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MatPlus.Net Forum General Castling convention
 
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(21) Posted by Nikola Predrag [Tuesday, Jan 7, 2014 05:11]

Yes, I can't now even recall why I have found it difficult.
 
   
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(22) Posted by Andrew Buchanan [Tuesday, Jan 7, 2014 20:36]

There are two sets of conventions. These days, they have been tidied up so that PRA has priority over RS, but let's focus on RS first here.

What is critical for fairy purposes is that we generalize in the right way beyond castling and en passant. The fairyist Ronald Turnbull proposed that we distinguish between what he termed the "constitution" and the "police courts". The constitution tells us what we have a right to do, unless there is some explicit reason why can't. The police courts tells us what we aren't allowed to do, unless there are explicit extenuating circumstances. Castling is a constitutional right, en passant is normally forbidden by the police courts.

So under fairy rules there can be numerous other activities where we need certainty to be given, and we need to assign them to one side or the other. By default, are they permitted or not? For example, Ronald produced a bunch of "fuddled men" problems. "Fuddled men", a condition invented by John Beasley, is very similar to "Disparate", but the limitation is that a unit cannot move twice in a row. The right to move is essentially constitutional. And so, I contend, in Disparate.

For example: 7b/k5rb/8/P7/rp4B1/4B3/8/6K1 (4+6) h#2 Fuddled Men. RS b) from mating position of a).

But the basic principle of RS remains. We are going forward in time, and we can make any move to which we have a constitutional right. And once that is made, we may reduce the number of possible histories which could have led us to this date. RS does not imply anything *directly* about legality of other moves in history or in the future. We prove *only* by doing.

So how does that affect rhe three problems supplied? In Nicolas' first problem, White can mate in two ways in 1 move. Similarly in Francois' first problem.
In Francois' second problem, 1...Rxf6 2.Qxh2 Rf1# is completely acceptable. White's first move nullifies the possibility that White could ever castle. But I agree with Jacques that the problem has many cooks ending 2.Kf1#
 
   
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(23) Posted by Dupont Nicolas [Tuesday, Jan 7, 2014 22:39]

Yes Andrew, according to your viewpoint “we prove only by doing”, the difficulty is solved. The problem is that your approach in not the one followed by the castling convention…

We can see the difficulty in a purely orthodox manner:

(= 2+1 )

White to move

The castling convention asserts that white can castle in this position. It logically implies that the two white units never moved, hence that the last black move was a capture (otherwise white is retro-pat).

But it is clearly not “reasonable” to claim that the last black move was a capture, and indeed your trick “we prove only by doing” tells that we can only claim such a fact after white castled "for real".

So it seems that the castling convention is badly formulated, it should be rephrased including your ““we prove only by doing” or something like that.
 
   
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(24) Posted by Andrew Buchanan [Wednesday, Jan 8, 2014 03:25]

Dear Nicolas,

The Codex of Chess Compositions was a great first draft, but sadly for the health of our hobby was never written up properly. Nevertheless, I think the telegraphic summary of the RS castling convention captures its essence: "Castling is permitted unless it can be proved that it is not permissible." But you have to interpret the words correctly :) And remember that this convention was primarily intended for conventional problems - they are an alternative to retro analysis to allow problems with forward stipulations to proceed without getting bogged down in retro concerns which for them are irrelevant. We retro enthusiasts of course want to play with these conventions, and that's fine, but we need to remember their original purpose.

So, I think your latest example is great because it gets to the core of the issue. Here we are in a position with uncertainty. The castling convention does not make that uncertainty go away, but says that despite that uncertainty, we are nonetheless *permitted* to make the castling move. And once the castling move is made, in the *new* position, the range of possible histories is reduced and certainly, *in this new position*, one can assert that Black must have captured in their last move, before the castling.

It's actually rather beautiful, consistent and generalizable to the fairy world, but you have to look at it in this right way. Mutually exclusive castling just falls out as a consequence, and does not need a specific convention. And if you generalize using the constitutional principle to the Disparate world, it also explains why in one try in Francois' second example 1... Rxf6 2.Qxh2 0-0-0? White's first move is *permitted*, but the second is now not *permissible* (because illegal in the branch we have gone down).

Conversations over the years with Ronald Turnbull, Valery Liskovets & Guus Rol have informed my thinking here, so I don't think I am just off on a tangent of my invention.

Hope this helps,
Andrew.
 
 
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(25) Posted by Nikola Predrag [Wednesday, Jan 8, 2014 05:22]

Codex starts with the most important statement that it deals with general principles. Too much of artifical conventions would be against the very spirit of Codex.
So, what would be a general principle relevant for this thread?
I'll try to formulate a kind of basic common principle for the Conventions. How would it fit with Codex? (Illegal positions are not strictly forbidden by Codex but anyway they don't fit with the Conventions.)

1.Orthodox chess problem must follow Chess rules in a legal play from the game-beginning to the end of the problem
2.The play from the game-beginning to the diagram position (pre-play) is a matter of retro-problems
3.Other problems start from diagram (post-play) but they still must satisfy no.1. In principle, all possible proof-games are considered as "equally valid", with a specific reduction in specific case of Castling Convention (Castling reduction):

-The side on the move may execute castling with a claim that only the proof-games which allow that castling are "equally valid", if at least one such proof-game exists. "Castling reduction" of "equally valid" proof-games comes only with the castling, not before. Hypothetical castling-right does not reduce the set of "equally valid" proof-games.

-The post-play must be legal in case of each one of "equally valid" proof-games.

So, e.p. capture is allowed only if all "equally valid" proof-games end with double-step of a particular Pawn.
A posteriori castling reduces the set of "equally valid" proof-games when e.p. capture is already executed. Looking at the whole play from game-beginning to the end, all (a posteriori reduced) "equally valid" proof-games allow e.p. in the moment of the diagram.
 
   
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(26) Posted by Dominique Forlot [Wednesday, Jan 8, 2014 18:40]

Hello to all on the forum, I allow to participate in the discussion to request your opinion.
here is a little problem (direct mat PRA ) with the castle/pep theme:

(= 8+5 )

#3 PRA

Unique solution :
1.dxe6! e.p. [Dxf7#]

1...0–0! 2.Dg5+ Rh8 3.Dg7#
-> castle Justify the p.e.p. "a posteriori"

the try for black:
[1...Tf8? 2.e7 (2.Rf4 Th8 3.Dxf7#) 2...Th8 3.Td8#]
-> is uncorrect because the pep is not justified by a castle here!

Are you all right with this analysis?
 
   
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(27) Posted by Dominique Forlot [Wednesday, Jan 8, 2014 19:32]; edited by Dominique Forlot [14-01-08]

Now with this same position: take the pawn d5 and put it on b6 !
and Consider the condition "PRA-Disparate "


(= 8+5 )

#3 PRA-Disparate ( the Nicolas Dupont's idea )

the unique solution is :
1.Té6+!
1…Rd7 2.D×f7+ Rç8 3.Dç7#

but what to think about the following try:

1.b7?
1…0-0! 2.Dg5+ Rh8 3.Dg7#

this last solution is illégal in PRA because of the castle.
i.e. : If the black can Castle that means their last play was e5!
and white Pawns are now paralyzed
 
 
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(28) Posted by Jacques Rotenberg [Wednesday, Jan 8, 2014 19:48]; edited by Jacques Rotenberg [14-01-08]

@ dominique for your diagram in post 26 :

It is quite different for me.

I'll try to give the solution as I can understand it, with details :

a) it is an orthodox 3# problem, so two usual conventions are applied
a1) it comes from a "game" it means that it is bound to the original set of the pieces, it means it has a past.
a2) the 0-0 it legal unless it can be proved not to be.

b) if I ask what was the last move, the answer is : or e7-e5 or a move by the rook or the king
b1) in case of e7-e5 I cannot give a proof against the 0-0, and so 0-0 is available as a move, but also the key p.e.p.
b2) in case of a move by the king or the rook, the 0-0 is broken.

So the full solution is

if last move was e7-e5
the key is 1.fxe6 e.p.
etc.

if last move was by the king or the rook
the key is
1.Qg5 ~ 2.Qc1 ~ 3.Qc8#

This is a case of the so called "partial retro-analysis" - pra

I don't think pra is a convention by itself, it is only a consequence - somewhat "special"- of the usual conventions for orthodox problems
 
   
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(29) Posted by Andrew Buchanan [Wednesday, Jan 8, 2014 20:20]

Hi Dominique,

PRA does not usually need A Posteriori. Your problem works quite well without A.P.

First let's solve it...

The PRA convention is described in the Codex. It reads in part: "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 exclusive parts."

But Christmas what could these words mean?

Let's go through your example to see.

There are two variable moves: White's e.p. (E) & Black's castling right (C).

There are four possibilities:
(1) E is not permitted, but C is permitted.
(2) E & C are both permitted
(3) neither E nor C are permitted.
(4) E is legal, but C is not permitted.

So the Castling Convention allows us to prefer (1) to (2), and also allows us to prefer (3) to (4). The En Passant convention allows us to prefer (1) to (3) and (2) to (4). If (1) is legal, then we will always have a single preferred scenario.

But here (1) is not legal. If Castling is permitted, then Black's last move was the double pawn move, and the en passant rule itself tells us that the en passant capture is definitely legal. So (1) is not ok.

Therefore in our quest to apply the conventions maximally, we can end up in two places (2) & (3). these are the mutually exclusive parts of the problem which must be solved separately. (4) is not an exclusive part, since either convention can apply to get us out of it. It is dominated by both (2) & (3). So we can ignore (4).

Case (2):
1. dxe6ep! [2. Qxf7#]
1. ... 0-0 2. Qg5+ Kh8 3. Qg7#
1. ... Rf8 2. e7 ~ 3. Rd8#
1. ... Rf8 2. Kf4 [3. Qb5#]
2. ... Rg8/h8 3. Qxf7#

Case (3):
1. Qg5! ~ 2. Qc1 [3. Qf8#]
2. ... Kf8 3. Rd8, Qc8#

So A.P. is not necessary for this problem.


Now let's consider A.P. Basically in any directmate, Black is attempting to avoid mate. Black has no tries. In an A.P. frequently Black is actually trying to avoid the requirement to castle, because such would legitimize the en passant. A.P. normally accompanies RS, although there are certainly some problems that try to combine A.P. with PRA.

The RS conventions and the PRA conventions are basically two very different paradigms for addressing problems of constitution & police court. In the old days, RS was the default, and PRA would only apply if the stipulation said so. But these days, Werner Keym has unified them as far as notation is concerned. The basic idea is very simple. There is no annotation required for the stipulation. If PRA works (i.e. there is a solution for each "mutually exclusive part") then that's that. But if PRA is not satisfactory, then RS is applied.

I wonder if there are any old RS problems which don't work any more because there is some bogus PRA solution? But I haven't explored that.
 
   
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(30) Posted by Dominique Forlot [Wednesday, Jan 8, 2014 20:32]; edited by Dominique Forlot [14-01-08]

You are right Jacques; It seems that I complicate a little too much the PRA by forgetting the orthodox aspect of this problem. Both solutions, mutually exclusive, are justifiable.
Thank you very much Jacques & Andrew for these exhaustives explanations and the time spent on my question.
 
 
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(31) Posted by Andrew Buchanan [Wednesday, Jan 8, 2014 20:48]

A couple of posts while I was writing my solution to 26. I agree with Jacques, and I hope my solution gives an idea of the systematic approach one can apply to solving PRA problems in general.

Now let's look at your 27. With Disparate, every move White move is potentially constitutional, and also the castling rights.

We can clump the White moves according to the type of pieces involved. Black doesn't have a queen, so there can be no constraints upon the White Queen. Basically, there are the following non-dominated states:

(1) Black moved K last: White can move Q,R,P, Black can't castle.
(2) Black moved R last: White can move Q,K,P, Black can't castle.
(3) Black moved P last: White can move Q,K,R, Black can castle.

These three mutually exclusive parts must each have a solution.

In (1) & (2) White can just play 1.b7! ~ 2.b8=Q/R#
In (3) White can play your solution 1.Re6+! etc.

That's it.

You ask:

>what to think about the following try:
>1.b7?
>1…0-0! 2.Dg5+ Rh8 3.Dg7#
>this last solution is illégal in PRA because of the castle.
>i.e. : If the black can Castle that means their last play was e5!
>and white Pawns are now paralyzed

In PRA, we must ask which scenario we are in (1),(2) or (3). For 1.b7 to be legal, we must be in scenario (1) or (2), and so castling is illegal, and White mates in 2 not 3.

Under RS, the logic would be different. White can play 1.b7 to deny Black castling, but Black must move K or R, and then 2.b8=
 
   
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(32) Posted by Dominique Forlot [Wednesday, Jan 8, 2014 21:31]

Thank you so much Andrew!
It's very clear in my mind now ( I hope :)
 
 
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(33) Posted by Nikola Predrag [Wednesday, Jan 8, 2014 21:47]

Andrew, the idea of constitutional rights and police court bans might nicely make the necessary clear distinction.
But it means that all particular cases must be classified as constitutional or police court cases. And it is not desirable to have such classification on the basis "It's so because we say so".
The laws and conventions should have a common origin in some firm general principle.
It's desirable to have a general principle as a non-ambiguous basis for the consequent laws and conventions.

I gave a rough example which might be correct or wrong. The point is that I expect to see some essential basic logic as the common origin of all potential constitutional rights and police court bans.
 
   
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(34) Posted by Andrew Buchanan [Thursday, Jan 9, 2014 04:08]; edited by Andrew Buchanan [14-01-09]

Hi Nikola,

I completely agree 250% that we should be looking for general principles rather than specifying lots of cases.

I like your approach which tries to unify the common origin of constitutional rights and police court bans. But if I am not wrong your example still identifies castling as allowing an immediate reduction in the set of "equally valid" proof-games, while e.p. does not. There is a fundamental distinction still required.

As we try to absorb some fairy condition into the conventions, there remains a *modeling* step where we have to decide whether the condition should be constitutional or police court. Modeling steps inevitably involve decision-making. However, the modeling is nearly canonical: if the move in question is likely "most of the time", then it's constitutional, while if it requires particular conditions to apply, then it's police court. So I don't see much source for dissension. Indeed I suspect that most conditions would be constitutional.

However one could probably deliberately construct a condition which would be difficult to assign. For example let me randomly invent "colour fuddling" - any move must be from a different colour square than that player's previous move. (Kingside castling counting as neutral in this regard.) Here exactly 50% of the moves would be permitted - so do we need a constitutional right or a police court ban here? But I contend the overall approach is still right and natural.

Nikola: if through some cleverness, you manage to eliminate this decision-making step entirely, then I will be a total fan. However for the moment I think this small element of modeling is required, and it does not reduce at all the value of Ronald Turnbull's constitutional & police court approach.

He is clear thinking, original and humorous, and I am sorry he doesn't compose any more. Instead he writes books on hill-walking.
 
   
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(35) Posted by Georgy Evseev [Thursday, Jan 9, 2014 20:13]

Nicola,
Andrew,

The rule of thumb seems very simple for me.
If some move is _generally allowed_, but becomes illegal if somethimg happens or under specific circumstances, then it is _allowed_, until it can be proved otherwise.
If some move is _generally not allowed_, but becomes legal if somethimg happens or under specific circumstances, then it is _not allowed_, until it can be proved otherwise.

If there is White/Black conflict then the side to move may force a decision. If in initial example white play 1.Qc1 (and this should be allowed) then black can no longer castle.

Of course, there may be some boundary cases, but I do not expect them to appear too often.
 
   
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(36) Posted by Nikola Predrag [Friday, Jan 10, 2014 08:06]

Yes Georgy, I was just prepared to say that I've been saying that all the time but I read again what I did write. So I found that my posts (8,11) are opposite of what I think and what I wrote later.
I confused myself with my own "example" in post 5:
-"(Some hypothetical condition "AntiDisparate wQ" might mean that wQ may play only if the last previous black move was played by bQ. In the same diagram with such a condition, wQ could play only if Black will castle a posteriori.)"-

That would be correct. Somehow I kept thinking of this hypothetical condition while talking about Disparate and my reasoning in 8,11 was a completely inversed nonsense, to say it shortly. Also, I have (probably) misunderstood the point of Kevin's posts.
I apologize to all!

Andrew, it's obvious that I must carefully read again my own posts before saying anything more :-)
 
   
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(37) Posted by Andrew Buchanan [Friday, Jan 10, 2014 19:28]

Hi Georgy,

Thanks for your input, which I generally agree with.

 QUOTE 
If there is White/Black conflict then the side to move may force a decision.

This is certainly correct, but in fairy chess, RS mutual exclusion is not just about "White/Black". White's first move may have implications for what is permitted in White's second move. This doesn't come up in orthodox chess, because White can't castle twice.
 
   
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(38) Posted by Dominique Forlot [Saturday, Jan 11, 2014 13:02]; edited by Dominique Forlot [14-01-11]

Hi! thank all of you for this interesting Debate!

So, my last diagram could be proposed in the following way: (MAT in Two -Disparate : with unique solution )

(= 4+5 )

#2 Disparate

1.b7! ~ [2.b8=D#]

The key denies the right for the castling. réf: (31) Andrew Buchanan (Wednesday, Jan 8, 2014 20:48)
This presentation not requiring the PRA.

N.B. [2.b8=T?? T~ and no mat]
 
   
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(39) Posted by Dominique Forlot [Saturday, Jan 11, 2014 16:53]

To be more "acute":

First case:
(= 4+3 )

#3 Disparate (4+3)
castling is illegal "De facto"

1.g7!
1…Rd8 2.Tç5 Ré8 3.g8=D‡

Second case:
(= 4+4 )

#3 Disparate (5+3)
1.g7!
1…Rd8 2.Tç5 Ré8 3.g8=D‡
The key (and the condition) denies the right for the castling
 
   
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(40) Posted by Andrew Buchanan [Tuesday, Jan 14, 2014 04:29]; edited by Andrew Buchanan [14-01-14]

Dear Dominique,

I pretty much agree.

PRA & RS are the two alternative paradigms to govern how multiple conditional moves interact. In the old days, RS was the default, and PRA required a special mention in the stipulation if it applied. Now PRA is the default, but if at least one of the PRA cases has no solution, then RS applies.

The conventions can be generalized in an obvious way to cover fairy problems, where castling is not the only move with constitutional rights.

Your problems (38) & (39.2) are both RS problems, because there is no solution in one of the 3 PRA options. (39.1) is a PRA problem, with the same solution in both PRA options.

Cheers,
Andrew.
 
   
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MatPlus.Net Forum General Castling convention