Chess will never be solved, here's why

Not true of all tablebases. True of DTM or DTM50 tablebases in basic and competition rules chess respectively, but not true of DTC tablebases in basic rules chess or DTC50 or DTZ50 tablebases in competition rules chess for example because their objective is not to minimize the number of moves to mate. They don't produce mates of a consistent length.

I'm suggesting the 'moves to mate' is cart before the horse.
Two types of positions: those that are doorways between classes of positions (at least one capture available) and those that aren't.
Is there a third? Well it becomes 'game tree'.
There's at least one capture available but it isn't played.
fourth and fifth: all positions with checkmate on the board and all positions with stalemate on the board.
sixth class: all positions where you couldn't mate because there's not enough material. Example: K+N versus Lone King. Or K+B. K+2 bishops moving on the same color squares. No checkmate possible.

The "rather obvious" positions can be omitted, like king + 3 knights vs Long king, king + 4 bishops vs king + 1 knight..etc, king + 2 queens vs 1 rook..etc, as those are easy wins for a basic engine and don't need a tablebase. I read that originally king + 5 pieces vs king and other obvious ones like above were omitted in the 7 piece tablebases initially, but then decided to include them 6 years later.

Interestingly, while you can generate most of each new tablebase file from retrogade moves from previously generated ones (backward transitions) followed by more of the same, you would always need to add all the positions with mate on the board and stalemate on the board anyhow, since they are not a backward move from anywhere. I think there is a way of generating just the positions that are mate or stalemate on the board for each given set of material (but it's not that simple).

One thing retrograde analysis does not do is come close to checking legality. Making backward moves can easily get to a position unreachable from the standard starting position. This happens more when you have more pawns.

Only 10 black pieces need to be captured to reach that, think it's legal?

@Elroch
"Making backward moves can easily get to a position unreachable from the standard starting position."
But you have to allow that for the time being.
As the tablebases proceed - that might become much easier for whatever 'algorithm' to be developed that crunches that.
In the scenario I'm thinking of - computers generate various types of positions with 8 men on the board before even dreaming about 'mate in x' or 'unreachable legally'.
So far I thought of five types but three of them are kind of final.
Checkmate and stalemate and King + 6 bishops moving on the same color squares.
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The other two are: at least one capture available (doorway to the 7 piece tablebases) and no captures yet available (no doorway yet).
Of those five types only two can be generated from the 7 piece.
Point: You don't have to use the 7-piece to originally generate those 8-piece with at least one capture on board.
But you might be able to use the 7piece to 'solve' some of those 8 piece positions. In other words 'forward motion)
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@Elroch - you don't necessarily have to use a 'reverse move'. To generate an 8 piece. Would apply in both situations.
Consider just adding whatever to the seven piece without a reverse capture.
Then the 8-piece doesn't have to contain a capture option.
Consider it for a minute.
Do any two positions thus compared have to be 'incompatible'?
No.
It would take multiple moves to get back to the seven piece you just used to create the 8-piece.
Could there be 8-piece positions where you 'couldn't get' to that position?
But then it could lead to some other 7-piece position or positions.
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I would rather have started with 3 and 4 piece ... but okay.
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what could be 'Group six'?
Lopsided lone king situations.
You can't get from 8 piece to seven piece unless the lone King captures.
And if he does the only way he draws is if the remaining six pieces are all bishops remaining on the same color squares. Or the result is stalemate because the other sides other pieces are locked by his pawns.
Which I already covered on both.
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So group six is all wins but with no mate on board.
And with one side with just his King.
Speed up the project by skipping those?
Yes - or assign them to a different computer to determine the 'mate in x'.
Wow - even a computer could complain about that?
What would that computer say?
'Hey we know these are wins! What's the idea?'
Programmer: Stop playing human.

An interesting factoid to note in terms of how many pieces possible...6 pawns from each side can pass each other without capturing other pieces:

Well spotted - it needs another white pawn on a7 AND a single black piece or pawn on the board. eg

That could easily have been a promoted bishop, you should join the "illegal position contest" thread, people make more and more complex illegal positions where the proof that it is illegal is extremely subtle.

Such as, "well in order for the bishop to get to this square it had to get around these pawns this way, which means these pawns had to have moved before the knight got here. But for the knight to have gotten here, the king and queen couldn't have gotten to these squares behind the rook, without the king passing through a check that is impossible"....the goal in the thread is to make the most subtle illegal positions that are harder and harder to figure out the reason why!

Here are 3 fascinating positions in that thread that you have to prove are illegal:

Proof of illegality:

The black knight must enter b1 through either c3 or a3. Once the white pawns are on c3 and a3, the knight must already be on b1.

But once the black knight is on b1 and the white pawns are on c3 and a3, the knight can no longer move without capturing a pawn.

The White rook has to get to d1, but it has to do so BEFORE the knight becomes trapped on b1.

But to get to d1, the c1-bishop also has to get out of the way. But the only way for the c1-bishop to get out of the way in this position is via b2 after axb3. But that would require the move axb6, and the only way to allow Black to make that move in this position is to already have played the move c3 to allow the queen to get out and move to b6. That takes away one of the entry points for the knight, and therefore the black knight has to get to b1 before the axb3 move is played. But that means that the bishop can't get out and therefore the White rook can't get to d1.

Credit where it's due I didn't create any of these three, but my point being retrograde analysis to prove/disprove position legality would be an interesting study in computer programming, not just retracting legal moves but in determining whether a positions is legal or not by working backwards or constructing a game that leads to the position!

Here's a basic but slightly more subtle one:

A king could never get to the 8th rank with bcfg pawns on the 7th that could never have moved. 6th rank is covered.

I agree on that last one.
No way the white King could reach a8.
But that isn't 'subtle'.
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Regarding the first diagram - the issue appears to be the two Kings.
I found a way for the three bishops to be where they are.
But how does either King at its final square allow the other King to legally get past?

Yes and that's the beauty of these illegal positions. Individual aspects of them may be possible in a real game, but not all the aspects simultaneously! I've seen examples where yes it would be legal for a white pawn to get to where it is by capturing and black piece, and it would be legal for a black pawn to get where it is by capturing a white piece, but both couldn't occur at the same time, or each side would have had to make the move before the other side/circular reasoning. You and Elroch should really participate in that thread!

This forum is okay.

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Regarding tablebase projects for reference ... or for 'solving chess' x trillions of years from now ...
its obvious that every position must have exactly two Kings on board of opposite colors.
Now just two Kings is drawn but does that mean such positions should be skipped?
No. Because every single position must feature an arrangement of the two Kings.
So it seems the computers should first generate all such positions that are legal and then count those up and then all subsequent positions with additional material would have to generate from each and every one of those.
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But even that turns out to be not so simple.
Consider the simplest case.
One of the Kings is on a corner square.
Which means the other King can be on 60 different squares.
Four possible corner squares.
Either side to move.
But what about colors reversed?
No you can't cheat and say its 'reflections'. Because then you'd run into trouble eventually with additional material and then finally - trillions of years later the tablebases so generated would be invalid or incomplete because white moves first.
But more practically - tablebases failing to reverse colors would be inferior for 'reference'. Including the applications to chess software they're probably already used for.
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So do you multiply by two to 'reverse colors'?
No. Doesn't work either.
Because the other King could also be on a corner square.
Gets worse with edge-Kings and worse still with 'interior Kings'.
You're getting repeats if you multiply by two.
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Using the variables for at least one King on a corner square -
Its 4 corners x 60 squares for the other King x 2 for who's on move - 
= 480 basic positions.
But reversing colors? Gets messy. How to do.
Would the tablebase people have had to deal with this?
How about 99% chance?
And they would have had to deal with edge-Kings and interior Kings too.
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In regular chess do players have to deal with any of this?
Players who want to get a good score or better score have to maintain objectivity about positions.
Your opponent is checking out possibilities - so if you want to win you have to also.

And - this discussion of tablebases and 'solving' and also discussion like the original poster intended - is a 'change of pace' from the regular forms of chess and chess discussions.
Such variants on playing and discussing are popular. Also obvious.

Not just with tablebases, but it would also be interesting to see how well engines could analyze illegal positions, but only illegal positions by piece count and not illegal checks/impossible positions like the ones I posted. Such as does 25 knights beat 10 queens..etc? I've seen a few puzzle compositions based off of illegal positions but that still had a very interesting forced mating sequence. One was like where half the board was filled with Bishops but there was a rook and king in addition on one side, and that side had to shuffle the bishops in a certain precise order to make room for the king and rook to eventually checkmate the king. Tablebases aside, even just the pure calculation ability tested with an illegal number of pieces would be interesting.

I actually had a thread on that once:

https://www.chess.com/forum/view/fun-with-chess/illegal-position-puzzles

I'm reading EE's posts?
25 knights versus 10 Queens.
Well the 25 knights in three ranks plus one would all defend each other.
Which means the queens could not safely pick them off.
So the 'wall of knights' could just keep advancing as a kind of juggernaut first completely controlling the center and then advancing more like a tidal wave.
The Queens would be directly swept off the board with their King soon to drown. The King with the knights would remain completely safe behind his cavalry.