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MatPlus.Net Forum General The Retro-Strategy convention: what is the correct way to interpret it?

### The Retro-Strategy convention: what is the correct way to interpret it?

Suppose that we have wPd5, bPc5 and bPe5. Suppose that it can be proved that Black's last move was either c7-c5 od e7-e5 (but it is not known which one). Now, if there is a way to fulfill the problem stipulation starting with 1.dxc5 e.p. as well as another way starting with 1.dxe5 e.p., then this would be two branches of a PRA problem.

But assume that there is a way to fulfill the stipulation starting with 1.dxc5 e.p., while if White plays 1.dxe5 e.p., then the stipulation cannot be fulfilled. Is it then correct or not to say that, under the RS convention, the problem is sound (with only one solution, starting with 1.dxc5 e.p.)? Namely, as I understand the RS convention, it is based on the philosophy that, in case of mutually dependent rights, the one that is exploited first is deemed permissible. However, for some reason, the Codex talks only about the castling rights with respect to the RS convention, and says nothing about the en-passant rights.

Hi Bojan,

The Codex today is kind of a summary of what folk have agreed: it's not a tutorial. There are various parts where I think it could be better written, but it is what it is. If you are looking for a genuine tutorial, you could try the Retro Corner, e.g. for e.p. https://www.janko.at/Retros/Glossary/EnPassant.htm. In a (large) nutshell, here's how I suggest that you view all this, starting from first principles. For your actual answer, skip to the end.

Each kind of conditional move (in orthodox chess: castling and en passant, but fairy chess offers numerous others) should have a convention which says what we can assume about the legality of this move if the history of the game is uncertain. Basically conventions are either optimistic (it's always ok to play an uncertain move, e.g. castling) or pessimistic (it's never ok to play an uncertain move, e.g. e.p.).

Critically, these conventions only apply to forward stipulations. General retros (e.g. last move, proof game) admit no conventions: everything must be proven. Retractors need no conventions, because any feasible last move can be retracted.

If there is only one conditional forward move, then we have enough information. However, there are many positions in which there are multiple possible conditional moves in the future, and there may be logical dependencies between them. How do we proceed? We need to move to a higher level of meta-convention. There are two common meta-conventions: PRA & RS, each of them built on the two basic conventions.

PRA (partial retro analysis) says that divide up the problem into different parts: each with a different subset of the conditional moves permitted. There are two constraints in defining these subsets. First the subset has to be legal, i.e. there must be a game which results in a position with exactly this subset of permitted moves ok. Secondly, no subset of can be "improved" to another set by applying one of the basic conventions.

This is actually quite a beautiful idea, but it cries out for an example. So suppose we have a position where two castlings C1 & C2 are in doubt, and we know that they cannot be both legal. So we start with 4 possible parts. {C1,C2}, {C1}, {C2}, {} where each bracket denotes the permitted moves. Constraint 1 immediately allows us to remove {C1,C2} because it's not legal. Constraint 2 allows us to remove {} because by the castling convention this could be improved to {C1} (or equivalently to {C2}. So we end up with two parts {C1} & {C2}. Both are possibly legal, and neither can be improved.

Let's have another example. Suppose we have a position (e.g. Longstaff) where castling, C, and e.p., EP, are in question, and if e.p. is not permitted, the castling cannot be permitted either. Then the 4 candidates are {C, EP}, {C}, {EP} & {}. We are told that {C} is impossible by Constraint 1. But consider now {EP}. We could improve that to {C, EP} by the castling convention, or to {} by applying the e.p. convention. Thus we can discount {EP} by Constraint 2. So we are left with two parts: {C, EP} & {}. This scales up cleanly to more complex retro structures.

And finally, the double e.p. where it's certain that the last move must have been a double hop, {} is impossible, while {EP1, EP2} is dominated by both {EP1} & {EP2}, which are the parts.

Retro-Strategy starts from a separate premise, that there is only one position. We consider all the optimistic conditional moves, bearing in mind the history of the game including the moves played in our solution so far. We can unconditionally play any of these optimistic moves, but when we do so the range of possible histories collapses to include only those in which this move could have been legal, and then we consider the next move. Pessimistic conditional moves never get to be played under RS: they only get played under the e.p. *rule* i.e. if you can proved that the last move was a double hop you can make that move.

Let's see how the two examples apply here. First the two castlings, where there are 3 possibilities {C1}, {C2} & {}. If both the castlings are by the same player, just play one, say C1. Now the history collapses so that we only consider those possible histories in which that castling definitely was legal, i.e. {C1}. In fact since a player can only castle once in the game, the legality of C2 is irrelevant. However, if C1 was by White, and C2 by Black, then when White plays C1, we enter the collapsed history of {C1} and Black cannot castle. For some reason unknown to me, this is called out as a special case in the Codex, but Mutually Dependent Rights for castling is an obvious case of the more general RS mechanism of history collapse at work, which is really what the Codex should describe.

Let's move on to the Longstaff case. E.p. must be played immediately if it's going to be played at all, but under RS we cannot play a pessimistic unsure move. So it will never be played. If we castle, then our state collapses to {C, EP}, but given that we are too late to play the EP it's kind of academic. You can see why this kind of problem is more suited to PRA.

The double e.p. is all pessimism under RS, and so neither can be played. If there are no other moves possible in the diagram, then the game hangs without ending. I find this situation pretty cool, but I can understand that some others think it's a strike against RS.

This point brings us to the question of meta-meta-conventions. How do we know whether PRA or RS should apply? In the old days, RS was the default, and PRA problems needed to be annotated in the stipulation. Werner Keym in 2005?2007? pushed through a change to the conventions which is shockingly badly described in the Codex. Unless you already know what it's trying to say, you haven't a chance. Basically, neither PRA nor RS need to be annotated as such. The first assumption is that the problem is PRA, but if that doesn't work out (one clean solution per part) then you assume it's RS. I tend to view this meta-meta-convention as a notational shortcut more than anything else, and it certainly has worked out well EXCEPT that if you don't know what's going on here then you haven't a chance. Werner Keym produced an excellent tutorial for this (which you can find in the Retro Corner) but if you don't know that this silent meta-meta-convention is going on, you haven't a chance of figuring it out for yourself.

This brings us (finally) to your question Bojan. Thanks for your patience. If only one of the two possible e.p. moves leads to a solution, then under RS you cannot force it. The problem is unsound. Many people, including some very creative ones, felt this was a shame, and so there is a wonderful idea called AP (for A Posteriori) which says that under RS you *can* play a pessimistic move, as long as later on in the game you or your opponent play some optimistic moves which collapse the set of possible histories such that the pessimistic move was definitely legal. There are some amazing effects which have been achieved with this wacky and unorthodox idea.

One will find problems in chess.com where an unjustified e.p. is given as the solution, because "the problem must have a solution". If this statement is given as a constraint in the problem stipulation, then the problem works, but otherwise it's just a joke. That a problem must have a solution is a requirement for soundness, not a retro premise. However in the world of jokes all things are possible.

That's an entry level intro to the orthodox conventions, meta-conventions & meta-meta-convention. I hope you can see how the conventions can easily generalize to any fairy format, if every aspect of conditionality can be classified as optimistic or pessimistic. Other issues not covered in this intro are: interaction with whose move, AP for PRA, "SPRA" and generalization to RS, touch-move protocol, dead position, 50 move rule, draw by repetition, jokes & illegal positions. Have fun and if you have any questions just ask.

Well, studying computer science, *I* have a question which
is rather obvious: Can the whole system be formalized to
a degree that given a position and the list of move
dependencies, a computer could solve it codex-compliant?

QUOTE
Well, studying computer science, *I* have a question which
is rather obvious: Can the whole system be formalized to
a degree that given a position and the list of move
dependencies, a computer could solve it codex-compliant?

Yes. After some basic formalization of the Laws and the Codex, if you have an ordinary forward stipulation in a position together with the list of move dependencies, a computer algorithm can determine the solution for PRA or RS, excluding AP. It would be able to determine the parts of the RA problem, solve them, determine whether it matches the PRA requirements, if necessary shift to RS and iterate forwards there, collapsing histories as required.

Dear Andrew,

What a marvelous answer, thank you very much! I was aware of most of the things you wrote (the only question was when exactly we can select a "branch" by means of RV; the answer is, as you have explained, that we can appeal to RV in order to choose among "optimistic" moves, but no "pessimistic" move can be played on the grounds of RV only), but it is great to have everything summarized so nicely in one place! I also appreciate your comments about transferring these principles to fairy problems, since I in fact arrived to my question from the fairy realms (but formulated it in an orthodox manner because it was the basic principle that I was interested about, and after making that clear, applying the same principle to fairy compositions should not be a problem).

Since you were so kind and eager to help, I will make use of that and ask one more question (not directly related to the previous one, but still about the same conventions). Suppose that we have three conditional moves, say M1, M2 and M3, all of which are optimistic. Suppose that M1 is incompatible with M2, as well as that M1 is incompatible with M3, but M2 and M3 can coexist together. Is it then correct to say that we have two parts, namely {M1} & {M2, M3}, and that by PRA they form two branches, while by RS we can decide on any one of those two parts by making a respective move (which is M1 for the first part, and can be either M2 or M3 for the second part)? In other words, the question is: since the possibility {M1} "kills" two optimistic rights, while the possibility {M2,M3} "kills" only one, this still does not mean that the first possibility has "lesser right to exist" than the second one, correct?

Dear Bojan,

Thanks for your kind words. I hope that this kind of tutorial material can find a more permanent home to help those wanting to move to retros beyond Smullyan.

QUOTE
Suppose that we have three conditional moves, say M1, M2 and M3, all of which are optimistic. Suppose that M1 is incompatible with M2, as well as that M1 is incompatible with M3, but M2 and M3 can coexist together. Is it then correct to say that we have two parts, namely {M1} & {M2, M3}, and that by PRA they form two branches

For PRA, you are exactly right, we have two parts {M1} & {M2,M3}. There are eight initial possibilities: {M1,M2,M3}, {M1,M2} & {M1,M3} are inconsistent, while {}, {M2} & {M3} are dominated by {M2,M3}.

However the concept of parts *only* exists for PRA. RS never divides in this way: instead you drive forward optimistically, collapsing the history by removing any possible past which is inconsistent with the optimistic moves being made.

QUOTE
while by RS we can decide on any one of those two parts by making a respective move (which is M1 for the first part, and can be either M2 or M3 for the second part)?

In RS our initial set of histories is [{}, {M1}, {M2}, {M3}, {M2,M3}] If someone plays M1, then the set collapses to just [{M1}], as anything else is inconsistent, and so M2 & M3 are no longer playable. On the other hand, if someone plays M2, then the set of possible histories reduces to [{M2}, {M2,M3}] M1 can now not be played, but someone is free to play M3. If they do, then the set of histories becomes just [{M2,M3}]

The concept of history collapse is a more precise way of viewing RS, rather than the vagueness of "Mutually Dependent Rights".

QUOTE
In other words, the question is: since the possibility {M1} "kills" two optimistic rights, while the possibility {M2,M3} "kills" only one, this still does not mean that the first possibility has "lesser right to exist" than the second one, correct?

Yes there is no comparison of this kind. Just drive forwards being optimistic, and throwing away histories that are inconsistent with what you've done.

A lot of the motivation for these problems comes from the composer setting up different dependency maps between various conditional moves. https://www.janko.at/Retros/Glossary/Castling-and-En-passant-Jun-cm.htm is a great article which showcases some classics, and shows how they interact with different kinds of forward stipulation: directmate and helpmate.

Some might compare RS with the Copenhagen interpretation of Quantum Mechanics, under which there is a notion of collapse of the wave function under observation, while PRA is more like a "multiple worlds" interpretation. That's a fun analogy: it's cool to pretend that we are doing something serious like physics.

I was really, REALLY tempted to write a Hollywood time travel SF blockbuster from all this. (Maybe with a dash of Game of Thrones plagiarism throw in.) Then, with only about 1000 problemists to watch, I realized that the FX costs would rob me blind :-) Some dialogue from the script leaked through, though...

Outside. A dark and stormy night.
The Witch Queen: Flee into the tower, King Haukon!
The Black Bishop: HERESY! Gods forbade this sin!
You won't escape the wrath of my mighty crosier!
King Haukon (draws his legendary +1): En gardez!
You'll never take me alive!
The Witch Queen: Old Ones, forgive me! I repair
that later! CINCINNATUS!
(A \$1000000 SFX happens. King Haukon is transported
to the safety of the White Tower)
The Black Bishop: Damn you to hell and back!
You won't escape the punishment for throwing spells
around en passant!

QUOTE

That's a fun analogy: it's cool to pretend that we are doing something serious like physics.

Chess composition is further along than physics however: Reto Aschwanden and Peter Gvozdjak published a 'Grand unifying theory' composition in Strategems in 2001.