Chess will never be solved, here's why

Solving chess is only feasible right now as weakly solving, just like was done for checkers (8*8 draughts).

Strongly solving chess i.e. a 32-men table base would require to visit all 10^37 positions. That would take 10^28 seconds on 1 cloud engine and would require at least 10^37 bit of storage assuming only 1 bit draw/no draw per position and a 1 to 1 relationship between natural numbers 1 to 10^37 and the 10^37 positions in the sense like Tromp did. That is not feasible with present technology.

Before offering to solve chess for us, it would be a good idea to understand a little of what is involved.  

There are 12579944 positions in the KNNK endgame. To strongly solve any one of these, as the Nalimov and Syzygy tables do, it is necessary to visit only 736 of those positions.

You obviously have some learning difficulties. As Tromp has shown, there are at least 2.6x10⁴⁶ positions in competition rules chess (2.6x10⁹ times as many as the figure you repeatedly give). His work is sound.

You apparently can't even distinguish between a position and a diagram (but that is the least of your problems).

A 1-1 mapping of positions to bits would not be enough for even an ultra weak solution.

Weakly solving chess allows to prune non relevant positions and visiting only the square root of the legal and sensible positions, like was done for checkers, to account for positions rendered irrelevant by each pawn move and each capture.

Weakly solving chess allows for significant pruning of the number of positions visited, but not for any of the pruning you have postulated.

You haven't shown that it allows you to visit the square root of the number of legal positions ( √{2.6x10⁴⁶} let alone the square root of the legal and sensible positions (whatever "sensible" is supposed to mean).

Weakly solving chess allows also to prune the opening variations needing evaluation. If the Berlin is proven to draw for black against 1 e4, then it is not  necessary to check if the Marshall, the Petrov, the Sveshnikov, the Najdorf, the French, the Caro-Kann draw as well or not. Hence only 19 ECO codes suffice instead of 200 ECO codes B00 to C99.

A proof of the statement would be in order.

As said the Tromp count is way too high as it contains almost all insensible positions with multiple excess underpromotions that play no role in solving chess. Take a data base with 4 million games, that gives about 320 million sensible positions. Take a sample of 320 million positions as counted by Tromp, that leaves 95% illegal positions and at best 1 sensible position.

I've shown you examples of multiple excess under-promotions that play a role in Sysygy's solution of seven man chess (and pointed out that these occur in practical games -though this consideration is strictly speaking irrelevant).

Are you sure it's the positions that are insensible?

A legal position is a position that can result from the initial position by a proof game of legal moves. I tentatively propose a sensible position as a legal position where the proof game has e.g. an accuracy > 90% or an average centipawn loss < 10. None of the random samples by Tromp is sensible.

Your proposed solution is not designed to take any account of accuracy.

Presumably you measure accuracy in terms of number of moves to mate. I've already shown you Syzygy playing perfectly but hugely inaccurately in #584 (have you got round to reading that post yet?). I could give you many more with a greater divergence from accuracy.

It is the norm for perfect play (and also practical play - though this consideration is strictly speaking irrelevant) to be not sensible in terms of your definition.

Your definition of sensible play/sensible position is in no way relevant to your proposed computation.

Even the Gourion paper gives too high an estimate: a random sample of 200 positions also contains many non sensible positions, mainly because of non sensible pawn structures like quadrupled pawns. 

This is almost certainly perfect play by both sides.

If the starting position for the game is a White win, the position shown could almost certainly appear as part of a weak solution. A weak solution in that case must cater for any moves by Black, however odious you personally might find those moves. 

The moves shown are clearly not accurate, but your proposed solution is not designed to produce accurate play. This could form part of your weak solution, in which case the final position could not be discounted.

You will note the final position contains quadrupled pawns.

The 50-moves rule plays no role, forget it.

You obviously have, in spite of many reminders. 

The fact remains this plays an increasing role in closely matched positions in perfect play up to the 7 men we know about. We also know it plays a role in 8 man positions.

The only reason you think it should stop playing a role at 8 and beyond  is you can't think of any cases where it would be relevant and you think your play is nearly perfect, so, if you can't think of it, it doesn't exist. 

But I don't think you'd stand an earthly of mating under your own steam against SF14/Syzygy from this position under basic rules (SF14/Syzygy could). You certainly wouldn't under competition rules (and neither would SF14/Syzygy).

You think you'd get better with more men. I think that defies common sense.

It is not necessary to double the number of Gourion positions. The side having the move can be inferred by counting the moves for both sides.

What a croc of manure.

Whose move is it in this diagram - the third of Tromp's introductory diagrams (and the first  which does not have a corresponding position with one of the players to move already excluded from his estimate of legal positions)?

or the one in #727 which you have conveniently ignored.

Moreover any position with black to move can be converted to a diagram with white to move by switching colors, as endgame books conventionally do.

This is true, but it's also true of checkers, so should already be taken account of in your (yet to be discussed)  assumption that the time taken is proportional to the square root of the number of legal positions.

(I'm assuming the checkers paper refers to legal positions rather than equivalence classes of legal positions under black/white symmetry - I should check.)

It is possible to cut the Gourion number in 2. As soon as both sides have lost castling rights, most often because both sides have castled, as is most often in 26-men tabiya, there is left/right symmetry. All positions with a white king on the left half of the board can be converted to an equivalent position with the white king on the right side of the board by switching wings, as endgame books conventionally do.

This is true. @playerafar already suggested it in #259

"Another big cutdown could occur - with positions that are rotations and reflections of each other. "

but you appeared to reject it in your response #261

"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."

so I have assumed you were not intending to take board symmetries into account in your program. 

If you are, this would halve the effective number of positions in Tromp's count, reducing it to something over 1.3x10⁴⁶.

This would reduce the calculation time on your (yet to be discussed) basis below 200 millenia.

For all Gourion positions without any pawns, the number can be cut in almost 8 by applying symmetry. The position can be converted to an equivalent one with the white king confined to the triangle e1-e4-h1. The syzygy table base does that.

Yes, but no real saving beyond the above. The vast majority of positions have pawns.

As to Stockfish against Stockfish at 60 h / move is like letting 2 toddlers play: If the calculation reaches a table base draw, then that means all moves of the black toddler were in retrospect good enough to hold the draw. As for the white toddler: we grant him takebacks starting with his last move and working backwards. That ascertains all his reasonable moves lead to no more than a table base draw.

Not quite.

Here is a cut down version. The task is to reach the 4 man tablebases from a 5 man position.

The toddlers are SF12 and SF12 with different coloured hats.

The game reaches a 4 man tablebase draw. Black toddler's moves were good enough to hold the draw. White toddler can take back as many moves as he wants, but with two knights that's obviously going to lead to no more than a draw.

So you can stick it in your cut down solution as a draw? You could, but it's actually mate in 52 (under either set of rules).

If SF can't manage to successfully negotiate a single phase with 5 men on the board, how would you expect it to do negotiating 19 phases with 26 men on the board? 

And there's that word "reasonable" again. You should have realised already from the numerous examples I've given that perfect play is usually unreasonable in your terms.

The table base decides draw or not, not the evaluation function of Stockfish. The evaluation function of Stockfish merely serves to guide the search in a meaningful direction.

Or not, as the case my be.

@playerafar

How would that procedure arrive at this (legal) position for example?

In the pre-engine era games were adjourned after 40 moves and 5 hours of play and play was then resumed the next morning after players and their seconds had analysed the position the whole night. They had neither engines nor table bases. They had only like 10 hours to analyse. Nevertheless they more often than not arrived at the truth about the position.

In reality you no more know that they arrived at the truth than you could beat SF/Syzygy in the position I invited you to try in #770, and neither did they.

They arrived at conclusions that would very likely work in the context (i.e. practical play at that level).  They were usually very well qualified for that. 

How did they do that? First they established who had the advantage, i.e. which side had to play for a win e.g. white and which side for a draw e.g. black.

In theoretical terms establishing who has the advantage means determining if either side has a forced mate (possibly in a trillion moves). Also, if the players are to play perfectly, both sides should be playing for the same result.

The terms you are using are only relevant in practical play. You can never make a move that wins for instance if the position is a theoretical draw, but you can, in practical play, make a move that is likely to increase the chances of your opponent blundering into a loss. Which moves might do that in practical play depends on the strength of your opponent.

Practical play is irrelevant to the problem unless you believe (as turned out to be the case in checkers) that practical players are close to perfection. But chess is not checkers. 

Then they looked at the position and its traits. Then they started analysis i.e. they played  a game against themselves from the position. When the outcome was as desired for one side, then they started with takebacks for the other side, starting at the end.

Same way anybody analyses their games.

The procedure wouldn't have worked for the toddlers in the example I gave in #770.

It is this procedure that I propose to emulate with cloud engines and table bases to likewise find the truth about a 26-men tabiya.

You intend to produce a weak solution of competition rules chess.

For this the Wikipaedia definition of "weak solution" is adequate viz:

"Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. That is, produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it." (My highlighting.)

As @btickler pointed out, asking two toddlers doesn't count as a proof. 

The tablebases I have no problem with (assuming they were complete; not quite the case yet) - it's the bit before.

If you call a cloud engine with 10^9 nodes / second running for 60 hours / move a toddler, then your desktop at 10^6 nodes / second running for a few seconds is not even an embryo.

Not at all.

I actually gave them 2 hours for the first 40 moves and two hours for the rest (which of course they didn't need). I would expect (though I'll leave it to you to try) that allowing them 60 hours a move would produce an almost identical game.  

It's not a shortage of time that you see in the example, it's a problem with Stockfish 12's algorithm. If it's asked to mate with the knights in any mate of depth greater than about 35 it can be provoked into taking your pawn in short order. I think the algorithm prunes all the winning lines quite quickly.

That's why I chose SF12 in preference to SF8, SF11 or SF14 , which I also have. The others can't mate either but they'll all draw under the 50 move rule. With the time settings I used, I didn't want to wait that long.

#784
I am only concerned about a weak solution of chess and without the 50-moves rule.

That changes the basis substantially. You said earlier you wanted to include it.

main changes are

(i) The number of legal positions is back to Tromp's (2.6+-2.9)x10^44 - no need to multiply by 100. The number that need to be taken into account can be approximately halved owing to left right symmetry.

(ii) Mates under basic rules which could not be won under the 50 move become wins instead of draws. Forced mates in more than 5898.5+50 moves are no longer automatically excluded.

I agree:
"Produce at least one complete ideal game (all moves start to end) with proof that each move is optimal for the player making it."

To speed up I start from a 26-men tabiya and I stop when the 7-men table base is hit.
The tentative ideal game is generated by letting the cloud engine of 10^9 nodes / second play against itself for 60 hours / move until it reaches the table base.
That is 1.2 million times more than your 10^6 nodes / second desktop at 3 minutes / move.

Yes, but that's a drop in the ocean when you consider a mate of depth 549 or say  Haworth's predicted 1200+ moves for 8 men or, if you take the liberty of extending the prediction to 26 men, 2,601,500,000+ moves.

I wouldn't even expect it to sort SF12 out on the toddler's problem, because I think that might only be sorted if it searches to a depth where it actually hits mate - 51.5 moves.

The problem is the exponential growth of positions to be evaluated with the number of moves. A 1000-fold increase in speed wouldn't produce a very large increase in the search depth.

Proof for the black moves resulting in a draw is unnecessary: if the black moves do lead to a table base draw, then they are good enough and the table base retroactively validates them all.

How is the distinction between colours arrived at?
Proof for the white moves comes by granting takebacks to white for his last move, his 2nd last move and so on to ascertain that the alternatives produce nothing better than a draw either.

As in the example I gave in #770?

"In theoretical terms establishing who has the advantage means determining if either side has a forced mate"
++ No, not at all. Determining who has the advantage is finding out who seeks a win and who seeks a draw.

In theoretical terms both players must seek the same result if they are both to play perfectly. For a weak solution, one players moves are arbitrary.

In the initial position white is a tempo up, so white has an advantage.

You can't mix up practical play with a solution of chess. If White has a theoretical advantage that means he has a forced mate. You have no grounds for assuming that White has a forced mate from the starting position.

White tries to win and black tries to draw.

If it were true that White has a forced mate in the starting position, then in any weak solution White tries to win (but not necessarily in a sensible way - any old way will do).  Black plays in a totally arbitrary fashion.

In the adjourned position Najdorf - Bronstein black had a positional advantage and more active pieces, hence black tried to win and white tried to draw. If an advantage is enough or not to win is the outcome of the analysis. Who has an advantage is at the start of the analysis.

Who, if anyone, had a forced mate from the position would be determined in absolute terms at the outset. Any analysis that occurred would attempt to assess the probable outcome of practical play.

Someone capable of reliably making an evaluation in absolute terms might well need an ELO rating millions of times that of anyone involved. You don't know. There's no way to correlate when the number of men on the board gets beyond 7.