Chess will never be solved, here's why

#1620
"Compensation doesn't have to take the form of recovering the material.
It can take the form of having a mating attack for example."
Checkmate is the ultimate material gain. Rate the king at 1000 pawns.

So now you want mate and recovering material to be the same ?
That's okay too.  

Plus of a rook 'sufficient to win'.
But how is the computer going to determine whether there's 'compensation' for solving purposes ?  
I like the idea of solving backwards from positions 'solved' but not just from tablebased positions.
From checkmate positions instead.  Without the amount of material on board to be the biggest issue.
Many of them are lopsided materially in favor of the player mating. 
So - the computer could do a job of generating all positions where adding material to the position doesn't affect the mate.  
A lot of positions could be eliminated that way as solved.
The next step would be - go back a move.
And again - all of those positions from which the mate is played 'solved'.
Unfortunately - gets tougher if you go back 2 ply.
Because then maybe there's a prevention move.

#1628
"But how is the computer going to determine whether there's 'compensation' for solving purposes ?  " ++ By calculation x moves deep

Unfortunately its not that simple.
To understand why - it might help to look at Tal's masterpiece games.
From the technical side - there's the number of nanoseconds needed to solve each 'rook up' position to see if the other side has 'compensation' of any kind.  
Based on math of the number of the positions - its going to take too many nanoseconds.  
One billion nanoseconds in a second.
Under four billion seconds in 100 years.
So less than  4 billion billion nanoseconds in a century.
That's not enough nanoseconds. 

Side point:  Players are 'solving' chess constantly.
Whether figuring out a mate move and then playing it or
deciding whether its time to resign or offer a draw or accept one..

#1630
"So less than  4 billion billion nanoseconds in a century."
1 century = 100*365.25*24*3600 seconds = 3155760000 billion nanoseconds
1 nanosecond = 1 position on a cloud engine of 10^9 nodes/second
There are only about 10^36 legal and sensible chess positions, of which about 10^18 are presumed reachable and thus relevant for weakly solving chess from the opening towards the 7 men endgame table base. Only 1/10 of that is needed by opening pruning.

Number of positions to visit = number of nanoseconds to calculate.

Here is an example of compensation for a queen.
The unaided human grandmaster before engines existed and with a chess clock next to the board calculated the whole line from move 30 to move 51 in his head:
https://www.chessgames.com/perl/chessgame?gid=1084375 
If a human can do that at 3.75 minutes/move,
then how much more can a cloud engine do with 60 hours/move?

Took me a while to work out the logic of why queenside castling is illegal after I found the solution to the problem. But Stockfish is not being clever: it's just that the FEN code tells it queenside castling is not legal 

@Elroch
" it's just that the FEN code tells it queenside castling is not legal "
You're guessing.  Right?
I did Not use FEN code to set up the problem on the diagram there.
And why would FEN code do that anyway unless the composer intended that? 
 Usually - problems are 'supposed' to have castling 'legal' ...
although I've seen some players complain Very Bitterly 'How were we supposed to know its legal.?' ...  Kind of disingenuous. 
Wouldn't the composer Say?  If he was 'arbitrating it as illegal' ?
I've never seen that ever.  Problem composers just don't so arbitrate.
Even in the diagram problem - its not arbitrary.   
The illegality is deducable !

I used 'Setup position' and 'clear board' and then placed the pieces.
But if you click the analysis button - and then play the first solution move - it won't let you castle long for Black in reply.
Its also announcing mate in two.
I'm thinking it checked the position for castling legality - has some kind of a program to see if a piece has to be a promoted piece.
Perhaps they even put it in in reaction to That Problem !
Yes I know that's unlikely.
Peculiarities of promotion to a bishop.
Anyway - that problem is absolutely the only one I can recall with an illegality of something having been deduced to get to solution.
And that's in many thousands of problems.

Many chess problems have been composed in which the solution depends on determining whether castling is legal. Here's one from The Chess Mysteries of Sherlock Holmes, by Raymond Smullyan. It is Black's move and White has just made a knight move. Holmes deduces that Black cannot legally castle.

I think you're way off beam there.

If you use SF over the UCI interface you have to give it at least a FEN. (For correct operation you need to give it a FEN with ply count 0 and the subsequent moves.)

If you use a GUI to set up the position the GUI will give you the option of specifying the castling options available; if you don't specify any, the GUI will generally assume none. Whatever - The GUI will produce a FEN to present to SF that either includes selected castling options or not.

If you click on the two fingers icon under your diagram and then on "PGN" you will see the FEN at the top of the window. As you set it up here it shows no castling options, so if you click on the magnifying glass SF will continue assuming no castling options as @Elroch said.

There's no way to get SF to attempt this particular puzzle.

I'm thinking it checked the position for castling legality 

AFAIK there are no programs that can do that... and even if there are, Stockfish (and other common engines) don't.

Actually Lasker never deliberately played inferior moves to confuse his opponents

Programs like Natch and Euclide that find proof games could do it, given the needed hours or days of compute time. A playing engine like Stockfish that tried to do it would lose every game on time, if it had to start from a middle-game position.

Very informative post.

But that's when its in game mode right?
I didn't use a FEN code to set up the position.
And I didn't set it up by copying or downloading or whatever.
I simply  placed each piece on the board manually with white to move.
From the position I'd seen over 30 years ago.
And when I clicked the analysis button at bottom (with only that and the Share button appearing there) - it announced Mate in Two.
Plus - on playing the first solution move - it would not allow an input of long castling in reply.  It simply flipped that black King and rook back to their original squares.
I am not 'picking a side' here. 
I usually don't - unless there's crushing conclusive anecdotal evidence or prohibitive logical evidence to do so.
Or both.  
I almost never choose to go with 'doctrine thinking'.    

What is your explanation of how the engine (Stockfish in this case I believe - although not necessarily the latest version - and can we rule out that engines have modes - how would we do that? )
how did the engine determine that long castling was illegal?
Yes we've seen the idea mentioned that its by 'FEN' code.
Do you have a different suggestion?  You don't have to ...  obviously 
And - I"m glad to see more posters now in the discussion - including new posters.

Wasn't Lasker the one famous for somehow getting out of trouble and even winning after 'blowing it' in the opening and middlegame?
And - 'inferior moves' have different definitions.
Could depend on who is asked.   
The words are there to serve us - not us to serve the words.

@Elroch - you're mistaken yet again.
I neither used FEN nor Pgn codes.
The position was set up entirely manually -
if you don't know how to do that - or seldom/never do so/aren't familiar or aren't aware that option exists - then you may have difficulty comprehending. 
I took steps to qualify that earlier.
You didn't 'guess' ?   You 'inferred' that?
Very inaccurately.  'Inferred' is generous.  
You formed an invalid premise and then 'built' on it.
But that's okay.
We're having a discussion.  Its not a personal thing.
We're demonstrating we know how to have the discussion - and publically - while addressing each other's posts - and also disagreeing and even criticizing from time to time. 

"You can confirm this by checking what you did "
I wonder how many times it will be 'necessary' to tell you I didn't use a FEN code.  (no code at all !)    s

@MARattigan -
That's good to know that there are many such problems where somehow its 'known' that castling or whatever is illegal or somehow deduced.
And I'll read your post further on that.
Regarding the 'two knights versus two knights' issue -
and as to how it pertains to the forum topic ...
there's 'something approaching'.
Say a supercomputer has 'solved' all such positions.
It could even report as to exactly how many are already checkmate or stalemate or somebody's about to lose a knight (and then that having to be 'solved' too) and how many are hopelessly drawn with adequate (and probably easy in this case of knights) and how many can be won by force.
If we had all that info - (never mind about the rest of the quarter million 'material situations') - then would that entire 'material situation' be 'solved' for forum topic purposes?  
No.   It would still have to be related to the opening position somehow.

That's at issue.  'Positions' are far less than 'game sequences'.  
Where 'positions' might someday be manageable to computers where 'games' might never be.
There's an analogy to the way people go at chess games and chess development.
Players crunch and crunch at 'calculations' while trying to invoke some 'pattern recognition' and premature 'theme assignment' ...  but so often that proves to lead to both inefficiency and inaccuracy.  
But players who distinguish observations from calculations and 'tactics detection' (GM Naroditsky) and motifs and 'what's going on in positions' from 'theme assignment' - are going to advance. 
How to 'look at the position'.  
Its usually subconscious - or keeps becoming subconscious.
But one can keep bringing it to the 'foreground' and examine consciously.  Both the position concerned - but also the 'general process'.  The 'overview' of how a position is examined.  Long before any process of isolating and comparing carefully prepared sequences of 'selected candidate' moves.  ('calculations')
'Selection' of calculations to be done - as opposed to 'calculations'.
Such selection process has a 'pre-process'.
Ironically - during calculations - one has to keep going back to observations again.  During 'lookahead' as it were.
Some would call that 'evaluation'.  Its not a good term.
Too ambiguous with what happens at the very end - 'move' Selection.

@MARattigan
I'm not 'off beam'.  Telling you what I did.  No 'codes'.
If you're saying that the diagram software will generate a FEN code anyway - and then base its analysis button/procedure on that 
well that's very Plausible ?  Except ...
Why would it arbitrate 'illegal' in this case ??
It would have an 'Illegal' Default ?  That's seems very unlikely ...
Very very unlikely.  Stranger things could be I guess. 
Castling illegal by default ???  Really ???

A while back when considering the setup options for chess.com diagrams - well there's many such options.  Like 'puzzle' for example.
There's a 'clear board' option.
And its irksome that the diagram will often insist on 1/2-1/2 when its not so.   I found a workaround for that.   It didn't always 'work' though. 
There's a 'move inputter' that one doesn't have to use.
Issue as to whether its desired that the algebraic moves at right and the move arrows at bottom right - appear initially in one's post.

@MARattigan might be the best here at looking things up.
How to do the searches effectively.
My experience on internet search (DuckDuckGo) and sometimes google when DDG doesn't seem to find - is that I find something close enough to what I'm looking for - over 70% of the time.
But if its not found pretty quickly - then I'm usually not going to find it.
About 80% of that time.  No matter how many rewordings of the search - includings of '-' and '+' (often makes it worse !)
Usually 'Quora' doesn't have it.  'Stack overflow' is even worse.  Reddit I avoid. 
Wikipedia is usually best.  If they have it that is !  

Castling is assumed to be illegal when you set up a position. I believe this was already mentioned somewhere.

For how little you say, you sure write a lot.

You know this for a fact?
Wouldn't it matter how the position is set up?
If that in fact is the case - (wouldn't be when you're inputting from the opening) 
And then there's the relevance to the forum topic.
How does the 'solving' approach the subject of illegality?
The forum topic is a big topic.  
And - it was I who posted the 'illegal by deduction' diagram.
A little - to get a lot of responses.  

Could you appreciate that 'illegal by default' is not the same as 'going by the FEN code' ?
I didn't use a FEN code.
I'm sure you can tell the difference. 

I  suggested that Stockfish might have found castling to be illegal there.
In problem mode.  Not game mode.
I'm not trying to insist it would always be doing that. 

Regarding 'castling illegal by default' ...
if that's well known  (rather than 'said somewhere') then that could have been said by whoever right away - instead of bringing up FEN codes and Pgn codes and 'Stockfish would lose if it had to do that every time'.
We could discuss that too.  'Castling illegal by default'.  Instead of about who.