Chess will never be solved, here's why

This is from the "paper":

<<<In terms of prunings in branch and bound tree search, a sound pruning condition when solving a weaker solution concept may not hold in stronger ones. This is caused by the removal of the assumption of optimal/perfect plays when dealing with stronger solution concepts. For example in alpha-beta prunings, when the min player obtains an A-costs which is lower than the lb (i.e. max player's last found best), we cannot immediately backtrack if we want to tackle weakly solved solutions, where we assume the max player is the adversary. The reason behind is that we cannot assume the max player must play a perfect move. We have to consider all moves for the max player. The situation is similar if we assume the min player is the adversary." (emphasis mine)>>>>

It should be clear that <<We have to consider all moves for the max player>> is untrue. We have to consider all reasonable moves. We have to know what is "reasonable". If we don't know that or can't determine it, we're stuck once more in the strong solution. It should be clear by now that the so=called strong solution is not a solution, so much as a list of all possible move-permutations, which cannot be assessed. The purpose of the weak solution is to assess moves. That is why the terms "weak" and "strong" are unfit for purpose. They should be something like "full" and "pruned", because it is also obvious that there's a very wide spread of pruning strategy, so that branches are more or less pruned in the same way that the solution is more or less weak.

Relying on stuff written by people who rely on terms like strong and weak, which are indications that the persons concerned are not focussed, isn't helpful. I'm writing this because I'm just wondering if there's anyone here at all who has the ability to understand what I'm saying. Perhaps there isn't. You can only refute it if you first understand it. Imbeciles needn't bother but is there anyone who is focussed enough to even be discussing this subject?

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'.   
😁😁😁

But Tromp has already done that. He gives an upper bound on the number of legal positions on this page.

The only difference is that by "legal position" he means diagram + side to move + en passant possibility + castling rights that can be reached in a game by a series of legal moves.

That I think is the same definition that everyone here except yourself is using as the definition of "legal position" under basic rules chess.

It's true that many people use the term "position" to mean just the layout of the pieces on the board immediately after a move has been made, but I think everybody else would call that a diagram in this thread.

Tromp has gone further and estimated the actual number of legal positions here by sampling and testing for legality.

There doesn't seem to be a lot of point in reinventing the wheel.

@MARattigan
I clicked on your link - 
Tromp admits he uses a 'more complex program'.
I chose to talk somewhat about how I arrived at a number in the 10 to the forties.
I don't understand why we have to use Tromp's definition all the time.
One could argue that Tromp's work is a 'paper' -
but now we see the other guy seeming to trash somebody's work of providing a paper to respond to somebody else's interpretation of a 'definition' by a notable 'ven den Herik' which could also be regarded as a 'paper'.
I've also seen 'Gurion number' and other numbers.
These references may be useful but we don't have to be bound by them all the time.
You asked me what I meant by 'positions' and I told you.
That can be seen as 'progress' rather than circles.
The discussion is different than it was a month ago.
But there's going to be references back to previous posts.
That's inevitable.
More surely than a bishop can do a 'diamond dance' around its seventh rank passed pawn ...  to drive off the defending bishop and promote for a win. 

@playerafar 

I don't think anybody has questioned the upper bounds on legal positions by Tromp or legal diagrams without promotions by Gurion (except that @tygxc has correctly pointed out, also accepted by all, that Gurion's figure relates to diagrams without excess promotions).

I would be awkward and assert that Tromp's figures relate only to current basic rules chess, not to chess under competition rules. 

When these things are generally agreed there seems to be no reason to discuss them further unless you think you have found a flaw.

You've said what you mean by "position", but it would be much more convenient if you could switch to the meaning in general use for this thread. It saves people from having to say anything about positions twice to accommodate two different views.

@MARattigan
I've said what I meant by positions - in context.
The normal meaning of positions.  Arrangements of pieces on a board.
"I don't think anybody has questioned the upper bounds on legal positions by Tromp"
I don't think anybody has either.  I didn't.   I said 'if'.
But I didn't claim to the contrary either.
I question 'general use' though.
tygxc has had his own 'general use' and its been 'questioned' for about 3000 posts.  
Ideally - posts could be expressed so that newcomers to the forum could understand right away - instead of having to refer to a link concerning Tromp which then might lead to a link about ven den Herik and then yet another 'paper' where there's then a conversation 'going in circles' about interpretations of what ven den Herik is saying - where somebody then complains about 'circles'.
In other words - idea: - for the conversation to be about the subject - instead of about what somebody on an internet article might have meant by something.
Having said that - @Haiaku is still right to remind @tygxc about a paper that disagreed with ty's interpretation.  

Regarding 'competititon rules' I've questioned that terminology because somebody just entering the forum won't know what you mean by that.
So I've suggested - if you mean 50 move rule then say 50 move rule.
If you mean repetition of position say repetition.
Is a suggestion.  I won't get bent out of shape if you don't do it.

Regarding Gurion's number it seems somewhat arbitrary regarding 'excess'. 
Regarding who has been right and who has not ...
I have yet to see any incorrectness in @btickler 's posts or in @Haiaku's.
When you've been inaccurate (rarely) - well in the one instance I remember you simply deleted the post while admitting it was off.  That was recent.
Regarding Elroch's posts - I've had minor disagreement with some of them.
He rightfully keeps reminding @tygxc about mathematical standards of proof.
My 'minor disagreement' with that is that the term 'weakly' in relation to solving would seem to be in stark contrast to 'strongly' when you're talking about solving.  
When I mentioned that - ty did what he did before - he started talking about ven den Herik.  But with or without ven den Herik - that word 'weakly' is giving ty a lot of latitude.  So is 'heuristic'.  
I believe only one person is worried about 'leadership of the forum' and I believe its not you.  
Ironically - its @tygxc who has essentially led the forum.
Perhaps without the slightest intention of doing so.  
There's a lot of things that work that way ...
chase after something - it runs away.
But do better enough than 'chasing' - and that 'something' comes right along with you or to you.

@MARattigan
I think your post #2948 was in response to my post # 2945 a few before.
This one:  https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?cid=68837185&page=148#comment-68837185

A main point of mine in that post (among other points) is the relevance of strong to weak.
Much earlier in the forum I was talking about 13 to the 64th and factorials about 32 squares having to be empty and two Kings only.
Those posts of mine got good reaction at the time.  
Strong math - to get strong results.  
When the discussion 'converges' on weak solving - which its been doing for about 3000 posts - then 'strong' is still relevant.
Including as part of the process before 'weak' and also to contrast with 'weak'.  So that its clearer what's being omitted.  
Terminology and worry about 'positions' was not intended.
There's quite a lot of controversy here about 'games' versus 'positions'.
'Positions' can be defined according to the context.
If its relevant in the context whose move it is - then that's included.
If its not then it isn't.
In some of the discussion we even had a suggestion that positions that would have to be illegal - like adjacent Kings - should be allowed in advance.  And then cleaned up later. 
I disagreed with that.
But maybe that's valuable in the programming aspects of it. 
Definitions according to context.  

By the way - when I went to the Tromp page you linked - there wasn't much there.  Something about 'complex formula'.  
Just now I went to a Wikipedia article about Claude Shannon (yes I believe Shannon was mentioned earlier) - he's got a neat formula that also ends up around 10 to the 44th.  
Saw this too:  But some of it is wrong:
https://chess.stackexchange.com/questions/5592/what-is-the-number-of-legal-positions-in-a-chess-game

Those posts of mine got good reaction at the time.>>

I thought I noticed laughter, jollity and some incredulity. Keep up the good work.

In spite of disapproval - @tygxc has led the forum it seems.
Doesn't let anything bother him.  
Regarding as to who here would qualify for the professional research projects on this subject ... four people here would seem to be up to it.
Regarding others ... well there'd have to be care regarding saying things like:
"lets take four candidate moves for each side on every ply - to do the weak solving".   That could disqualify. 
As could 'no solution exists even though the number of positions is finite'