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MatPlus.Net Forum Retro/Math Kofman's castling idea with en passant

### Kofman's castling idea with en passant

There is a famous Kofman problem where two castlings are mutually exclusive. White retracts castling to plays it, as otherwise he couldn't prove that castling is legal. Yea, this is obsolete now, but whatever. Enjoy!

(= 5+2 )

SH, Original
White retracts a move, then checkmates in one move

Solution: White retracts 1.h:g6 e.p., then plays 1.B:g5 mate. He can't play 1.h:g6 e.p., as there is no proof the last move was the double-step.

Unfortunately, that's not how retractors work. If you retract a move, you can play that move in the forward play. In Kofman's case, the retraction and forward play purely is played to ensure the invalidity of the black castling, because actually playing the castling move is the only way in that position to prove that white did castle.

IIRC there's a fairy condition 'Amnesia' which causes the loss of game history after a move, and with that fairy condition, your composition would be correct, because white indeed can't capture ep after retracting hxg6, because he can't prove that g7-g5 was the last move.

See also the Champagne tourney from this year, Marko Klasinc' second prize in category B.

That's what I meant when I said, it's obsolete now.

Interesting! What Joost says, I said for decades but doubt appears to have endured as I still meet with resistance. I had given the "amnesia type" the name "Alzheimer" but I agree "amnesia" is much less offensive! Another interesting point is that Kofman produced both types, the standard type for e.p. and the amnesia type for castling. Which is OK provided you enable the solver to find out which retraction rule applies. Which he never did.

In the context of natural language, the word "retract" implies undoing a prior action but not undoing any of the conditions enabling that action. Subsequently, the correction starts with the knowledge that the retracted move was legal and therefore the conditions enabling it are the same as before. The original action, the retraction and the correction are in one (looped) time line. Proof games should account for all and guarantee the consistency of the whole series.

Addendum: I agree with that part of Joost's story but not the remainder. If you can replay a retracted castling move for another reason than per convention (note that the replay of an e.p. move is not permitted per convention), then that reason can only be that you have "absolute castling right". The convention only gives you "castling permission" which is stated as irrelevant. Once you have absolute castling right, there no longer is any requirement to castle (just as in a PRA part), In fact, after the white castling retraction the black castling right has already disappeared. That's why the problem is cooked. The time looped proof game tells the story. This is precisely what makes the "amnesia rule" different. You forgot the rights you had on your previous move and you must replace them with a "convention".

Here's a stab at making a "true" version of Koffmann's idea with en passant. Trying for economy is always key, of course, and protecting the Black pawn was the tricky part of it.

Retract a White move & #1
(= 6+4 )

b) Remove bRg4

EDIT: I just had a thought: I stole Siegfried's idea for a twin, just for the lulz of it.

That's "amnesia" retraction. A "standard" retraction is like a legal move you take back in a real chess game. If you want to you can always replay that same move for why would your options be any different the second time in that position from the first time?

Nice problem!

Well the point is that is, after the retractions, in a) the ep is provable as allowed, and the only way to mate in one. Meanwhile, removing the Black rook is b) no longer allows for the ep mate, but it does open up another. So it's still an amnesia retraction, as intended, just with extra content.

And thanks!

Hmm, (a) is always true, (b) is only true in an "amnesia retraction" like Kofman's castling problem. In a "standard retraction" you can always replay the move you retract due to proof game logic.

Ah, didn't read well. This is what you intended! But actually you should announce the rules you use. You now rely on the smell of people to figure out what you intended. This happens a lot in the retro-field but it is wrong.

You do have a point there, but there is a trail to follow leading to the diagram, making it somewhat unnecessary to stipulate it here, IMHO.

Everything in retro-analysis an retractions is governed by PROOF GAMES. A diagram equals the cluster of proof games leading to the diagram. By choice, there are no restrictive conventions for retraction moves - anything goes. But of course you cannot retract just any move in all proof games for the diagram - only in those where that move was actually the last move. After you retracted the move you lost all proof games in which the retraction move was not the last move and you proceed with the remainder. The reason you have castling right or e.p. right after the retraction is that you have castling right or e.p. right in all the remaining proof games. It's absolute.

The relationship between proof games and retractions is the same as between proof games and forward solution moves. The information gathered by (a) retro-analysis, and (b) the moves played or retracted, determines which proof games are valid for the current diagram at any stage. The retro-conventions always only apply to the relevant proof game set and not to the diagram itself because the proof game set reflects the additional information received by the actions we observed - the history consisting of retractions and forward moves. Proof games do not listen to conventions, they follow the (assumed) game rules. The conventions only come into play to decide on choices not unambiguously covered by the current proof game set. Once a convention is applied it delivers new information which further reduces the proof game set.

This is PROOF GAME LOGIC and it is standard for all regular forms of retro-analytical or retro-active problems, like standard retractors. If you want anything else you must not only define it but also accompany it with a good story to make it digestable for people looking for a realistic scenario (everyone).

The "amnesia" retractor does not follow proof game logic so it is weird. It makes a cut in the time line which interrupts the flow of information. The story line is one of two phases. In phase A we attempt to find the starting diagram for phase B which is a completely new problem. Now there are many ways to invent a problem where phase A delivers a desirable diagram for B. For instance you can hand someone a box with pieces to be correctly placed on the a- and b-file. But instead, in the amnesia type we give a diagram where you may retract a move. Then we get a new problem with that diagram, phase B.

The reason I say this is weird is that the natural language concept "retract" does not in any way reflect what the amnesia retractor is doing. We commonly act, retract and correct in a single time line. Why split it up in multiple histories?

There is more to say on retraction but I'll leave it here for now.

Here is an example of a standard retractor in the context of proof game logic.

-1 & #3
(= 8+3 )

The relevant point is that no special permission is required to replay a retracted move even when it is commonly pessimistic like e.p. (Andrew's terminology). You can replay that move because ALL proof games remaining after a standard retraction permit you to replay that move. And that's why you can also choose the twin e.p. move which is equally supported by all remaining proof games! In spite of the fact that neither e.p. move could be proved in an amnesia retractor.

Retractors, like almost all chess or retro variants are based on a concept or a story line. The orignal retractor was this one. Two chessplayers play a friendly game. One of them says "I have a good position, right?" "Sure, but not as good as a move ago; you could have checkmated me in 3 moves!" replies his opponent. Formalized in a composition type with just 1 solution this was the first retractor and it still is the standard (help) retractor.

The amnesia retractor - similar as it may appear - is not anywhere near this story line. It is highly contrived and a typical product of a community rolling chess variants and new composition types off an assembly line by remixing ingredients in a random fashion such that the new drug rush helps them through the cold winter months. During their career they increasingly disconnect from the original emotional motivators and replace them with a robotic technical process. "You forgot where you came from" as they say about this pattern in real life. And that gets you for instance the "amnesia retractor" or the "defensive proca retractor" which have alien story lines. Btw, I like the defensive proca type though it is far from home :-)

While this is true for the derailed composer club, it is not how the general public looks at retractors. They have a significant affinity for the standard retractor type because of the wonderful and realistic story line that comes with it. Several times I placed retractors as Xmas puzzles under titles such as "take back your sorry move" and they drew a surprising response considering that most participants were unfamiliar with the type before. But standard retractors are very easy to explain and people get it amazingly fast.

This explains why the 2 famous Kofman retractors are so popular. They appear to fall in the feel good "take it back" storyline (though only one did it properly) and delivered a paradoxical gift wrap on top of it. What could be more shocking than to take something back only to replace it with the same thing as the only road to victory (other than ZZ)? I personally believe Kofman didn't notice that his original "mutually exclusive castling problem" was an amnesia retractor that didn't follow the standard story line. After it was brought to his attention he made a second version (perhaps there is even a third). Probably not because he was fully aware of the issues but to make everybody happy.

About 15 years ago I made a quadruplet containing corrections to Kofmans logic but I never reworked the original problem literally. Here is the version I believe Kofman should have made to honour the retraction story line, retain the paradoxical switchback operation (though delayed), and deliver a decently motivated solution with tries and variation! More content than in the original.

After Kofman, -1& #3
(= 10+10 )

Maybe off-topic, but the recent Christopher Nolan movie, "Tenet" has "unfiring" bullets and "unexploding" buildings, interspersed with normal forward time flow! Is he a closet Retro/Retractor fan? ;-)

I'm inclined to believe the reverse - retro-fans love time travelling movies. They probably engage their DeLoreans every year around this season. But in composing they also need to give account of the laws by which they travel and be sufficiently detailed in that for others to be able to follow them. My feeling is that the last step is a bit beyond the desires of movie producers. Their secondary if not primary interests are probably more inspired by the box office.

Nolan's "Memento" retracts scene by scene all the way back, although each scene rolls forwards. It is a masterpiece of technical plotting and continuity management. Primer is a fabulous time-travel movie where every element in every scene counts. The world of movies and TV shows is as populated with nerds as is chess, imho, and the internal logics of these linear art-forms (see TV Tropes) define a structure that creatives play against, even though many offerings are disappointingly formulaic.