Raymond Smullyan retrograde analysis puzzles

Retrograde puzzles usually contain one or more of these ugly characteristics:

1) Pawns b + d and/or e + g (blocking bishops) remain unmoved

2) Such bishop(s), despite blocked, are missing there and are found elsewhere

3) Pawn structure contains unlikely multiple pawns in vertical lines

4) King and rook(s) are in their starting position uncastled

5) Oppositely colored pawns are passing each other at 4th or 5th horizontal line

6) Some (minor) piece is redundant, created by dubious underpromotion

7) One side has no pieces movable, or only one

So what? In retros, we couldn't care less about 'likely'. All we care about is 'legal'.

I mean I haven't seen retro-puzzle resembling normal game position yet.

(Well, one exception maybe - mate in 3, starting with 1. 0-0-0, the point was if white can castle, black can't, and vice versa, thus 1. Rd1 was met by 1. ... 0-0. I still don't like it though, because if 1. 0-0-0 is illegal - and nothing can disprove that, black can castle and puzzle has no solution.)

Well, then I suppose we can eliminate castling from all the non-retro problems as well, since you can rarely prove that it is still legal.

No. My point is that the condition (proven by retroanalysis) only one side can castle is insufficient to assume 1. 0-0-0 as definitive solution, because there is no reason (or even convention) to prefer white over black. I can claim black's 1. ... 0-0 is legal move and defensive resource proving incorrectness of the whole puzzle - the only conclusion is that white can't castle. And nobody can disprove that.

For that particular puzzle, there is a (conventional) reason to prefer white in castling - it's his move. By playing 1. 0-0-0 you prove that white can castle by executing it.

Imagine it was a tournament game position (suspend disbelief) and neither side recorded moves. You play 1. 0-0-0, your opponent calls the arbiter. There is nothing your opponent can use to show that you can't castle, and your move will stand. It's something of the same logic in the puzzle. Black's 1...0-0 is illegal after white plays 1. 0-0-0, so there is no defence.

In other words - you make illegal move legal by executing it. It's very interesting, maybe I will apply that in real life sometime. :)

(robbery, murder, smuggling drugs, quackery ...)

Let's say 1. 0-0-0 is an illegal move in a blitz game, but white plays it anyway. Black player calls an arbiter and claims win by opponent's illegal move, but he can't prove it and white denies it. The arbiter orders to continue and black responds with 1. ... 0-0, resulting in illegal position. However now white can't claim win by black's illegal move and arbiter can't prohibit black's castling as well, because they can't prove which move was illegal.

In your example, white can claim win by black's illegal move since after he played 1. 0-0-0 (we assume players and arbiter know and remember this was just played) which was allowed to stand (and therefore legal), now 1...0-0 is illegal (thanks to quirks of the first position) and the arbiter can prohibit that move.

There was nothing making 1. 0-0-0 definitely illegal in the starting position, so the arbiter allowed it; however, when it was executed on the board and allowed to stand by the arbiter, that proves that it was a legal move (insofar the current game is concerned) and by extension, also proves that 1...0-0 is now illegal.

Of course I'm not an arbiter, but this makes (common?) sense. Would be interesting to hear views from a certified arbiter...

One big no. The burden proof is on white player to prove which move was illegal. Even if it was obvious only one's side castling can be legal, executing an illegal castling can't make opponent's legal castling out of blue sky illegal.

Hm. If all this happened chronologically (white plays 1. 0-0-0, black calls arbiter protesting illegal move, no mention at all of 1...0-0 yet), then I'm honestly not sure where the burden of proof lies. With white to prove his castling was legal? With black to prove white's is illegal? If it was a real game where there was some legal sequence of (unrecorded) moves preceding this, it's obvious someone's wrong, but to whom does the benefit of doubt/burden of proof go? (My personal view is that black has to prove it's illegal since he's making the claim to the arbiter. At no point does black's castling come into question during this claim, as we're only concerned with whether white's king and rook must have moved at some previous point.)

I'm obviously disregarding the sequence of moves leading up to the situation, which could very well make black's castling rights be stolen from him! From the position alone, there is nothing to say that white's (or either side in fact) castling is illegal, so he can play that move (since it's his turn first... too bad black.)

Also, I went to read the FIDE handbook and there was nothing about this strange possibility in it. It just effectively says the arbiter makes his own judgement on the situation. (In case it wasn't clear until now, I don't care about the composition aspect of the position, this arbitration business is far more interesting.)

You are simply wrong when you claim there is no convention to allow white to castle in this case. It's well known enough in the problem world to have a name - "A Posteriori (AP)" or "Retro-Strategy (RS)" - you prove you have the right by exercising it.

http://www.saunalahti.fi/~stniekat/pccc/codex.htm

"Article 16 - Castling and En-passant capture

(1) Castling convention. Castling is permitted unless it can be proved that it is not permissible."

....

(3) Partial Retrograde Analysis (PRA) convention. Where the rights to castle and/or to capture en-passant are mutually dependent, the solution consists of several mutually exclusive parts. All possible combinations of move rights, taking into account the castling convention and the en-passant convention, form these mutually dependent parts. If in the case of mutual dependency of castling rights a solution is not possible according to the PRA convention, then the Retro-Strategy (RS) convention should be applied: whichever castling is executed first is deemed to be permissible. (my emphasis)

In such real blitz game (no recorded moves, no witnesses) a reasonable arbiter would allow castling both sides, if the resulting position remained playable, i.e. illegal only by retroanalysis, not directly (king en prise). White's stubbornness couldn't stand to prevent black from castling, because both sides deserve equal treatment.

@ BigDoggProblem

This is exactly what I dislike about that puzzle. The blogger you linked has unreasonable mindset like the author.

What I quoted is not just some random blogger. That codex has been followed by problemists for decades. (There's no money in chess problems, of course, so the website doesn't have an ornate design.)

Retros are not to everyone's taste. I really don't have an issue with you not caring for them. I just wanted to make clear that, from a retro enthusiast's point of view, the objections you raised carry no weight.

Oh yes i loved his retrograde analysis books!

He is more of a logician than a problemist!

Has anyone considered the fact that the White rook could be on h8 instead of a1.  If all the pieces moved to the other side of the board then this position is possible.

Impossible; too many captures required to get pawns past each other. (A complete set of pawns passing each other requires eight captures; removing one reduces the count by at most two, but there are only three missing pieces. Of course removing a piece won't help either, four missing pieces versus eight necessary.)