Hardest Mate in 4 of All Time

Actually, the other proof game is easier since you have [Ra1] available to be captured; need not promote on h8.

Although for the first proof game I have comment #13 available, which lays out how the game needs to go.

@KiloNewton: Thanks for calling my logic faulty by the way. ;-) At least you seem satisfied the position is legal (I'm following the other thread as well.) Can't help it if you don't like the solution, it's quite hard to get started in this whole retro business.

@Arisktotle: Unfortunately I don't know of any generic PG engines other than the usual SPG ones (Euclide, Natch).

All I have to add on the convention issue is that Polar_Bear probably won't be convinced, and he has good reason to be. Chess problems are by nature quite arbitrarily regulated (even the underlying chess rules themselves are arbitrary, and that's not even going into the fairy realm) and it's thus difficult to give any sort of justification why the rules should be one way and not another, plausible alternative. Polar_Bear seems to have in mind a different but sensible set of rules (he hasn't said exactly what, but I gather it'd be stricter in the sense of not permitting the special moves as freely) which should be perfectly fine too, if a little too restrictive for composing than composers would like.

The current situation is a product of trial and error and history; it's a monumental work to try and hoist all that onto a solid logical foundation a posteriori. Personally I'm quite open whatever conventions are in play, as long as they make sense ("to the first order approximation" as it were), they are spelled out clearly somewhere, and the fringe cases are addressed as they come along.

If Polar_Bear has a suggestion - one that covers all the issues and not just some - I am interested to hear it. You are right that composers won't be happy if all space for retro-creations is taken away. There was a time in the early 20th century when you couldn't make a common castling move unless it was expressly permitted in the stipulation. Problemists didn't like it and it evolved to what there is today. If Polar_Bear suggests going back to that time, I predict he won't get a large following.

Remellion, I hope it will make you feel better to hear that I think your logic in #24 is just fine. But I find implausible your suggestion that Polar_Bear may have worked out a consistent set of alternate rules for chess compositions.  If he has, he could refute my thinking by publishing it.

i found it!

@n9531l: I promised to deliver a detailed explication of #73. Hereby.

First the preliminaries. Before you can move into solving #73, a number of conditions must be established:

A. By retro-analysis that the last black move was either a move by K or R or it was Ne6-f8. In the latter case, the prelast moves was Bg8-h7+ and the move before that either again K or R, or N-e6. If black played K or R in any history he has no castling right. Thus, If he has, then the last moves before the diagram were -1 ... N-e6 0. Bg8-h7+ Ne6-f8. This knowledge is essential for the solution.

B. You must know and understand article 18 in the Codex: "A position is considered as a draw if it can be proved that an identical position has occurred three times in the proof game combined with the solution"

C. You are to be aware that there is no obvious way to treat this problem as a PRA situation, certainly not if you take article 16.3 literally.

As indicated before (and consistent with the Codex), there is no castling right in a diagram only "a permission to castle". If diagram rights were absolutes than you could conclude with certainty that Ne6-f8 was the last move and such is obviously baseless. This is also made clear by the start of the forward solution: 1.Bg8 Ne6 (or 0-0-0, Qb4) 2.Bh7+ Nf8 3.Bg8 Ne6 (or 0-0-0, Qb4). Together with the preliminary analysis you can now conclude that the same position occurred for the 3rd time if black has castling right, i.e. after blacks move -1, move 1 and move 3.

Here comes the critical phase in the solution. Presumably by article 18, you cannot draw after blacks move 3 since you cannot prove it for the "proof game" (presumably all proof games). Continuing however disables blacks castling permission as there is no legal proof game that combines the non-drawing repetitions with black 0-0-0. White uses that acquired knowledge in his move 4.Qf1 after which black would have loved to castle - but he can't. The rest is plain sailing.

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Obvious? Not at all. In fact there are several issues with these proceedings. The one I will concentrate is this one "what happened to the draw-claims and the draw pre-claims?" Many retro-specialists believe that these exist besides article 18, implying that not-claiming still is a possibility. It means that black can castle after 4.Qf1 on the basis that he chose not to claim a draw. This opinion comes from the conviction that article 18 is not a Codex change to the FIDE-rules, while it in fact is.

Interestingly, article 18 is nothing but a rule change, it isn't even a real retro convention. And this while an essential retro-convention is missing in the Codex (also for 50M). How can you tell? True retro-conventions solve a problem that is common to all retro-problems, i.e. missing history information. Article 18 doesn't do that, it only seems to do that to those who want it to be so. How can you tell? Article 18 is about a condition that occurs in all proof games - which it consequently narrows down to the proof game - and no true retro-convention can ever be about a condition in "all proof games". All retro-convention are about conditions in a part of the proof games, example "you can castle as long as it is legal in just one proof game", "you cannot e.p. even when there are proof games in which you legally can". For conditions that are absolutely certain no retro-convention is required; anything true for all proof games is true for the current diagram. Example: if e.p. right can be proved in a diagram, then e.p. right is always a fact. Once you see article 18 is not about resolving missing history information, then you quickly conclude its only function is to replace the FIDE-claim-rules. And that of course is how it should be.

The situation becomes more clear when you see which convention is missing. It also potentially opens the road towards PRA-applications if desired:

MC (Missing Convention): No position is assumed to occur for the 3rd time unless it is unavoidable (there is a similar missing convention for 50M)

Note that this is a true retro-convention. It says that a position did not occur for the 3rd time even though it is historically possible. Secondly, it says nothing about drawing rules. Retro-conventions have nothing to do with game terminations. Article 18 can now be simplified to clearly state the change to the FIDE rules:

New article 18: When a position occurs for the 3rd time, an automatic draw is declared. This Codex convention replaces the FIDE claim articles for chess compositions.

This article need not mention proof games since it is an amendment of a FIDE-rule; these are always about single games. The "Missing Convention" provides the proof game feeds for the new rule. It would be natural to combine the two together as the new article 18.1 and 18.2.

The power of the "Missing Convention" is tremendous. All by itself, it is sufficient to make problem #73 work. Article 18 is not even required as you can verify. Even with only FIDE claim paragraphs, the "Missing Convention" resolves most repetition issues in compositions.

The point of the preceding explication is to show how #73 exposes frailties in the Composition Codex. And I haven't even addressed the priority arrangement between RS and PRA. That can wait for another time and context.

Thanks for the detailed explanation. I need to think about it a little more before I'm ready to give the problem to my friends at the chess club.

Actually, if you can present #1, then you can present #73. They are logically the same but the latter one doesn't suffer from the PRA-issues in the current Codex. In explaining #73 you can ignore the insanities of the Codex on repetitions; my amendments only formalize what most of us believed these Codex conventions always were!

The missing component for solid presentations of these problems is the  understanding of the nature of Retro Strategy. I made some notes on that in my reply to Polar_Bear but what's really required is my book on the subject. I expect it will take 10 to 25 years for the new paradigm to sink in.

Quick shot from the peanut gallery: The compulsory 50-move draw missing convention - would this invalidate 50M compositions where the last pawn move/capture/castling occurred >50 moves ago, since the position would be illegal (cf. DR play continuing in a dead position)?

Article 17: Unless expressly stipulated, the 50 moves-rule does not apply to the solution of chess compositions except for retro-problems.

Article 17 supplement: In retro-problems, a position is a draw whenever it can be proven that necessarily (i.e. in any proof game) fifty consecutive moves have occurred with no capture, no pawn move, and no castling.

SHORT ANSWER: No, this is independent of the "missing 50M convention". A past position could not have been DR under "FIDE claim rules", since you cannot be sure a draw claim will be made. A past position could sometimes have been DR under "automatic draw rules" but not in the case you describe. However, as explained in the long answer, the automatic 50M draw does not apply to the past!

LONG ANSWER: The confusion about this topic comes from the (Tom Volet) example with the "50 moves rule" supplement in the retro corner. How can you get to 75 moves without pawn move or capture when an automatic draw takes place after 50 moves? Answer: you cannot! Therefore, the supplement to article 17 can only be understood as a rule change in the midst of the game. Before the diagram, the players were under the "50M claim rule" - though they clearly didn't claim anything. From the diagram onward, the "automatic 50M draw" applies as soon as the occasion presents itself. Strange? Yes, very, very strange. Note that the 50M supplement must be marked as a FIDE rule change since the 50M condition needs to occur "necessarily in any proof game". Therefore it cannot be a retro convention.

Since we still need the "missing 50M convention" we will model it after the "missing repetition convention": One cannot assume that 50 consecutive moves have occurred without pawn move, capture or castling unless such is unavoidable.

The article 17 supplement will then read: In retro-problems, from the diagram onward, a position is a draw whenever fifty consecutive moves have occurred with no capture, no pawn move, and no castling. The 50M FIDE claim articles no longer apply in this phase.

This is a FIDE rule change and needs no reference to proof games. These will be properly filtered by the "missing 50M convention".

Is there no relation between DR and the 50M convention? Well, yes there is! But it cannot refer to the past of a diagram since the past lacks automatic draws. Starting with the diagram though, a DR condition due to 50M might occur at any time. Example: the diagram is preceded by at least 49.5 moves without pawn move, capture or castling. Suppose the next move cannot be a pawn move, a capture or castling either, assuring the upcoming automatic draw. Then indeed, the diagram is a draw by DR. Not because of the "missing convention" but because of the automated draw.

Peculiarly, it is possible to have illegally ignored DR in the past with the repetition convention. Different from the 50M convention, automatic repetition draws (presumably) apply to the whole game and could therefore have interfered in the manner described in the previous paragraph (with a 0.5 move phase shift). Actually, this was the reason that my 2nd prize winning repetition problem was incorrect. As said in an earlier post, nobody noticed. I guess it is safe for the next 25 years.

holy crap, op just post the answer already

Is anyone still surprised by people who post without reading the previous comments?

The OP posted the answer at #72. Where were you?

now that i saw the solution i realized my ignorance

This puts you ahead of the people who had the solution explained to them several times and still couldn't understand the reasoning.

I just stumbled across this simpler problem of the same type.

https://www.chess.com/blog/Shivsky/retro-puzzle

I posted this improvement about 5 months ago on this forum:

Mate in 2 moves

I can't remember it. What was the topic title?