solving Losing Chess. For example 1 d4 and 1 e4 are better than 1 a4. Thus if 1 e4 and 1 d4 fail to win for white, then 1 a4 will fail too and needs no investigation. Likewise 1 e4 e5 2 Ba6 is the worst move. If 2 Nf3, 2 Nc3, 2 d4, 2 Bc4 cannot win for white then surely 2 Ba6 cannot win either and needs no investigation.

"You stated that to be sure the optimal move is among those candidates, you would just leave SF calculate 60 hours per move." ++ Yes, that is right.

"If I understand you well, it should do that at any increment of depth; otherwise, you cannot be sure that the top 4 candidates generated in leaf positions before the endgame tablebase are the best, since the engine did not calculate for 60 hours those positions, right?"
++ Yes, the optimal move must be among the 4. Not all 4 must be the best: occasionally top 1, top 2, top 3 will all be mistakes and only top 4 wil be optimal.

"The closer the endgame, the less reliable would be those 4 candidates."
++ No, the closer to the endgame the more table base hits and thus the more reliable.

@MARattigan - I guess we could debate the semantics of 'unique' ...  but that could simply be one of those situations where there's an argument where both parties actually Agree !  (whether both realize it or only one or neither realizes that)  
In other words it could be about what meaning is preferred for 'unique positions'.
Or is 'assigned' for 'unique positions'.

so people like chess and don`t like chess but they`ll try and e4 e5 e6 f6 f7 g8 d4 = good so chess is fun and like acting in a real army, let your friends go and login at chess.com play blizits learn lesson so go and tell them.

but`s what the anwser?

Best-first searches are not a novelty invented to solve antichess.

You don't understand, or you pretend to not understand? Don't be elusive. You answered everything but the last question, that I ask for the third time, I think: how many hours to select those 4 best options at any increment of depth? 1 position = 1 nanosecond is not the right answer, and neither 1 nanosecond per candidate move.

@tygxc is still trying to assign 'time per position' as a constant ??
and as a too small inadequate constant for 'solving' Too ?
He's still on that?
I only had to read @haiaku 's post - to be 'notified' about that 'possibility' ...  

I try to keep my mind open.  Objective to possibilities.
Would it not be funny if @tygxc is proven Right ...  about Everything ? 
Hey it is a possibility?
Chess puzzles and other things can teach us ...
'Things aren't always what they seem to be'.

Regarding 'solving' chess - another concept:
the status of positions - how many true categories are there ?
I'm not talking about the material situations there.
Like for example:  "in this position the supercomputer could not find a forced win for either side - after a default number of hours of time invested in it - but there's Much capacity to 'go wrong' in the position.  Neither side need offer a draw"
And that could have additional 'attributes'.
Like - the supercomputer was able to look at all possible ensuing move sequences - or - it didn't have time for that within the 'default' time assignment.  

I'm too lazy to read this

#2029
"You don't understand, or you pretend to not understand? Don't be elusive. You answered everything but the last question, that I ask for the third time, I think: how many hours to select those 4 best options at any increment of depth? 1 position = 1 nanosecond is not the right answer, and neither 1 nanosecond per candidate move."
++ I am not elusive. I guess I do not understand your question. Do you want to know the time to find 4 candidate moves in 1 node of the solution tree? What do you mean by the phrase 'at any increment and depth'? What precisely do you ask and even for the 3rd time? I am willing to think about it and come up with an answer. Please bear in mind that I have not solved chess, so I cannot tell you how I have done it. I have to think about how it can be done. I even refine my own thinking.