Chess Will Never Be Solved. Why?

The point about Ziryab's excellent example is that it requires retrograde analysis to find out.
As opposed to something that can be defined as inherently illegal.  
If such 'inherently illegal' is already factored into the 45 digit number of positions - well then that's different.

I actually posted that I thought Ziryab's example was impossible.
But then realized (yes two people showed how it was possible)
so I deleted that post !!   

I got the position from Ilya Maizelis, A Soviet Chess Primer

,,🙄🤔

A point about that position you posted is that its an example of what I'm talking about.
It has to be analyzed as opposed to something we 'already know' like a King being in check from three pieces at once.

It's elegant for having so few pieces, and one clear idea. For whatever reason I particularly like that the answer can't be e5-e6 uncovering the bishop, because the pawn would have been attacking the king.

I always intended to read that book... didn't realize it had a puzzle like this.

In children’s after school chess clubs, I often see a king in check by three pieces. Sometimes both kings are in check. When I ask the students how they reached the position, they never know.

Many of the puzzles are entertaining. There is one that is mate in one where every legal move is checkmate. With White to move, there are sixteen legal moves. With Black to move, there are twelve.

Err, wait, I was thinking of Soviet Middlegame Technique by Romanovsky... Primer is still a good book of course. I hear that the title is a bit misleading since it's not for beignners.

I have Romanovsky, Chess Middlegame Planning.  One of two volumes based on the Russian classic. Maizelis offers elementary instruction with examples that are quite challenging. I bought it a few months ago and have worked through the first 100 pages or so. I also recently acquired volumes 1, 3, and 4 of the Russian Chess School set. I bought a used copy of volume 2 five or six years ago from the same guy that sold me volumes 1 and 3 in February. Paid a total of $45 for the three. Volume 4 was purchased new.

The exercises are first rate.

😁^✅

That's what I noticed from working parts of Yusupov's books... the positions are just... such high quality. It's hard to explain to a non player I guess. Besides being highly instructive they're often aesthetically pleasing too, and sometimes beautiful.

"bumph"
What we usually see on that are just more repetitions.
With two + symbols in front.  They are like gravestone markers.

And the task of solving chess isn't just about numbers of positions to solve and hardware speeds of computers.
Other tasks within it - like things that would require huge projects within them to even define the positions to solve. 
Purely Semantic definitions aren't good enough for mathematical/chess/computer tasks.
And without viable definitions - then numbers of positions in the tasks can't be found - nor can ratios of same be found either.
Which means that the number of positions in the tasks has to revert to the previous mathematical upper bounds like the 45 digit number often mentioned.

#426
"You have already made a (to my mind misguided) reduction in the number of legal positions by an arbitrary factor 10^39/10^44 or 1/10000000 to account for your vague notion of what counts as a sensible position."
++ No, it is from 10^44 to 10^32. It is neither misguided, nor vague.
A legal position is a position reachable from the initial position by a series of legal moves.
A sensible position is a position where said series of legal moves has > 50% accuracy.

"a further reduction of 1/10000000000000 on the same grounds."
++ No, it is not on the same ground.
Ground 1 is legal or not.
Ground 2 is sensible or not.
Ground 3 is reachable in the course of the solving process or not.
Ground 4 is relevant for weakly solving or not.

"There is no further reduction to be made on the grounds of reachability"
++ No, legal = reachable from the initial position. Reachable in the course of the solving process is different. Suppose e.g. that the optimal strategy for black to achieve the game-theoretic value of a draw consists of answering 1 e4 with 1...e5 and 1 d4 with 1...e6. Then the position of Ziryab #411 above is legal and sensible, but not reachable.
That same position can never be reached from a Ruy Lopez, a Petrov, a French Defence, a Queen's Gambit Declined, a Nimzovich Indian Defence etc.
I hope you now understand what reachable in the course of the solving process means.

"if a sensible meaning is assigned to "position""
++ Diagram = position of pieces on the board
Position = diagram with side to move, castling flags, en passant flag i.e. FEN without ply count
Node = position with evaluation (either provisional like +0.33, of final draw/win/loss) and history (like ply count and array of previous positions)

"That depends on the solving process." ++ No, it depends on the strategy.

"The first of Tromp's"
++ This position is clearly not sensible because of its multiple underpromotions to pieces not previously captured.

"I've added "ply count 0" to make it a competition rules game position."
++ You seem obsessed with your competition rules.
* The 50 moves rule plays no role as it is never invoked > 7 men.
Chess is already strongly solved with 7 men or less.
* The 3-fold repetition rule is a major drawing means and for the purpose of solving chess can be simplified to 2-fold repetition: twice the same FEN.
If repeating 2x is the optimal play, then repeating 3x or 5x is the same.

"If the solving process were extending the Syzygy tablebases up to 32 men"
++ That would be strongly solving chess,
requiring 10^44 nanoseconds of time and 10^44 bit of storage and thus not feasible.

"So it will necessarily be reached in the course of the solving process."
++ No, this position will never be reached in weakly solving chess as it is not sensible.

"It's probably worth noting at this point that, when invited, you failed to show that any of Tromp's basic rules game positions failed your (ill defined) definition of sensible."
++ Definition is clear: a sensible position is a legal position where the proof game from the initial position has an accuracy of > 50%.
The Tromp position shown is clearly not sensible.
It has 7 white rooks, 3 black rooks, 2 black dark square bishops, 5 black knights.
Underpromotions to a rook or a bishop only make sense to avoid stalemate.
Thus the losing side can never have underpromoted rooks or bishops:
optimal play would have been to promote to queens.
As both sides have underpromoted rooks/bishops one side must have blundered.

Promotion to a queen (worth 9 pawns) for a pawn yields +8 pawn units.
Underpromotion to a rook (worth 5 pawns) for a pawn yields +4 pawn units and thus
in comparison to promotion to a queen is equivalent to
blundering -4: 1 rook for 1 pawn, or 1 minor piece + 1 pawn
Underpromotion to a minor piece (worth 3 pawns) for a pawn yields +2 pawn units and thus
in comparison to promoting to a queen is equivalent to
blundering -6: 1 rook + 1 pawn or 2 minor pieces

If this is too hard to understand, then you can just take my shortest PGN proof game of legality and enter it in the analysis tool and see for yourself that the accuracy is < 50% and that position is thus not sensible and thus cannot play a role in weakly solving chess.

A legal position is one that can be reached by a series of moves from the starting position, so all illegal positions require retrograde analysis to find out.

It's true that there are many criteria that can be used to immediately determine if a position is illegal but the criteria depend on retrograde analysis. To prove a position is illegal it is necessary to know that no legal sequence of moves can be played from the starting position to arrive at the position; determining that is retrograde analysis. 

@MARattigan
"so all illegal positions require retrograde analysis to find out."

I disagree.  Logic can be used as opposed to 'retrograde analysis'.
You would know they're not the same.
But we might continue to disagree on that.
Perhaps you'll maintain you don't know what I'm talking about.
But nobody can do somebody else's thinking for them - in many contextes.

This example addressed to everybody:
If we know that a King in check from 3 pieces at once is an illegal position -
do we then need to do 'retrograde analysis' and computer 'move by move' retrograde analysis to determine that a King in check from Four different pieces is therefore also illegal ???!!!
No.  We don't.
Hence the terminology ...  'illegal on the board' as opposed to 'it couldn't have got there'.
That's hairsplitting?  Hardly.
If it is - hypothetically - then the hair being split is about two feet thick and a sharp knive splits it as easily as that knife cuts a sandwich into two. 
If the terminology 'immediately illegal on the board' isn't liked - is disdained -
then is there a better one?
Point:  You don't need to go back on that 4-check.  Nor the 5-check ...
You don't need to consider umpteen trillion move orders to know its illegal.

😁^✅ 👋 🎵🎸🏠🌹👍 😎🙂😡😂😈👻😿😹😄☘️

#432

"how many of Tromp's positions can be reached by a series of moves with > 50% accuracy."
++ No position sampled by Tromp can be reached by a series of moves with >50% accuracy.

"to prove a single one of the positions in Tromp's sample could not be so reached"
++ I proved it in 3 ways but you fail to understand.

"what percentage of positions that will be reached in the course of your solving process will be sensible, nor even what percentage will occur in the solution." ++ 100% of course

"you don't say what you mean by "accurate" in your definition of sensible position."
++ Load the PGN in the imperfect analysis tool and read what accuracy figure it gives.

"In positions that are drawn there is no distinction between accurate moves and moves that don't produce a position that is won."
++ The accuracy figure is to distinguish between what is sensible and what not and thus what positions can turn up in the course of the solving process. It is to distinguish between reasonable positions that can occur and non-reasonable positions that cannot occur like the positions randomly sampled by Tromp.

"Well that's not what you said immediately before you posted the figures"
++ 'Reachable' is shorthand for 'reachable in the course of the solving process'.
Reachable from the initial position is the same as legal.

"which is not remotely true"
++ How do you know? What are your 4 figures for the number of legal, sensible, reachable (in the course of the solving process), and relevant positions and your reasoning for these. Mine are 10^44 legal, 10^32 sensible, 10^19 reachable (in the course of the solving process), 10^17 relevant and I gave my reasoning.
Look at Losing Chess, essentially the same number of legal positions and solved with 10^9 positions only. So for Losing Chess only 10^9 legal, sensible, reachable, relevant.

"This presumably means that what you class as "relevant" is not previously covered."
++ I have already explained what is relevant and what not.
Example 1) if 1 e4 e5 draws, then it is irrelevant if 1 e4 c5 draws as well or not.
Example 2) 1 e4 e5 2 Ba6? loses for white, all resulting positions are not relevant.
Example 3) many endgames with opposite colored bishops are known draws, any further analysis is not relevant.

"what you mean by the solving process"
++ The solving process is the engine calculation from humanly prepared starting positions towards the 7-men endgame table base.

"By a sensible definition of "position" I meant one that determines the nodes in the game tree."
++ I take the definition of diagram, position, and node as usual in literature. E.g. diagram per Gourion, position per Tromp and per FIDE Laws of Chess 9.2.2, node per link I provided.

"The evaluation is an attribute of a node dependent on the method of evaluation."
++ Yes, that is right. Provisional evaluation is by Stockfish only to guide the search, final evaluation is by the 7-men endgame table base.

"What is "provisional like +0.33" supposed to mean anyway?"
++ In the course of the solving process the final evaluation is not yet known, it only becomes known when the process hits the 7-men endgame table base.

"Are you proposing to define "node" in terms of a Stockfish evaluation?"
++ The definition of a node is the position plus its evaluation and history. The value of the evaluation is provisionally that of Stockfish and finally that of the 7-men endgame table base.

"how long you run it for" ++ Until it reaches the 7-men endgame table base
"on what type of machine" ++ a cloud engine of 10^9 nodes/s
"change your meaning of "node" every time a new Stockish version came out."
++ The meaning stays the same only the provisional values of the evaluations change.

"No it's not clear." ++ I proved it in 3 ways, but you seem unable to understand.

"taken from the basic rules and should be vastly altered in the competition rules game"
++ You keep repeating this nonsense. The 50-moves rule plays no role. The repetition rule is essential.

* The 50 moves rule plays no role as it is never invoked > 7 men.

"It is very rarely invoked in practical games because all practical chess players are out of their depth with that many men in sufficiently closely matched positions. They just agree a draw instead." ++ No, they move a pawn, or capture. Example:
https://www.chessgames.com/perl/chessgame?gid=2127373 

"I've already given you positions with eight men that are won under basic rules but drawn under competition rules." ++ You have not proved that these positions can turn up during perfect play. You cannot. In perfect play like ICCF WC draws it never comes to such positions.

"you can't meaningfully incorporate the agreed draw into the rules you assume"
++ Yes, the good assistants can terminate a calculation if a known draw of >8 men is reaches, just like ICCF grandmasters agree on a draw in a position they know none can win, e.g. most opposite colored bishop endings. 

"it's weakly solved for any such ply count 0 position without castling rights."
++ No, chess with 7 men or less is strongly solved with or without 50-moves rule. Castling rights do not matter, they are already lost when a 7-men position is reached.

"You can never get twice the same FEN in a game."
++ Yes you can, FEN without ply count that is. That is also how engines track 3-fold repetition. They compare the new FEN with the previous FEN disregarding ply count.
The ply count is part of history of the node.

"Syzygy would be strongly solving chess, that is under basic rules only."
++ No, the Syzygy table bases have strongly solved chess with up to 7 men with or without the 50-moves rule.

"The proof game? Clear?"
++ To prove a position legal requires a proof game. To establish that a position is sensible requires said proof game to have > 50% accuracy.

"to prove it with your definition of "sensible"."
++ I gave you the PGN of the shortest proof game.
Put it into the analysis tool and read the accuracy, then agree it is < 50%.

"so all the excess promotions could in fact have been blunders (11 moves in total)"
++ Yes, that why the Tromp position can be dismissed at first glance as not sensible: it can never occur in a reasonable game and thus a fortiori not in an ideal game with optimal moves from both sides i.e. perfect play. That is what I say the whole time about all Tromp sampled positions and even about the vast majority of the 10^37 Gourion positions. They are not sensible and thus play no role in weakly solving chess.

"That would never have occurred to me."
++ Glad you at least understand this now. Each underpromotion is like a sacrifice of a piece, so it is a blunder unless there is compelling reason to sacrifice. The only reason to underpromote to a rook or bishop is to avoid stalemate and only the winning side has reason to avoid stalemate. So there can never be sensible underpromotions to rooks or bishops from both sides. One side can be winning and thus avoiding stalemate, but both sides cannot be winning at the same time. Even more as chess is a draw, there never is a winning side in an ideal game with optimal moves from both sides i.e. perfect play, so positions with underpromotions to rooks or bishops  play no role in solving chess.

"there's any correlation between the analysis tool and accuracy"
++ That it works: put in your PGN, get the accuracy from the imperfect analysis tool

"you have shown only that you haven't found a proof game to prove the position is sensible under your definition."
++ It is proof that there is none. The underpromotions are all blunders of pieces and they are inevitable to reach the Tromp position. You can change the move order, you can add moves ( I presented the shortest proof game), but the accuracy stays < 50% and the position remains non sensible as is also clear by reasoning and even obvious at first glance.

"any connection between sensible positions and the positions you might encounter"
++ Weakly solving chess comes down to finding ideal games with optimal moves from both sides i.e. perfect play. When perfect play is judged by the imperfect analysis tool, it will give some accuracy near 100%, say 98%. The failing 2% then says nothing about the perfect game, but refelects the imperfection of the analysis tool. Now if the imperfect analysis tool indicates < 50%, then it is clear this is no ideal game, no optimal moves, no perfect play and thus not part of the weak solution to chess.

hmm...

wow 435 posts