Too difficult for computers

@Elroch. By now there's not much point in debating the details, since you're not taking in what Arisktotle and I are saying and hence we're just going in circles. For instance:

Using words like "note that" and "presume" shows that you have already forgotten (or never realised) that this minor dual in the main line has already been brought up by me and it's also covered by the WFCC Codex quoted. As I wrote in post #22: "The intended solution of this study ends with a mate on move 21, and this has some minor duals that are sometimes tolerated even in the main line." Then in post #28 the Codex says: "Studies are unsound if there is a method of fulfilling the stipulation which is different from the author’s solution, and may also be rendered unsound by serious [16A] duals in the main line, but even in the main line many kinds of duals are normally tolerated."

So I'll make some broader comments. The thing about the chess composition field is that most chess players don't realise how distinct and different it is from the practical game. Since it's a complex field with its own theory and concepts, players approaching ideas like soundness and unique play – which don't really exist in the practical game – are actually beginners in this regard, no matter their chess-playing strength. The trouble is that many such players don't realise they are beginners, and coupled with some arrogant scepticism, they may view such new ideas as nonsensical. Composed chess problems are called "the poetry of chess" for many good reasons. Thanks to compulsory education, everyone knows that poetry is an art form distinct from prose, but imagine a naive grown-up person seeing a poem for the first time – it may seem like nonsensical and ungrammatical prose.

The reality is that concepts like soundness and unique play are very basic, Chess Composition 101 stuff that are not contentious and are accepted by all problemists. Just go to Wikipedia for the articles on Endgame Studies and Chess Problems and you'll see that they agree with us. And no, these Wiki pages haven't been taken over by zealots (try not to be a conspiracy theorist). Both Arisktotle and I have been composing top-level problems for decades, so we know what we're talking about.

The standards of unique play in compositions are a bit like the standards of legal play in the game. Think of a beginner who is brand new to the game playing a more experienced person. The beginner makes an illegal move, moving his king into check, which the other player points out as incorrect. Now the beginner gets defensive and says, "There's no need to be such a purist and disallow all "illegal" moves. I enjoy the freedom of making such moves occasionally and who are you to tell me what I should enjoy? Are you some kind of snob? So what if the FIDE rule book claims it's illegal – the book is not ideal as it's too restrictive in my view. I'm now a chess player and part of the chess community, hence FIDE should listen to me in deciding what kinds of moves are allowed."

The analogy of poetry is nice. Rhyming, numbers of syllables, and various other conventions are chosen by some and rejected by others. There is certainly no hard and fast definition of a poem, merely a body of work with various conventions. Some poetry looks like short prose to the average eye.

Back to chess, I am only interested in truth (i.e. the solving of positions to evaluate results and how to achieve them). Sorry for the offense this may cause. I am agnostic about the preferences of the chess composition field, and whether a position is an endgame study or a problem doesn't have any fundamental relevance to solving it: the objective and the rules of chess are all that matter. (That being said, knowing the conventions might allow clever reasoning that would help solve a problem - not of much interest to me).

Arisktotle's post said "To prove a fighting mate you'd need to provide all of the minimax analysis". Sorry to be blunt, but to prove a mate (I have no idea what the adjective "fighting" is doing there) you don't need to provide all the minimax analysis. Rather you need to provide a complete winning strategy, selecting moves for white (just one in each position will do) and dealing with all moves for black. You can ignore most white moves. This is how chess is played and more complex problems have to be solved by humans - there is not time to look at all possibilities for both sides, at least not at depth.

Being interested only in the objective truth of a chess position is fine, and this probably parallels your preference for objective truth in the real world, i.e. the scientific perspective. If you're into philosophy, we can consider how most complex things have both a subjective aspect (e.g. artistic) and an objective one (e.g. physical sciences). Thus a painting has both subjective/artistic properties (in the minds of viewers) and objective/physical properties (its paints and wood). Likewise a chess composition, where its objective "truth" – win in X moves or draw – is uncovered by analysis or tools like tablebases.

The issue of soundness/unique play, though closely related to the artistic, actually belongs to the objective side. This is why, even though it's normal for problemists to have different (subjective) views on the value of a composition, they practically never disagree on whether it's sound. Soundness is on a higher objective level compared with the more fundamental "win/draw" lower level. Using paintings as an analogy, soundness is the colour/chemical properties while win/draw is the particle-physics properties.

It's fine to focus on the objective side of things, as scientists do, but this can be carried too far when subjective things are devalued or viewed as just illusions (e.g. emotions are nothing more than chemical processes in the brain). That's a type of reductionism common in the modern world.

@Elroch: We've come closer on nothing but the minimax analysis. Indeed you need not provide all the white options only all the black ones which is let's say just 1483664754 variations. That's quite a bit more than 1. "Forced mate" and "forced win" are total non-concepts that replace proof with a result. It is loosely used to suggest that a proof can be delivered in a few lines - taking into account the knowledge level of a decent chess player". The truth is that unless a win or a mate is a forced mate it is not a win or mate at all. A truth seeker will never use the term "forced anything". It does have a deeper meaning though. It's another way of saying "we are playing fighting chess". Fighting chess is the description of the relationship between the 2 parties in a chess game with regard to a goal and their presumed relationship in solving certain composition types like studies and directmates. It is not universal as it is replaced by different strategies and goals for helpmates and selfmates. The fighting condition is not self-evident in goals and strategies of composition land. What we know as minimax evaluations formalizes the decisions in fighting strategy and thus all "forced" outcomes.

Btw, "winning strategy" is either meaningless in proofs or it is also the same as "forced win" and "fighting win". The way the term "strategy" is used in chess game analyses is 90% based on the knowledge level of players and seeks to avoid delivering actual proof lines. But I suppose you know that.

Indeed, you know nothing about "solving". Though chess compositions have a solution they are not made "to be solved". They are made to present a panoramic view of ideas in the composer's mind. The solving approach is an elegant way to demonstrate them plus a challenge for the mind. Did you know that most readers of composition magazines do not seriously attempt to solve the challenges? They much rather browse through the solutions and comments to enjoy the views. And the last thing any composer will want the solvers to get away with is some accidental solution. His task of course to prevent that. He only wants to see it "solved" in the exact way he created it because that is his piece of art. And that includes for instance "the thematic white failures" which are lost in the pruned minimax analysis. And it includes discarding the lines not showing any part of his artistic creation. They only muddy the scenery. Therefore in solving competitions the focus is on thematic content. Providing 1 thematic solution line gets you a point while 6 others may get you naught. There is some arbitrariness in the judging of solutions and points and referees have backroom discussions about it with solvers (occasionally). Just to show that solving is not about mathematical proof. 

Your sort of solving is imaginary. - not only because it is uninteresting but also because it is undoable for any but the simplest puzzles - unless of course you are cheating with non-existent forced win lines and computer or poster generated counterplay. You missed out on the design perspective as much as the math requirements.

Note: I will not go into your example as it is atypical for endgame studies like most of drdos7 posts; that's just his interest. Due to the narrow algorithmic solution there is not much choice to go by unlike most endgame studies.

I have great respect for mathematics and very little for mathematicians. Usually when they leave their universities - even when they are still pursuing professional careers - they start replacing their expertise with authority as happens in so many other fields. I know from another subject that is certainly true in chess. I did not complete my math education though I was considered one of the most talented students in the country - by test. Never lost my talent and caught up some of my backlog by studying formal systems later.

Instead of arguing expertise I choose to dismantle one of the corner stones of your approach. The "win" stipulation for studies can be restated as "forced win" or "forced mate", absolutely identical concepts. Which gives us the recursive definition "a winning position with white on move is one where either (a) white can checkmate black on his next move, or (b) white can play a move which still gives him a winning position after any black countermove. That should do. What does this tell you about the traditional abortion points in solution lines? Let's see your answer: "give a line providing a forced mate". That's awkward isn't it? That is simply restating the same action that was part of the 'win' definition and has been applied on every move so far. So your process is empty besides that what we did all along. One difference. Without any justification you dropped the requirement to assess all the black defenses which were part of the preceding solution procedure. Suddenly there is a whole new meaning to the term "forced mate". That's called inconsistency. The truth is here that nothing can change in the tail-ends handling until you include external knowledge sources which teleport you to Mecca in no time.

Now, if you are a true mathematician you will appreciate the power of this argument. If not, well, be happy with your diploma's.

Second note: I am not concerned with duals here; that's another subject.

I am not responsible for your multiple failures to understand things clearly stated by me.

But I am sufficiently bored of this not to be going to waste any more time on someone who first states "'Forced mate' and 'forced win' are total non-concepts", then says they mean the same thing (don't you mean the same nothing?) then tries to argue that they aren't relevant to problem solving!

You could sum this up with something like "I am way too smart and literate to admit that i was saying nonsense".

I was not the one who said that "forced mate" is a non-concept. I was the one who pointed out it is a fundamental concept.

I was also the one who pointed out that the example in the OP was an explicit counterexample to the claim of the confused @Arisktotle, who dealt with it by saying "I will not go into your example as it is atypical", which makes me wonder what the heck he was doing in a discussion about it.

Offensive comments sometimes need a factual response.

But I agree with the general sentiment.

Excellent article! 👏

:D

Try putting the FEN for a classic puzzle into the Stockfish 15 analysis tool.

7k/4K1pp/7N/8/8/8/8/B7 w - - 0 1

How is it that the strongest chess computer in the world can't solve it? My belief is that it relies on unreliable heuristics about remaining material.

Thanks to @GhostNight for drawing this puzzle to my attention.

Is it not showing the mate in 3?

Here it is on my computer:

It is not showing up the position. Maybe I can try to post it here?

Here is the starting position if it comes out? White to move.

The Stockfish analysis shows a mate in three in that position with 1.Bf6 gxf6 2.Kf8 f5 3.Nf7#

Great, but did you try to figure it out on your own first. That is the point of this chess problem. You don't learn/gain anything if the AI does the thinking for you. Oh btw I did! It was one heck have a hard problem for me.

It was easy for me, I thought Elroch was insinuating that the chess.com Stockfish had trouble with this mate in 3 problem in post #55

Love to have a game with you! You can teach me a thing or two!