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[Title "#1 - W. Keym. Die Schwalbe, 1969. Ded. K. Fabel"]
[FEN "qrbR4/rP1P1pp1/pQ1pp3/pPp5/6P1/1P3BB1/3PP2P/R3K1k1 w - - 0 1"]

The solution to the problem is simple. Black has only two possible last moves: c7-c5 and c6-c5.

But which is the correct retro protocol to apply?

RS spoke first: "just do it 1. 0-0-0#"

PRA: "We see two solutions here. 1. 0-0-0# (not e.p.); 1. bxc6ep# (not 0-0-0). But 16.2 will say that this is not our case."

RV: "Why not ours? Very much ours. 0. ... c7-c5 1. bxc6# (not 0-0-0); 0. ... c6-c5 1. 0-0-0#"

Which of the three of them gave the correct answer? Or maybe it’s a SPRA instead?

Background: problems like this need a protocol to solve them. The two main protocols are PRA (Partial Retro Analysis) & RS (Retro Strategy), explained here.

There are also two rarer protocols, RV (Retro Variants) & SPRA (Special PRA)? All four are discussed in an authoritative article here by IM Werner Keym who authored the relevant sections of the World Federation for Chess Composition Codex (and who composed the above problem).

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    What is a RS? PRA? RV? SPRA? Recommend the asker edit the question to include definitions of these acronyms to help future visitors. Commented Jul 3 at 21:16
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    Respectfully, I was only trying to help improve the question so it can attract more upvotes over time, and attract high-quality answers. I find your questions very interesting. The value of posts is much bigger than just an answer to the asker--it is for future visitors on the site. Commented Jul 3 at 21:59
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    To be clear, no one is telling you what to do as a Vsevobuch. My comment clearly uses the word recommend. Commented Jul 3 at 22:01
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    Coming from the HNQ (the title is currently shown on almost all SE sites), curious what are PRA, RS, and RV in chess, never heard of them until now.
    – Andrew T.
    Commented Jul 4 at 9:33
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    @ЭлсиРинген People may very well be able to help you or be interested in the problem even without knowing some acronyms in English. What's the problem with explaining what they are?
    – JiK
    Commented Jul 4 at 9:59

2 Answers 2

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This is half of a twin problem. The other half has white knight d8. See link in PDB. Good, in my opinion, to keep the integrity of a problem unless proposing an explicit version.

Black's last move was c7-c5 or c6-c5.

In a) wSd8, we can eliminate c6-c5, so ep is on, but White has lost castling rights. So the only combination of rights possible is S_ep. Hence 1. bxc6ep#!

In b) wRd8 shown here, both c7-c5 & c6-c5 remain a possibility. Castling is possible, but only if the last move was c6-c5. So 3 combinations of rights remain: S_castling, S_ep & S_neither, but not S_both. If we apply the conventions, we may castle but not ep. Hence 1. 0-0-0#!

But what is the name for the protocol used in b)?

Let's take a step back. RS (Retro Strategy) & PRA (Partial Retro Analysis) are the two main alternative protocols to help us resolve multiple interpretations of conditional moves. They are defined here.

As someone who's spent a lot of time doing pure mathematics, I like the idea that our definitions of RS & PRA should scale all the way down to situations where we only have a single interpretation, after applying the castling & e.p. conventions.

scaled down

For example, if there are no conditional moves, then the situation is like in the lefthand box in the picture above. There is just one interpretation. RS & PRA will behave the same when applied to it. The same is true if retroanalysis has eliminated all uncertainty about the conditional moves, as in twin a) of Keym's problem.

If we have a single conditional move, then things aren't much more complicated. See the middle & righthand boxes in the picture above. If the conditional move is castling, then the castling convention tells us that by default we are allowed to castle. And if the conditional move is ep, then the ep convention tells us that by default we cannot castle. So either way, there is a single green box representing the interpretation which we follow. The yellow boxes represent combos that are globally dominated due to the castling/ep conventions, and we don't need to consider them.

In all three of these simple cases, RS & PRA will behave the same as one another. Now this may all seem very trivial, so let's turn to twin b) of Keym's problem.

two diamonds

The lefthand diamond above is the relevant one. As can be seen, there is still only one green box. Due to the conventions, we never get to ep, but we may castle. Because there are no choices to be made, RS & PRA behave identically to one another, just like they did in the earlier trivial cases.

So do we say that this is RS or PRA? Or both? Or neither? That is a matter of taste, but I hope the general message gets across:

Just one green box => RS & PRA behave the same

For complex cases, of course RS & PRA behave very differently to one another. But I enjoy the fact that they agree in simpler cases.

Special PRA (SPRA) & Special RS (SRS)

It's instructive to compare with SPRA (Special PRA). SPRA is defined to mean that ep is optimistic. So the ep convention is different: there is no change at the protocol level. It's hence misleading to call it SPRA. And we might just as well have SRS for "Special Retro Strategy".

Now looking at the righthand diamond above, it's clear there are two green boxes. While there is no significant difference in the behaviour between SRS & SPRA here, they are distinguishable. SRS gives two solutions, as we can play either of the optimistic moves to checkmate. SPRA on the other hand has a single solution with two parts, and in each of them one of the mating moves is permitted.

It's obvious that optimistic ep is not intended here. The twinning between a) & b) obviously asks that the solution in one is the retro try in the other. So normal pessimistic ep is the answer.

Retro Variants (RV)

While not condemning RV, it's a term whose meaning has shifted, and is generally deprecated. Rather than reusing an old term with a new meaning (argh!) as Werner Keym seems to propose. I would rather use a new acronym ARV for "All Retro Variants". This indicates the meaning, and avoids confusion with previous usages.

So basically ARV means that the castling & ep conventions are suspended. All the arrows are gone in the boxes below. All the yellow boxes become green. We still have the choice between RS & PRA protocols for ARV, although I suspect that existing ARV problems are designed for PRA.

In this particular problem, the solutions to twin b) are a mess with ARV, and do not harmonize with a) as intended.

Wrap-Up

I hope this is a useful worked exercise, to help clarify a complicated space. The main lessons for me are:

  1. Conventions and protocols are very different things. We need both.
  2. The two main protocols, RS & PRA, are indistiguishable in very simple cases.
  3. SPRA uses a different convention, but the protocol remains PRA.
  4. Similarly, ARV throws away the conventions, and we are still free to choose the protocol.
  5. When analyzing a problem from the past, we should look at what the author was trying to achieve (in so far as we can determine this), and this will help us best to communicate it to a new audience.
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    In the original, yes, a twin. On d8, there is a knight instead of a rook. With the knight, the case is unambiguous - only one last move of black is possible. And there are no questions "What is it?". Commented Jul 4 at 4:19
  • There is a good article with examples: janko.at/Retros/Glossary/Castling-and-En-passant-Jun-cm.htm It is clear that the problem is being solved, as RS. It's more interesting why it's not a PRA. Please note - only because of the strict limitations of 16.2. Pay attention to task 15. There is a similar case. There is an RS solution. But the task is marked either RV (the options are determined by the last move of black) or SPRA (e.p. by default). And two answers. The same could be done with this task. Commented Jul 4 at 4:42
  • In general, it turns out like this. Without marking, the problem is solved as RS. PRA does not work because of the very rigid position of paragraph 16.2. But if desired, you can mark RV or SPRA to the problem and make two solutions in the problem. RV and SPRA will give the same answer - there is only a difference in the division approach used. Commented Jul 4 at 4:51
  • @ЭлсиРинген You keep saying "paragraph 16.2 [of the Codex, about e.p.] is rigid". I do think it's badly written, and I interpret it in my own way as "if we don't know whether last move was double hop, then ep is not permitted". But what is this rigidity that troubles you?
    – Laska
    Commented Jul 4 at 5:34
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    There is an obvious error in the response. How did I not notice right away? e.p. and castling are interdependent and incompatible. They are impossible at the same time. Commented Jul 7 at 4:43
1
[Title "#1 - W. Keym. Die Schwalbe, 1969. Ded. K. Fabel"]
[FEN "qrbR4/rP1P1pp1/pQ1pp3/pPp5/6P1/1P3BB1/3PP2P/R3K1k1 w - - 0 1"]

==

[Title "#1 (RV or SPRA)  - Karl Fabel. problem 1953"]
[FEN "8/1B4p1/8/3Pp3/7b/4P3/1P1PPQ2/R3K2k w - - 0 1"]

The first task is a part of gemini. There were considerations for choosing a mark. The second part was interesting for our question. Just in case, I brought a second similar task.

Both tasks have the same structure: incompatibility of e.p. and castling. In the first one, there is a rather serious preliminary retroanalysis.

Until 2008, the problem was solved without marking by the RS method (one solution), marked RV - two partial solutions. Moreover, RV could mean any method: PRA, SPRA, according to the last possible moves of black. The solution is the same for any method.

After 2008, the PRA method became the default method, and RS software is now applied secondarily if a PRA solution is not possible. Therefore, without marking, we first need to understand if there is a PRA here.

The PRA Convention is explicitly described in the Codex.

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.

The initial position can have three states: S_castling, S_ep, S_neither. The PRA Convention, guided by paragraph 16.1, will exclude S_neither from consideration (there is no reason for white's lack of castling). And we got two interdependent rights (one excludes the possibility of the second) and two mutually exclusive parts. Everything is fine here! But it was not possible to come to an agreement with paragraph 16.2. Unlike the PRA, rule 16.2 considers that the case of S_neither may be in the starting position (for which, of course, there is no solution). And therefore, we will not be able to apply PRA in this task. And by default, it will be solved by the RS method. Moreover, it is necessary to bring at least a few last moves: 1. ... c6-c5 2. Qc7-b6 b6xNa5 3. Be4-f3 Kg2-g1

==

If the author wants (as in the second problem) that the problem has two partial solutions, you need to put a mark. But how? In the well-known article by Werner Keym in the 2010 version of the article, the problem was labeled RV, and the solution was as follows:

.1. ... c7-c5 1. bxc6ep#

.1. ... any other move by black (exd5, Be8-h5, Kg1-h1) 2. 0-0-0#

But in the 2011 version of the article, the mark was already SPRA and the solution, respectively:

.1. bxc6ep#;

.1. 0-0-0#

Personally, I like the RV method much more. Determining options based on Black's last move is much easier for a simple user than delving into the logic of PRA, for example, and there is no straightforwardness, as in SPRA (where paragraph 16.2 was simply taken and canceled).

But there is a problem. The RV name will cause confusion with the old RV and, probably, it is better to come up with some other name for the "black's last move" method. By the way, this will also be useful for tasks like Results.

==

UPD. About "do not disturb the dead." Andrew condemns the use of the outdated term RV. Only it wasn't my idea.

Many retro problems which were published with the supplementary stipulation “Retro Variants” or “RV” before 2008 are PRA problems after the modification of the codex 2008 and need no supplement any more. Yet the term “Retro Variants” is not superfluous. I propose to use this term, which is not used any more in the codex, when all possible last moves and their effects on the solution are searched. Because of this new definition “Retro Variants” clearly differ from the PRA convention. The latter deals with the combination of special move rights, the former with all possible last moves.

This is a direct quote from Werner Keym (2010).

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  • (1) I have made changes to my answer, including RV at your request. Please review and respond (in a focused but informative way). (2) It's important in SE to keep focus on the original questions. If you want to solve the Fabel problem, put it in a new question, and I will respond there. (3) Fabel is genuine SPRA, Keym is genuine RS/PRA, so there is no real connection, although both are #1. Thanks
    – Laska
    Commented Jul 8 at 9:12
  • (1) I agree that RS and PRA use the same facts in their constructions. But I don't agree that they behave the same way. They can't behave the same way because they have different goals from the beginning. The separation into parts in both methods follows the same principle: the S_neither state is considered impossible by default. But after that, they already behave differently. RS excludes one part and gives a solution for only one part, PRA wants to give a solution for each part. Commented Jul 9 at 14:03
  • As a result, there is no solution to PRA in the problem (due to the fact that rule 16.2 considers the state of S_neither possible, but there is no solution for it). And the task can only be solved by RS. Commented Jul 9 at 14:16

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