Chess will never be solved, here's why

"#573
That is already applied: there are never more than 32 men on the board: 16 white and 16 black.
Promotions to excess queens happen in real games, but rarely."

That doesn't mean they've done the cutdowns where promotions are limited according to how many pawns left - and how many captures on each side - which is always known - by piece count  ...
they probably have - 
but I think you've missed the points:
which is that those are legitimate cutdowns - whereas 'nobody in his right mind' and so on - are not legitimate.  
Also - moves that appear to be blunders - sacrificing material - or positions in which that has been done ...  excluding such positions isn't legitimate.

#533
The given Tromp position is legal: we have a proof game from the initial position that leads to it.

True of all his examples. That obviously increases the likelyhood that they could occur as positions in your proposed solution or occur as intermediate positions in your proposed computation.  
It is not a sensible position: it will never arive in a perfect game of chess.

This is a very basic error. You are confounding subjectively "sensible" positions with positions you may need to take into account in arriving at your proposed solution. (By "sensible positions" I understand you to mean positions you subjectively judge could be arrived at by what you subjectively judge to be "sensible" play.) 

These bear little relation to one another for several reasons.

Firstly the solution must arrive at a method of winning or drawing for one side only. All possible play by the other side must be taken into account. This will result in positions that are losing for the other side (possibly the starting position) after which random moves are perfect for him. This would probably not result in what you would judge to be sensible play and hence not to positions that you judge to be sensible.

Secondly, even the player that has the solution is not confined to making moves that you would judge to be sensible. They can randomly choose from moves that maintain the win. This would usually result in play that you would also not judge to be sensible and again to positions that you would not judge to be sensible.

Thirdly your computation would not restrict itself to positions that occurred in the final solution.

Fourthly your computation would be designed to produce only a weak solution, not a weak efficient solution on some criterion of efficiency. This would produce play that differs more markedly from "sensible" play than the play recommended by current tablebases which are all based on minimising/maximising the number of moves to meet some criterion (e.g. mate for DTM tablebases, but these necessarily work only in the absence of the 50 move rule, conversion to a winning endgame with fewer men or mate for DTC tablebases, which again don't necessarily work in the presence of the 50 move rule, advancing a pawn while maintaining the win, conversion to a winning endgame with fewer men or mate for DTZ50 tablebases, which work irrespective of whether the game is basic rules chess or competition rules chess from positions with ply count 0 and that is sufficient for a weak solution.) This would in turn lead to positions that differ more markedly from what you would judge sensible.  

E.g. this is an amended version of the Syzygy v. Syzygy snippet I posted earlier. I've added a "Syzygy alternative line" which also follows Syzygy best moves, a "Nalimov line" that follows Nalimov best moves and what I've called a "scenic route alternative line" which follows perfect play according to a possible solution of the sort you're looking for (incomplete - you could finish almost however you like so long as you mate.) 

All the lines shown are perfect play, but probably only the Nalimov line you would judge sensible.

If you look at the "scenic route" line it should be apparent that almost all positions with the starting material or possible promoted pawns could occur with that flavour of perfect play. Similar considerations would apply to positions with more men than the current tablebases accomodate.

You'll also notice that even Sysygy play, which corresponds closer with "sensible" play has no aversion to underpromotion. It obtains two knights less than Nakamura obtained in the real game I posted earlier (see Syzygy alternative line move 24), but it's obvious it could obtain ten from some positions with more pawns. 

In short you haven't shown, or made any progress in showing, that the first of Tromp's positions can be ignored so far as your proposed solution is concerned. I suggest the same applies to the rest of his positions and vastly greater number of similar positions included in Tromp's estimate of the total number of legal positions under basic rules chess. (Which must be increased 100 fold since you intend a solution under competition rules). 

Multiple promotions e.g. to 4 queens rarely happen in real play, maybe once in 500 games.

But real play is not relevant to the problem. The above perfect play has five.
Underpromotions to knight, rook, or bishop rarely happen in real play, usually to avoid stalemate, or to exploit the unique properties of the knight. Maybe once in 500 games.

Again real play is not relevant to the problem. The above perfect play has four of those too.
The 3 random positions on the Tromp website are all proven legal, but non is sensible i.e. none can happen in real or perfect play because of the multiple excess promotions and underpromotions that make no sense. It is not that these are rare examples of the Tromp count: it are random samples, i.e. all ordinary positions from the Tromp count look that way. That is why the Tromp count is way too high for the purpose of evaluating the feasibility of solving chess.

You haven't shown, or made any progress in showing, that any of his positions are not germane to your proposed solution, so your conclusion makes no sense.  
Even more: a sample of 200 random positions without excess promotions also contains most positions with non sensible pawn structures or piece arrangements.

Same applies.

So even the 3*10^37 is way too high.

Pointed out before; under competition rules that figure would be 3*10^39 not 3*10^37 and represent as your source says the total number of legal chess diagrams without promotion.

In view of the fact that you've made no viable case for ruling out any of the remaining positions so far as your proposed solution is concerned that figure should be (2.6+-2.9)x10^46 - Tromp's estimate (not upper bound) of the number of legal positions under basic rules times 100 to account for the 50 move rule.

#584
Please stop your lament about the 50-moves rule. As pointed out #581 above the 50-moves rule plays no role at all.

As incorrectly pointed out. 

It plays a large role in positions covered by the tablebases and an increasing role as the number of men increases (starting with no role with less than 5 men).  There's no reason to suppose this stops beyond 8 men. 

It is simply a fact that competition rules chess contains around 150 times the number of positions that basic rules chess does. (But for the purposes of a solution that can be reduced to 100 times).

It's not a lament; it's just a fact you find inconvenient. (As you find also the distinction between diagrams and positions inconvenient.)

Your Syzygy vs. Syzygy example proves nothing. 1 Qb8 Ka2 2 Qb2#. If the position starts at DTZ 1, then that means white has been hopping around aimlessly to let such a situation arise. Hence the preceding play was not reasonable let alone perfect.

All the play in that example is perfect - in each of the lines. By both sides. Perfect play is usually not reasonable.

With the flavour of perfect play your solution is designed to produce White is allowed to hop around aimlessly without actually worsening his position, and with any perfect algorithm for White that starts from a White winning or drawn position Black can simply make random moves and still play perfectly.

The Tromp count leads to insensible positions. These can never ever result from a game between reasonable players let alone perfect play.

I'm in perfect agreement that Tromp's count would include many positions that would not occur with what most people would call reasonable play, but a solution must explicitly deal with positions that are not arrived at by reasonable play.

Reasonable play is not relevant to the problem. 

When you say, "... let alone perfect play" you in any case have it the wrong way round. Reasonable play from the starting position in my example would lead to only three further positions. Perfect play, particularly with no efficiency objective - which would apply to your proposed solution, would result in many more, and, more relevantly to your computation, potentially vastly more.

That is why the Tromp count is way too high for the purpose of assessing the feasibility of solving chess.

I think my post #584 shows you have produced nothing to support that statement.

In particular for the position you show - your line is probably not perfect White play, but it's not the only line to arrive at the position. You have said nothing to discount the possibility of a different sequence of perfect White moves (not necessarily accurate for any particular objective) each followed by some (any) Black move that would arrive at the position.  You have said nothing to discount even the first position you tried.

Please try reading my post #584 more carefully - you appear to have missed all the points I made.

#586
If you sincerely believe the first Tromp position can be reached by a reasonable game, then construct one and show it.
Of you sincerely believe the 50 moves rule plays a real role, then show one grandmaster game where the 50-moves was invoked with 8 or more men.
Show it or shut it.

#573
...
Nobody right in his mind promotes to a second light square bishop.
...

#579
When you promote a pawn, it is to a queen in 99.9% of cases. Underpromotions only happen for good reason: to avoid stalemate, to promote to a knight with check. When an underpromotion happens, it is usually to a piece that has already been taken, i.e. no excess promotion. Multiple excess underpromotions never happen in a reasonable game.

Likewise the lament about the 50-moves rule should stop. Most chess games human/engine end before move 50. In the rare cases where the 50-moves rule is invoked, it is in a table base position. As long as there are many pawns and pieces on the board, one side is compelled to move a pawn or capture, with or without the 50-moves rule. I know no grandmaster game where the 50-moves rule was applied before they were down to 7 men.
This is the world record longest game ever. The 50-moves rule only started to become relevant after they were in the table base position.
https://www.chessgames.com/perl/chessgame?gid=1268705 

This is the longest World Championship game ever. The 50-moves rule played no role.
https://www.chessgames.com/perl/chessgame?gid=2127373 
So just forget the 50-moves rule.

As I said in my last post, you have to stop believing practical play is relevant to the problem.

It is also not true that there are twice as much positions as diagrams.
1) It often is possible to see whose move it is by counting. E.g. the position after 1 e4 e5 it is clearly white's move. You could argue it could be black's move after 1 e3 e5 2 e4, but that makes no sense. No reasonable white player would play that way unless 1 e4 e5 were a win for black. In that unlikely case no black player would play 1 e3 e5, but rather 1 e3 e6.

The advice still pertains, but if your solution is for White it must account for all play by Black in response to White's moves. 
2) In positions where one side is in check, that side must have the move.

Agreed. I already pointed this out earlier in the thread.

I still used the factor 2 in adjusting your estimate to a quarter of a million years, because 1.9 or whatever would have made no difference. Feel free to multiply by whatever you can show to be an upper bound in that respect. But you have to multiply by something; you can't conflate diagrams with positions. 

3) Castling rights are usually lost early in a real game: because the kings and/or the rooks move, most often by castling

What happens in 'real' games is not relevant, but this consideration would I think have only a minor impact on your assumption.
4) En passant needs no special count. f2-f4 e4xf3 e.p. can be treated as if it were f2-f3 and e4xf3

It would still be two different positions, but again a minor point.

Conclusion: the Gourion count 3*10^37 is a reasonable figure for all legal and sensible positions that can occur in a real game between reasonable human or engine opponents.

Then the figure is irrelevant to your argument.

It actually relates to a small subset of legal diagrams rather than positions in any case.

It errs to the high side in including many positions with non sensible pawn structures
It errs to the low side by excluding few positions with sensible excess promotions e.g. 4 queens

How do you define sensible pawn structures?

It errs to the low side by excluding of the order of 10^46 positions that you can't find any justification for ignoring.

The Gourion paper writes 'no promotions', but I correct this here to 'no excess promotions'. An excess promotion is a promotion to a piece that has not yet been captured. In a queen ending it is impossible to tell if the queens are the original queens or if the queens are promoted pawns. So the Gourion paper includes promotions but excludes excess promotions.

Agreed on your last point.

#586
If you sincerely believe the first Tromp position can be reached by a reasonable game, then construct one and show it.
Of you sincerely believe the 50 moves rule plays a real role, then show one grandmaster game where the 50-moves was invoked with 8 or more men.
Show it or shut it.