Chess will never be solved, here's why

Lots of possibilities, but nowhere near infinity.

#248
Nakamura could have won much faster, but he chose to troll and have fun with 6 knights.
Underpromotions rarely happen and usually have the point to avoid stalemate or to exploit the unique properties of a knight. Multiple excess underpromotions play no role at all. That is why the Tromp count is way too high for the purpose assessing the feasibility of solving chess.

Your KQBN example has neither underpromotions nor excess promotions. Indeed 1 Qc7+ 2 Qa7# is faster hence 1 Qc8+ is trolling.

If a position is a draw, then neither side has a valid reason to avoid the draw by 3 fold repetition or by the 50 moves rule. If a position is lost, then the losing side has a valid reason to claim a draw by 3-fold repetition or by the 50 moves rule and the winning side has reason to avoid a 3-fold repetition or the 50 moves rule taking effect. Thus the fact that the draw has to be claimed plays no role: the losing side claims.

Would chess being solved require a proof of the existence of a perfect strategy or the actual construction of a perfect strategy. If it's only the existence that's necessary, I could see that happening in the next century. If it's actually getting a computer to be able to play the perfect strategy, I doubt we're capable.

Regarding elimination of 'illogical' positions as opposed to illegal ones ...  that could become error-prone.

The business of the 50 move rule greatly increases the maximum possible positions ...  but I'm suggesting that the 50 move rule and the 3-fold repetition rule could both be ignored for the purpose of maximum positions.  
There could be adjustments for en passant possible or not - and castling legal or not ...  but the issue with such increases - is that its beginning to discuss possible games again ... instead of positions - a much more Concrete thing.

Regarding the game aspect - I'm suggesting the number of positions only needs whose move it is - and perhaps a cutdown regarding positions that are 'legal' but could not have been legally arrived at.  

Regarding positions where castling might or might not be legal because a King might have moved or not - those could be added to a special category for special cases.
Regarding  the 50 move rule being added - could that 50 move rule potentially increase Every Single Position ?
No.   Positions of King + King + Knight can't be increased by the 50 move rule.  
Could a position of the original Grand position be subject to the 50 move rule?  Knights hopping out and then returning again ?
I would say no - because repetition would take precedence ....
Therefore - again - the number of positions where a 50 rule might be relevant - could be qualitatively and quantitatively reported separately.  
Like with castling and en passant 'maybe possible - maybe not'.

no, it is simply how dtz works

qc8 and then the 50 move rule is zeroed in 1 move

qc7 ka8 qa7 and then the checkmate is achieved in 2 moves

this is just a problem with dtz, which is used by syzygy(i presume)`

Regarding players refusing to resign in hopeless positions ... many many times I've taken all of an opponents pieces and pawns - leaving me with as many as 7 promotable pawns.
As I make it clear that I'm not going to robotically pursue fastest mate in such situations - half of such opponents resign - realizing that I'm going to go for many knight-promotes.
So whether getting four knight promotes or up to seven ...  some don't resign.  So I take them up on it - and don't block them.
Preferring to mate with the knights alone and little or no King or other piece assistance.  A very few opponents have moaned and whined about me doing so ...  .   They get blocked.
Four knights can be brought to the four central squares of the board.
Confines the Lone King to the Edge !    Mate from there.
But the more knights - the easier.  You can make a wall - that constricts from the sides ....

#251
Solving chess = proving that black has at least 1 move that draws against every sensible white move.

#254
A position with castling rights is different from a position without castling rights. A position with possible en passant is different from a position with en passant possibility. It is counted differently as such in the 3.8125 legal chess positions. See also
https://en.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notation 

#255
Do not push the agnosticism too far.
Yes 1 e4 e5 2 Ba6 might win for white, there is no proof of the contrary.
Yes 1 e4 f5 might win for black, there is no proof of the contrary.
However we know that is not so.
Likewise underpromotions to rook, bishop, knight are sometimes useful to avoid stalemate or to use the unique properties of the knight, but every human or engine player promotes to a queen when there is no compelling reason not to. Hence the random samples from the Tromp count represent positions that never result from a perfect or even reasonable game of chess. That is why the Tromp count is way too high for the purpose of assessing the feasibility of solving chess.

@tygxc
Yes I think we know they're different.  With/without castling/enpassant and 50 move rule and 3-fold too ...
But I'm suggesting - that for practical purposes - that can either be ignored - or seen as Secondary.
With the actual max piece setups as primary.

Another big cutdown could occur - with positions that are rotations and reflections of each other.  
Note that whose move it is matters - but then does that 'cancel' with color reversals ?

In many endgames - many positions shifted to left or right on the board - play the same.  Many don't.  Especially when the edge of the board is too close.
Endgame positions shifted up and down the board - might not change either.
The most Notable Exception is with Sixth Rank King ...
such a King does not need opposition to win the basic K+P ending because there's no Ninth Rank.
There are ways to relate the discussion back to 'regular chess'.

#260
The endgame table bases use symmetry to reduce the size.
https://en.wikipedia.org/wiki/Endgame_tablebase 
The count of 3.8125 * 10^37 positions does not take symmetry into consideration. Left/right symmetry is broken by castling. Up/down symmmetry is broken by white pawns maching up and black pawns marching down.

#261
This is what solving chess means:
https://en.wikipedia.org/wiki/Solved_game 

The premise that removing positions that "don't make sense" will reduce the problem by 7 orders of magnitude is not feasible.

The very calculations to check the criteria you would need on each position in itself is a huge amount of processing power at that scale...or, were you planning on having the human assistants check the criteria manually?

[Note that *even if you somehow predetermined every position that is not sensible* to avoid those calculations, just skipping the ones that are on the list (3.1622776e+44 if you accept the faulty 10^37 number) would again be a huge amount of time spent]

The 50 move rule potentially greatly increases the number of positions because of the variable number of moves left in the 50 - with potential for players to inefficiently pursue a fast win - and with some controversies whether there is in fact a win available with the variable number of moves left.
Therefore - the claim that it 'only doubles' is invalid.  Because it wrongly premises that all such positions are 'solved'.   Which is not the case. 

Only in some cases.  And in endgames - castling is seldom even theoretically available.
Up/down equivalency is not broken by 'pawns marching'.  

#266
No, not at all.
There are 2 different things: 1) assessing the feasibility of solving chess and 2) solving chess itself.

1) To assess the feasibility we must estimate the number of legal, sensible, and relevant positions so as to estimate the resouces required i.e. CPU time on cloud engines. So the estimate should exclude illegal positions, non sensible positions like random samples from the Tromp count, and non relevant positions which are legal and sensible, but which will become unreachable in the course of the calculation, e.g. all positions with a white pawn on e2 after 1 e4.
2) To actually solve chess the cloud engines calculate from a humanly prepared 26-men tabya e.g. C67 towards the 7-men table base.

I essentially agree with all of this post.
'Don't make sense' is far too arbitrary and subjective.  
But there are other methods of 'cutdown'.
And people actually use these cutdowns in their studies of chess ...
For example - King and rook against King.   
Its simply a book win unless the rook falls immediately or its already stalemate or the side with the rook blunders.  
Once players have it 'down' they go on to other things.
The number of possible K+R versus K positions is in the thousands - but its essentially two for practical purposes.  A win is possible or it isn't.  

Ahh yes, I forgot, you still think that current engines can determine perfect play and ergo make the evaluations by simply extending their horizons out to reach tablebase endings.

Sorry, you can't bootstrap yourself to perfect evaluations using imperfect engines, and the only way to ensure perfect engine play is to solve chess *first* .

Still too arbitrary about 'don't make sense'.

Much better:  cut down the positions where there's obvious equivalency.
I'm also suggesting that's part of how improved chess is learned.  
Many positions are in fact 'solved'.  Or clear enough.