Chess will never be solved, here's why

#861
There are two different things: 1) solving chess and 2) assessing the feasibility of solving chess.
Mathematically chess is a finite game and hence it can be strongly solved.
However, people argue solving chess is not feasible as it would take too much time.
To make such statements needs the number of positions involved.
Tromp counted 8726713169886222032347729969256422370854716254 possible positions and found 5% of these legal after sampling and thus arrived at his 10^44.
However the vast majority of his positions contain 9 excess underpromotions. That never occurs in any real game between humans or engines.
Hence the newer estimate 10^37 without excess promotions is a better estimate.
It is not true that there are twice as much positions as diagrams: every position with black to move can be converted to a diagram with white to move by switching colors: up/down symmetry.
Every position with lost castling rights can be converted to its left/right mirror image.
Randomly sampled positions without excess promotions like the four #860 probably play no role either in solving chess. This might reduce the count by another factor 10^6, leaving an estimate of maybe 10^31.

Is chess a game? The same may apply.

Incidentally, in tic tac toe, "whoever goes first and has first move, the same square always wins", is a bit optimistic. With perfect play it's a draw.

Most kids are introduced to it at about the age of five and strongly solve it the same day, so they know that at least.

Seems quite hard to explain to @tygxc that while when you are playing a game you can ignore options for the other side and truncate analysis lines, this is _absolutely_ _not_ true when you are solving a chess problem rigorously (and the same goes for the problem "solving chess", which can be described as "From the standard starting position exhibit (or prove the existence of) a forced mate by one or the other side, or exhibit (or prove the existence of) a forced draw for both".

I DONT GET THIS

The bolded statement above is characteristic of your arguments in general.  Imprecise and "selectively detailed" (i.e. you try to use realistic numbers in some stages, then summarily make leaps of faith in other stages).

I guarantee you that the "vast majority" of the aforementioned positions do not contain 9 (no more and no less) excess underpromotions.  Which is exactly what you just claimed. 

You then go on to toss out your usual offhanded comment about throwing out another 6 orders of magnitude in a manner that seems to defy any realistic understanding of exponents .

This is the difference between you and Mr. Tromp, who had to keep shooing your extrapolations about his study away.  His careful and accurate study eliminated between 1 and 2 orders of magnitude after all his work, while you routinely eliminate 6-19 orders of magnitude on a personal whim with seemingly no more than some pie-in-the-sky musings, loosely tied to somebody else's estimates.  You're like a conspiracy theorist that takes X number of good scientific studies, then mashes them together into a set of ridiculous conclusions by taking wild liberties with how those numbers correlate.

Solving chess is a problem (in the sense of some question seeking a rigorous solution).

'Biggest number' ...  Lol.
There is of course - no such thing.  And there's no 'biggest prime number' either.  And there's a short neat proof of that. 
There's something in math called 'infinite series'.
But is there a good way to express the plural of 'series' ?
Mustn't get too 'series -ous' about that.

Chess isn't solved - might never be solved (humanity might not survive that long) - nor is an exact number of legal possible chess positions known.
There are ways to precisely state 'upper bounds' on the maximum number of legal chess positions.
Those 'upper bounds' are of course always positive integers (just mentioning that obvious point on the side for now - when dealing with integers - there's particular math that can be applied)

The first and very simple upper bound is 13 to the 64th power.

Because every square can only have 13 states in legal chess.  
(my keyboard not user-friendly about the exponent 'hat' symbol)

That 13 raised to the 64th ... is an extremely humungous  number !
Could it perhaps be more than an upper bound on the number of atoms in the observed universe ?
Is it 'good news' that that 13 raised to 64th power can be substantially cut down?
Yes I said this before - but repeated ...
The number of ways to have 32 squares empty on an 8x8 board 
is mathematically  (64 x 63 x 62 ...  x 33) divided by '32 factorial'.
32 factorial is written 32!
That's right.  An exclam mark is used in math to denote 'factorials'.
Should I explain or try - as to why the division by 32! is necessary ?
Its so that 'ways' are not overcounted. 
Each single way can only be counted once.  
The 32! on the bottom will always cancel out with the term on top.  
It must !  Has to be an 'integer' result.  But not because of a 'want'.
How could it not be an integer ? 

#867
See for yourself that the boldened statement is true: this is Tromp's breakdown of all positions:
excess promotions:  0 positions: 19201527561695835455154058755564594798074
excess promotions:  1 positions: 382355871178268365234183218244670372695068
excess promotions:  2 positions: 3666683498600457464891752992187014354136188
excess promotions:  3 positions: 22267499667290257736558400874926183060238400
excess promotions:  4 positions: 95095065373967146179514528215894174339720228
excess promotions:  5 positions: 300571414300527313744528888013946849776424304
excess promotions:  6 positions: 721668497316402902485416452421325823057710432
excess promotions:  7 positions: 1329934072135692805837128923570048899100334756
excess promotions:  8 positions: 1874962044164806332602085236357597905810647344
excess promotions:  9 positions: 1980800128935921108339671872170042183548439128
excess promotions: 10 positions: 1492529839915108301878747832838229979840571492
excess promotions: 11 positions: 722080907452760073481816196266539169729817880
excess promotions: 12 positions: 175351843526979273665005184194531833618491680
excess promotions: 13 positions: 7338473695924787177946719990630518998574920
excess promotions: 14 positions: 45087168602668580254351850721788483191140
excess promotions: 15 positions: 55323182237139471340692375109727946960
excess promotions: 16 positions: 11716401834002951530424702440978260
Total:                         positions:  8726713169886222032347729969256422370854716254

#864
I agree with
"From the standard starting position exhibit (or prove the existence of) a forced draw for both".
We know white enjoys the first-move advantage.
Hence black tries to prove a draw and white tries to disprove a draw.
"White must play to win, while Black must play to draw" - Sveshnikov
Hence for all reasonable white moves prove the existence of at least one black move that holds the draw.
Hence if we arrive at a game that ends in a draw, then in retrospect all black moves are good, good enough to draw, and it is the white moves that need takebacks to prove there is no winning way for white.
Example:
1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 a6 6 Be3 Ng4 7 Bc1 Nf6 8 Be3 Ng4 9 Bc1 1/2-1/2 draw by repetition.
Hence the white moves need takebacks: Bc1 and if that leads to a draw too then Be3. 

And so now we see that you don't even know the definition of "vast majority" ...in order to call it a majority, the positions with 9 excess promotions would have to be greater than all the others combined.  To be called a "vast majority" would mean not just a majority, but at *least* a twofold to threefold majority (personally, I'd say a fourfold majority).

@tyxgc

And in any case all you have done in #880 is tell us just how far adrift you are in your estimate of legal positions.

So, the emboldened class (exactly 9 excess promotions, I believe?) is 22.7% of the total. Which I call a minority.

Interestingly 50.17% of the positions fall into the classes with 9-16 excess promotions), BUT I believe these include those with excess queens, so the positions with 9+ underpromotions would be much less than 50%.

#884
Those are legal and illegal positions as counted by Tromp. about 5% of these are legal.
#886
That is right, people keep squabbling.
Focus.
Chess can only end in a draw, a win for white, or a win for black.
Chess has a finite number of legal positions e.g. 10^37.
Thanks to the 3 fold repetition rule each chess game thus ends in a finite number of moves e.g. 10^37.
Thus all positions including the initial position are either a draw, a win for white, or a win for black.
So there are 3 possibilities.
A) The initial position is a draw, the first-move advantage is too little to win.
B) The initial position is a win for white, the first-move advantage is enough to win.
C) The initial position is a win for black, white is in Zugzwang.
If there is proof for one of those, then that automatically disproves the other two.
Most top chess players believe A) to be true, but technically it is a hypothesis or a conjecture.
Theoretically chess can be strongly solved: it suffices to work backwards from the 7-men table base to create a 32-men table base.
That would need to visit all 10^37 positions, which would take 10^28 seconds on 1 cloud engine of 10^9 nodes/s and would need a minimum of 10^37 bits draw/no draw to store.
Neither the time nor the memory is feasible with present technology, so right now strongly solving chess is not possible.
That leaves weakly solving chess, just like checkers was weakly solved.
The same 3-pronged method as for solving checkers is possible.
1) Prepare 26-men tabiya to kick start the calculation.
2) Calculate with Stockfish from the 26-men tabiya to the 7-men endgame table base
3) Look up the exact verdict draw/win/loss in the 7-men endgame table base.
Each capture and each pawn move are irreversible and render huge numbers of positions irrelevant.
Checkers was solved visiting only the square root of the number of legal and sensible positions.
For chess we do not know yet, it will only be known after chess is solved.
Meanwhile it is plausible to assume it is about the square root too, maybe more, maybe less.
For weakly solving chess it is not necessary to look at all 500 ECO codes A00 to E99.
For example to prove a draw against 1 e4, only 19 ECO codes suffice.
That takes 5 years on 1 cloud engine of 10^9 nodes/s.
Likewise a 2nd cloud engine can prove the draw against 1 d4 and a 3rd cloud engine can treat the relevant other openings that do not transpose.
Hence present cloud engines can weakly solve chess in 5 years.
That is what GM Sveshnikov predicted.

You would do better to conclude that your understanding of the topic is not as good as those who define these terms.

The solution of checkers was a weak solution. It was not a strong solution. Read about it if you like.

A much simpler example is to consider the game exactly like chess except it starts with this position with white to move.

A weak solution of this game is the solution of this position as a chess problem with white to move (left to reader). A strong solution of this game is to have a perfect strategy for white in every position that can be reached from the opening position and the same for black (the only non-triviality in the latter is that black should capture the rook when it is hanging).

Now you can see that the two are not equivalent.

I don't know if Chess will ever be solved, but If it does get solved ... I don't think it will happen in my life time 😿🐶