Chess will never be solved, here's why

Is there a way to reconcile two Kings always there with 62 other square 32 of which always must be empty - 
with a max of 16 pawns confined to 48 squares of the 64 ...
its not so simple which is why I had to delete several paragraphs of mine in several posts.  It is not required that 32 of those 48 always be empty - because of the two back ranks - which could account for some of mandatory empty 32 squares.
Reconciling an 8x8 board with an 8x6 board.  Not so simple.

#513
Of course captures are included. Here is the breakdown:
32 men 1.89 × 10^33
31 men 1.71 × 10^34
30 men 1.64 × 10^35
29 men 1.53 × 10^36
28 men 5.46 × 10^36
27 men 1.05 × 10^37
26 men 1.08 × 10^37
25 men 6.14 × 10^36
24 men 3.19 × 10^36
23 men 5.66 × 10^35

#514
The newer paper counts no positions with adjacent kings.
The previous paper with the higher count included positions with adjacent kings and then manually removed these from a random sample.

@tygxc
Again - quote from your paper ...
"The number of legal chess diagrams without promotion is bounded from above by 2×1040.
This number is obtained by restricting both bishops and pawns position and
by a precise bound when no chessman has been captured."

You can read from your own link.
https://arxiv.org/pdf/2112.09386.pdf 
One can just accept anything they say or check up on them and see what they're really pushing.  
Another option - totally accept anything from any link - without even considering.  Take somebody else's position. 
Often on the net - opposing links are 'peer review' ! 

#517
Read the next sentence:

"We improve this estimate and show that the number of diagrams is less than 4×10^37"

But have you read how they developed the math -
have you read through the algebra ?
It sounds like you are conceding that their first estimate is not legitimate but you are continuing to defend 'promotions' and maybe some 'inferior lines' too.  
Maybe I'll be the only one in the forum to try to reconcile two Kings on a 64 board with 16-max pawns on a 48 board with mandatory 32-min squares empty on the 64 board.
If so - that's okay.  
The link stuff has already conceded it seems - that 8 men on the board is too much for them ...  going by what @tygxc has said ...  
notice I said it 'seems'.  Qualified.  Its not a claim.  

#519
Also read the conclusion of the paper:
"For these reasons, we conjecture that the number of legal diagrams in the game of chess without promotions is between 10^37 and 3.5 × 10^37, probably close to 3 × 10^37."
Hence my appreciation that the figure 3.8521*10^37  should account for all sensible positions also with e.g. 4 queens.

ok

You just said 'without promotions' ...
and even if I stipulated that they've probably done valid work to establish a an upper bound under 10 to the 38th power ...  its still not a valid upper bound.
Also - if you've read the article thoroughly and thought about it - can you articulate the valid algebraic steps yourself?
you've already also conceded they only went up to 8 men in the tablebases ....    
even going by what you are saying - it seems to be neither well put nor valid ...  by confession.
But on the other hand - you're trying to present a case that attempts to challenge the forum title.
You've presented science links to support such challenge ! 
Good for you  !    I mean that !

This conversation is meaningless in real terms. People playing at sounding impressive.

Incidentally, @tygxc, positions with four queens are sensible if the material is reasonably balanced. When a position is reached that's obviously a win, that branch of the solution becomes redundant in meaningful terms, just as if white dropped a queen in the first five moves.

Therefore, one necessary part of this project is to develop an algorithm that can tell if a position is an easy win. That in itself is an interesting project. If it could be achieved in a completely foolproof and accurate manner, it would provide one of the necessary shortcuts. In order to "solve chess", it's necessary to do it algorithmically, rather than by brute force calculation of all possible lines. The algorithms that are necessary haven't been developed, so a solution is still a very long way off.

#523
Such algorithms exist and are part of every chess engine.
There are two kinds:
1) look ahead x moves and count material.
2) look ahead y moves and apply a more difficult evaluation function.
Both have errors, as otherwise no engine could ever lose and they do lose a game from time to time.
The cutoff is probably:
-0.50 to +0.50 = draw
> 0.50 white wins
< -0.50 black wins
The ultimate evaluation is when the calculation hits the table base and retrieves the exact result draw/win/loss.
Meanwhile the imperfect evaluation can be used to limit the number of candidate moves.
1 e4 e5 2 Ba6? leads to -3 and is a sure loss for white. It needs no further calculation.

You say they exist and that's partially true but they aren't properly developed, because they are still dependent on the horizon effect. That is, they are still dependent on brute force calculation with all its inherent errors.

I'm talking about a possible new paradigm in strategic assessment. It would depend on the possibility of breaking chess into coherent systems that themselves are reducible to a mathematical form. My son tells me that's completely impossible though.

#526
In this paper they explain how AlphaZero does it
https://arxiv.org/pdf/2111.09259.pdf

However, a simpler evaluation but looking deeper seems superior. That is how Stockfish does it.

The aim is to hit the table base with its exact evaluation.

@playerafar gives an upper bound on the number of legal chess diagrams 

the title of the paper you link to is

An upper bound for the number of chess diagrams without promotion

(my emboldened text)

You consistently ignore the phrase "without promotion".  The figure you quote is taken from the the sentence, in that paper

Summing over all possibilities yields that the upper bound for the total number of legal chess diagrams without promotion is equal to 3.8521 . . . × 10³⁷.  

(again my emboldened text)

You also ignore the fact that a chess diagram is distinct from a chess position.

I did ask previously in this thread if you could stop repeating the misinformation you just posted. I ask again.

This is an important point in respect of your assertion that (competition rules) chess can be solved in 5 years.

Your estimate is based in any case on the dubious assumption that the time taken will be proportional to the square root of the number of legal positions, but:

For the purposes of solving, your upper bound on the number of legal positions needs to be multiplied by 2 to account for the fact that the side to move is an attribute of a position but not diagram and 100 to account for the fact that the 50 move rule is an attribute of positions under competition rules which is the version of chess you intend to solve. (Your assertion that the rule can be ignored flies in the face of what is actually known about perfect play from the tablebases).

On your own calculation this would amend the time you need your Summit machines from 5 to around 70 years.

That point, however is quite minor in comparison with your assumption that positions with excess promotions can be ignored. (You are correct in assuming that promotions that are not excess are already included in the figure you keep quoting.)

In this case you throw away almost all your legal positions. Tromp's latest estimate (not an upper bound) for the number of legal positions quoted in the paper is (4.48 ± 0.37) × 10⁴⁴. Your estimate needs then to be multiplied by (4.48 ± 0.37) × 10⁴⁴/3.8521 . . . × 10³⁷. This would further amend the time you need your Summit machines to around a third of a million years.

Your assumption that these positions can be ignored also flies in the face not only of information from the tablebases, but practical play. Almost everyone will have used an upside down rook at some point.

I gave a recorded game with six knights on the board in post #244 here https://www.chess.com/forum/view/general/chess-will-never-be-solved-heres-why?page=13.

Your response was, "Nakamura was trolling and so are you". This is a non answer.

Trolling is not related to perfect play. It would be a simple (if tedious) matter to prove, without computers, that each of Nakamura's promotions was a perfect move.

Syzygy, who can play perfectly within a limited range of positions, also has a penchant for trolling. Here it is playing a KQPPPPK mate perfectly.

Nalimov, who is much too serious to troll, neverthess less also indulges in excess promotion. Here he is playing a randomly chosen KPPKP mate in 30

Now, repeatedly posting "facts" that you know very well are false. That probably comes a lot closer to "trolling".

#528
Please stop with your smoke screens.
The Tromp count has a vast majority of obviously nonsensical positions with multiple underpromotions etc. Look at Tromp's 3 diagrams of random samples:
https://github.com/tromp/ChessPositionRanking 
I acknowledge that some positions with 4 queens make sense and are excluded from the newer count. On the other hand the newer count still includes many nonsensible positions.
So all in all the newer figure 3.8521 × 10³⁷ is a fair estimate for all legal and sensible chess positions including those with 4 queens and excluding those with e.g. quadrupled pawns.

@MARattigan - your points are valid.
 tygxc on the other hand - does seem to believe what he's saying -
pushing for that website's version of 'solve' ...
and he's doing so with little or no personalization.
Even though many of his points seem invalid to me -
by pushing his points and us responding to them - he keeps the forum topic going ... 
There is this thing called 'Devil's Advocate' ...
often useful even if he doesn't mean it that way (likely)

and I cannot resist this Complete Irrelevancy ...
in a titanic struggle just completed - Rafael Nadal has made History ! 
21 Majors !  

I would call them facts that negate your argument rather than smoke curtains. If you refute any of them I will gladly stop posting them.

A count of legal positions is quite a different thing from a count of positions that you personally consider sensible. And positions that you personally consider sensible is quite a different thing from positions that might occur in a solution of chess run along the same lines as the checkers solution. And positions are quite different from diagrams, which you persist in ignoring in your last paragraph.

(Incidentally if you count the queens in the Syzygy v. Syzygy game above there are five. It's obvious from the way Syzygy is generated there would be more from positions with more men on the board.)

Edit: I will withdraw the following statement in #528.

"In this case you throw away almost all your legal positions. Tromp's latest estimate (not an upper bound) for the number of legal positions quoted in the paper is (4.48 ± 0.37) × 10⁴⁴. Your estimate needs then to be multiplied by (4.48 ± 0.37) × 10⁴⁴/3.8521 . . . × 10³⁷. This would further amend the time you need your Summit machines to around a third of a million years."

Tromp's estimate is of positions rather than diagrams, and the factor of 2 that you should apply to your estimated number of legal postions was already included in my earlier paragraph, so I have double counted it. This would reduce the calculation of the time required (on your - dubious -  basis) by a factor of  √2 bringing it closer to a quarter of a million years.

Thanks and I'll enjoy looking at the paper, provided I don't need an advanced knowledge of maths. Even so, my comments stand. I'm talking about a different type of assessment, certainly from SF's.