Chess will never be solved, here's why

A large part of the reason the thread is, as @Optimissed put it, going round and round in circles is that there is not general agreement on what is meant by many of the terms that are in frequent use.

Including, but not necessarily limited to; "chess", "solved", "weakly solved", "strongly solved", "position", "diagram" and "proof". 

As far as the term "chess" is concerned, there are many candidates. FIDE define several games; a basic rules game and various flavours of game with competition rules added. There are also  games played according to ICCF rules or TCEC rules and versions defined by USCF that many American readers would understand as chess.

With my meaning of "solved" I don't believe any of those versions can be solved, but I'll leave that for a different post.

As regards "position", your meanings are, I believe, different from those of most of the people contributing. Also different from the meaning in any of the documents that have been linked to (including the FIDE laws). 

You actually have two different meanings in your above post. In the first definition you specify, "One piece per square" and (subsequently implied) "legal possible arrangements ", but those specifications are omitted in your second definition (the latter specifically).

The difference is that "positions" with your first meaning would not include "positions" with your second meaning that could legitimately occur in a game such as the one below.

Notice I've edited out the White square in the lower right hand corner indicating that it's White's move (compared with the similar image I posted here) to conform with your definition. (Though the "position" in your second sense could legitimately occur in a game only if it's White's move.)

Nor "positions" in your second sense that couldn't legitimately occur in a game such as the following:

Obviously which of the definitions you choose would affect the number of "positions" - finite in the first case, unlimited in the second.

But either of your definitions would fall under what most people here, and some of the linked documents, refer to as diagrams, not positions.

I would say that it is inconvenient for most purposes to have the term "position" refer to anything that doesn't fully define what play is legitimate from the position. With your definitions it is not possible to say exactly what play is legitimate from any "position".

You are talking about playing chess, not solving chess. Your whole mode of thinking is wrong.

"Moves that do not even try to win for white can safely be ignored, like 1 e4 e5 2 Ba6 or 1 a4."
I disagree.  1) a4 has insufficient losing chances and more than sufficient winning chances - that it cannot be ignored.

For threats of chekmate in one move, some lines can be pruned, but that requires some computations too, so it would not have a great impact on the whole search for a solution of chess.

#2983
"You are talking about playing chess, not solving chess."
++ No, on the contary when playing chess it is sometimes advisable to play an inferior move, like Lasker often did and like most simul players regularly do.
Weakly solving chess is about determining a strategy from the initial position to achieve the game-theoretic value against any opposition. If the strategy is proven against the stiffest opposition, then the weaker moves that do not even oppose to the draw become trivial.

I have provided a paper that clearly contradicts the interpretation of "any opposition" you give.

@MARattigan
I don't keep repeating maximum of one piece per square because that is to be understood.
For example - I also don't specify that the 64 squares are in one plane.
In an 8x8 arrangement.
Nor that knights move in a particular L shape.

Regarding 71 digit number - when I re-looked up 13 to the 64th power on the web - over forty years later.
it gave a single digit coefficient followed by 10 to the 71.
I'm going to concede that one to you.
72 digit number.  10 squared is a three digit number.
So 1 has to be added to the length of the number.
I'll concede that one to you ... Literally.  Pun intended.

As for whoever complaining about 'conversation going around in circles' we're coming up on 3000 posts now - so whoever is so unhappy with the conversation has an odd way of showing it by making it a point to be present and posting.
Suggestion:  if more progress is desired - then whoever could try refraining from imposing narrowness of view with authoritative thoughtlessness.
Didn't he imply something about 'asking for proof' that you very quickly Crushed?
He's invested a lot of posts in personalization and then complains about 'going in circles' ...
But that hasn't been totally useless because others have made it a point to put their postings in much better ways than that. 

Yes.  And I'll be curious to see how ty sidesteps or parries or ignores.
Stands. 
(While whoever complains about 'going in circles'. 
While he's spamming/trolling at the same time. )

'Weakly solving chess' could be about anything anybody wants it to be.
The latitude built into the word 'weakly' is so broad - that it could mean - 'chess is a draw if nobody makes a mistake - but with possible exceptions because nobody has ever conclusively proven that'

Maybe ty will get out of responding - by somebody else posting for him.
With 'narrow and inaccurate authoritative view' getting confused with 'focus'. 

A maximum of one piece per square square is to be understood only if you make it explicit that that is part of your definition or that your definition refers only to positions that can legitimately occur in a game. Your phrase 

Without regard to en passant nor castling nor 50 move rule nor repetitions of move nor 'how it got there' and initially - not even whose move it is nor even if its legal or not.

in your second definition seems to mean the opposite.

A maximum of one piece per square in any case applies in the first example I posted and many of the diagrams that legitimately occur in a game are similar to that example.

The fact remains that, if the discussion is to converge, the meaning of the terms in use needs to be agreed as far as possible and what you define as "positions" in either case would generally be referred to rather as "diagrams", both by other contributors and in the linked documents that refer to diagrams.

Regarding "positions", it is natural from a game theoretic perspective to only be interested in "states". A state provides full information about the future possibilities. The fact that much of the information in a state is containing in the locations of the pieces provides no reason for ignoring the smaller amount that does not.

This description of the balance of information is only true when an n-fold repetition rule is omitted. With such a rule states are vast in number - similar to legal games.  But for most purposes this is superfluous - storing the count for an analog of the 50 move rule suffices or even more simply just considering, for theoretical purposes, an infinitely long game to be a draw (no problem for solving chess or for a tablebase, but not practical for real play!)

@MARattigan -
again - the argument about max one piece per square ...
well we won't agree on that one.
I believe that's understood already.  Its already 'converged'.
Also - I wouldn't go with 'diagrams' either.
Because I'm referring to arrangements of pieces on the board.
Which are commonly called 'positions'.  
I don't see any reason to reject that term.
Regarding 'convergence of discussion' - there is some convergence.
But its a democratic discussion.
Which means there'll be divergence too.  
You asked me what I meant by positions.  Right?
I told you.
If it wasn't worded well enough for you to understand it - that could be addressed.
But you would understand more than well enough the math of upper bounds.  
In the process I'm suggesting - there's a process of enhancement.
It starts Basic - and then goes on to 'more advanced'.
Tromp's number has been mentioned many times in the discussion.
I'm stating once again - that I arrived at a number in the ten to the forties power my way.  No Tromp.
But after that - there became no feasible way to do more straight math on it.
With computer assistance - I could have done more 'cutdowns'.
Regarding 'leadership of the discussion' - there would need to be somebody more capable than the person so desperately wanting that leadership.  
Several here would be much more capable of that ... including
@btickler I believe.
but this isn't his forum.  He's not the original poster.
If he was - I think things would go differently.  But that's not the case.

Only 'correct' if one wants it to be.
Terms like 'stiffest' and 'do not even oppose' have to be proven.
Semantics are not proof.  Neither are arguments that try to self-validate at the beginning in a circular way.
Related to this - persons who rely strictly on semantics when they are studying math - and reject diagrams ... may struggle and fail to understand more advanced math.
Try teaching trigonometry with no diagrams ...
and coordinate geometry and calculus ...
the saying 'a picture can be worth more than a thousand words' has considerable validity.

Chess has intense mathematical aspects. 
But it uses a two-dimensional display.  With no words on the board.
That's part of the relation to math.  And part of the practicality.

The salient phrase there, I think, is, "for most purposes this is superfluous".

For constructing Syzygy tablebases it is entirely superfluous - even the 50 move count is ignored (the rule is implemented backwards in the solution). 

If you attempt to solve from a forward search, however, the information is not superfluous (though the 50 move rule count is).

If you have a solved line that contains a basic rules position and you investigate another line that reaches the same basic rules position you can't assume the result in the second line will be the same as in the solved line. You need to know that the specific positions that have occurred in each since the last ply count 0 position are the same and have occurred with the same frequency before you can make that assumption.

Also you couldn't identify nodes in the search space with positions unless you include the "superfluous" information in the meaning of position because that information determines the nodes deeper in the tree to which a node connects.

The 50 move rule count is still superfluous because that is just the sum of the repetition counts, which you need to know anyway.

I don't recall - but is the 50 move rule ignored in All of the tablebases?
Repetition?
I remember that en passant is factored somehow - but castling is skipped.
Hopefully they'll eventually fix that castling one - to ensure totally 'strong' solving of positions.

I think I understand the paper and explained with simpler words its meaning.

I think it's not correct, because an opposition is considered "stiffest" according to a non exact result (not a tablebase hit, nor a 3-fold repetition or 50-moves rule).

I cannot see why you consider checking all the possible replies for one player (the opponent) the same thing as cheking all the possible moves for both players. The first thing is required for a weak solution, the latter for a strong solution. There is quite a difference, indeed. For a weak solution you don't have to search all the legal positions, for a strong solution you do. To weakly solve checkers, around 10¹⁴ positions have been searched; to strongly solve checkers the entire search space has to be searched, around 5 ×10²⁰ positions.

Just don't fix on the meaning of "weak" and "strong" in common dictionaries. We could use "level 2" and "level 3", instead. Level 2 is enough for most players, because generally they don't want to know how to deal with every possible legal position; it is enough to know how to get the best from the initial position.

But if you consider only the "reasonable" moves for the opponent and you cannot prove beforehand that those reasonable moves cover all the possible exceptions, you cannot be sure that any "solution" (level 2 or level 3) is really a solution, there's no escape. I think that we will solve chess by searching all the possible opponent's moves before we solve (and I mean exactly) chess by your or @tygxc 's approach.

The fifty move rule is ignored in tablebases that are classified without a 50 on the end of the classification, so DTM (e.g Nalimov), DTC, DTZ ignore the 50 move rule and don't work for all positions under competition rules. DTZ50 (e.g. Syzygy) and DTM50 (some produced, but not generally available) work under both, but not for all positions under some previous FIDE variations of the 50 move rule.  

#3001
"an opposition is considered "stiffest" according to a non exact result"
I also provided a paper saying that incorporating 'knowledge' is beneficial in solving games.
I also provided a paper with 'knowledge' in its title ranking 1 a4 not among the top moves.
I also consider it 'knowledge' that 1 e4 e5 2 Ba6 loses for white.
There is more 'knowledge' than a table base hit or a 3-fold repetition.
Forget the 50-moves rule: it does not happen with > 7 men.
I presented 2 examples of positions in the ICCF WC agreed to be draws with > 7 men: one with opposite colored bishops and one with rooks and pawns on one wing. That is applied 'knowledge' too.

Opinion: (a method of many possible methods of going at the subject)
Start with positions defined by where each piece is on a square.  
Develop upper bounds on the numbers of such positions.  
Use computer enhancements to further develop (reduce) the upper bounds.
Factor in the tablebases.
After all the 'strong methods' have been exhausted to do so - (which does Not mean they're irrelevant - obviously - because something has been accomplished )  Mathematical reduction is part of the anatomy and phsyiology of 'solving'.  
then start considering alternatives to 'strong solving' - to be applied at that juncture.
Only factor in other information like whose move it is - en passant and other information - when timing is Ideal for each element and only after 'establishment' is complete for the stage concerned.
Horse before the cart in other words.  Walking before running.
That's apparently what they've done with castling in the tablebases.
They're not ready for it.  So they're doing something more basic first.

But the 'weakly solving' has to be factored in too.
A while back I mentioned computer evaluation numbers.
But @MARattigan rightly pointed out about the computers Pathetically unable to recognize drawn positions as draws.
Does that mean that sufficient/insufficient losing/drawing chances and the Whole Project are therefore Doomed?
No.  But its not good news for 'solved in 5 years'.   
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