Alexander George, 6 Dec 1995

Richard Sabey is right to point out that Ceriani's problem, taken as a PRA (or retro-variant), has no solution. Here's what I say about it in my "Paradox and Partiality" article in _diagrammes_, No. 15, July-September 1994:

"In other problems, however, there is a reliance on the CCC [the Common Convention for Castling, according to which it is legal unless it can be proved not to be], which arguably leads to unsoundess. Consider L. Ceriani's [Europe Echecs 1960]. Here the CCC permits us to infer that Black can O-O-O. But it also has us conclude that White can O-O. Therefore, by the CCC, Black can O-O-O and White can O-O. Retroanalysis reveals, however, that this is impossible: if White can O-O, then the wR on a6 is promoted and the promotion must have caused the bK to have moved. Again, the CC leads to contradiction.

"The composer's intention seems to have been this: if the CCC is applied first to Black to conclude that Black can O-O-O, then b7b5 must have been Black's last move, allowing White to PxP e.p., followed by Qf8. If, on the other hand, the CCC is first applied to White, then (by the previous reasoning) Black cannot O-O-O and White can mate by O-O, followed by Rf8. I claimed that general application of the CCC leads to contradiction. Might Ceriani's reasoning furnish a response to this complaint? That is, might it not be replied that one cannot simply apply the CCC blindly to both sides, as I did? Rather, it might be suggested, one must apply it to one side and then, if this application leads to the conclusion that that side can castle, apply it to the other side *in the light of this conclusion*.

"This suggestion is not satisfactory, however, for according to it what follows from the CCC (for example, in this case, an answer to "Can Black castle?") is sensitive to one's decision as to whether to apply the convention first to White or to Black. Its rulings are inappropriately sensitive to the ordering of the questions one employs it to answer (e.g., in this case, "Can White castle?" vs. "Can Black castle?").

"Finally, and importantly from the perspective of a thorough retroanalysis, the CCC leads to an artificial narrowing of the retroanalytical possibilities considered. Thus there is no reason not to assume that the position in [Ceriani Europe Echecs 1960] arose as a result of a sequence of moves that permit neither side to castle. Yet no mate is provided for this case: both 1.Pc6 and 1. Rf1 fail to 1....Sxc2+[*].

"[Footnote *:] Those in the grip of the CCC would disagree with this analysis. Thus John Nunn, commenting recently on this problem, writes: 'In fact, the solution depends on which player gains the benefit of the castling convention first. However, in each case there is a unique solution, so this problem is perfectly legitimate.' (_Solving in Style_, 1985, p. 172.) And A.S.M. Dickins, in agreement, claims that [Ceriani Europe Echecs 1960] provides 'a full solution for all retro-analytical possibilities.' ('Alice in Retro-Land (or, Leap Before You Look,' _The Problemist_, September 1973, p. 376.)"

Most retro experts do not share Alexander Georges opinions about the castling convention, nor would they accept his phrasing of it: "legal unless it can be proved not to be".

In general, there are billions of proof games leading to a position and the legality of a proposed solution move may depend on the proof game. The convention is that a castling move is considered legal if it is legal after some proof game, while en passant captures and draw claims are considered legal if they are legal after all proof games.

Ceriani's PRA splits the set of possible proof games in two, then solves the problem for each half separately. This is what PRA is about!

Mr. George gets my vote!

The convention is that a castling move is considered legal if it is legal after some proof game

This doesn't deal with the difficulty of moves whose legalities are mutually exclusive.

An earlier formulation of the common convention for castling (CCC) didn't deal with this. So a more precise formulation was needed, to legislate as to who may castle. Doesn't this make you suspicious that something is wrong? If someone has composed a problem with different solutions needed for different proof games, do you consider it a good idea that some convention should legislate that some of those proof games are not to be considered? I quote Philippe Schnoebelen:

The emphasis is on "castling first" and not on "having the convention applied to oneself first". Assume mutually exclusive castling rights. If a convention tells me that I, as white, may castle but I decide to pick another move, then Black may still castle (thus forbidding later white castling) under the usual rules.

Thus giving a player an incentive to castle, not because it would be good chess to castle (that he can't achieve his aim unless he castles) but to prevent his opponent from castling. It's interesting but it isn't chess. It's like the dog in the manger. I look forward to seeing an example of the double Fischer theme, where a player castles just to prevent his opponent castling, then moves king and rook back to where they were in the diagram.

In Ceriani's problem, 0-0 and ...0-0-0 are mutually exclusive castlings. Each is legal after *some* proof game. According to Mr. Eriksson's formulation of the castling convention, a solution which relied on White's ability to castle would have to account for Black having retained the right to castle in the diagram position (after all, ...0-0-0 is legal after *some* proof games). If there were such a solution, it would not be legal after *any* proof game. This is absurd. And, as regards Ceriani's problem, there'd be no solution where White may castle, for the solution beginning 1 0-0 relies on Black not being allowed to castle.

Ceriani's PRA splits the set of possible proof games in two, then solves the problem for each half separately. This is what PRA is about!

No it doesn't! Ceriani's problem depends on CCC. Ceriani has cunningly worked in a 2-way PRA for those proof games where at least one of 0-0 and ...0-0-0 is legal. Thus the problem works regardless of who gets the benefit of CCC. But (as I pointed out yesterday) there is a third possibility: that all castling rights are lost.

PRA must account for *all* proof games. You show me your proof game for Ceriani's problem, I'll add some moves to the beginning of it which destroy the castling rights your proof game kept, and then I'll show you my proof game which destroys all castling rights.

Richard Sabey opposes the castling convention on the grounds that it gives "a player an incentive to castle, not because it would be good chess to castle (that he can't achieve his aim unless he castles) but to prevent his opponent from castling. It's interesting but it isn't chess."

He is right there, of course: the retro genre is classified as fairy chess by the FIDE problem commission. To me, the important features of a chess problem are perfection, beauty, the sense of wonder - I don't mind if "it isn't chess".

It is not clear to Richard that the formulation "a castling move is considered legal if it is legal after some proof game" deals with the case of mutually exclusive castlings. This is because he uses "is considered legal" to draw conclusions about the proof game leading to the diagram position. The Codex states that no retroanalytic conclusions may be drawn from the castling convention. It simply means what it says: a move in the solution is considered legal if it is legal in some proof game. With mutually exclusive castlings, the first castling is OK, for it is legal in some proof game, the second isn't, for it is no longer legal in any proof game.

Ceriani's PRA splits the set of possible proof games in two: those where Black castling is legal and those where Black castling is illegal. The e.p. capture is always legal in the first subset, so it gives a solution for these cases. The White castling is legal in some of the other proof games, so according to the convention it is OK in these cases.

The Codex states that no retroanalytic conclusions may be drawn from the castling convention.

Are you sure? Anyway, conclusions based on proof games are retroanalytic.

Ceriani's PRA splits the set of possible proof games in two: those where Black castling is legal and those where Black castling is illegal.

Please explain why the set of proof games is split as you describe. The following argument seems to be consistent with what Henrik wrote: "Ceriani's PRA splits the set of possible proof games in two: those where White castling is legal and those where White castling is illegal. For the first set, 1 0-0 works. For the second set, there is no solution. Therefore the problem is busted."

The solver has to choose how to split the set of proof games. If you split the set of proof games one way, the problem works; if you split it another way, it doesn't. Do you consider such a castling convention workable?

Henrik Eriksson says that the convention with regard to castling is this: "a move in the solution is considered legal if it is legal in some proof game." First, note that if this means "is legal in some game terminating in the initial diagram position," then the convention does lead to contradiction. Consider, e.g., Ceriani's Europe Echecs 1960. There is a game terminating in the diagram position in which White can castle and also one in which Black can castle; therefore, on this way of understanding this convention, both castling moves are legal in the solution. Yet we can prove that these castlings are mutually exclusive. We must interpret the convention differently. Perhaps as follows (this seems to be what Eriksson suggests): "... is legal in some game terminating in the current position." It would follow that White can castle in the initial diagram position, but that Black could not respond by castling, since there is no legal sequence of moves leading to the post-White-castling position in which Black can castle. No contradiction now arises. But I still maintain what I said in my "Paradox and Partiality in Retroanalysis" (_diagrammes_, No. 15, 1994):

"This suggestion is not satisfactory, however, for according to it what follows from the [convention] is sensitive to one's decision as to whether to apply the convention first to White or to Black. Its rulings are inappropriately sensitive to the ordering of the questions one employs it to answer (e.g., in this case, "Can White castle?" vs. "Can Black castle?")."

This can also be seen by considering how this convention interacts with the convention regarding e.p. capture. Eriksson says: "en passant captures and draw claims are considered legal if they are legal after all proof games." Consider, then, whether White can capture e.p. in Ceriani's problem. If we apply this convention to the diagram position, then, since there is a proof game leading to it in which e.p. capture is not legal, we conclude that White cannot capture e.p.. On the other hand, the convention governing castling would have us conclude that Black can castle in the diagram position (since there is a legal game leading to that position that would allow Black to castle). But if Black can castle, then Black's last move was b7-b5 and White can capture e.p.. In short, as I say in my article:

"we get conflicting answers to the question "Can White capture e.p.?" depending on whether we apply the convention for e.p. capture first and the [castling convention] second, or the other way around. [...] And surely this is troubling: if we are to have conventions at all, they should be such as to yield the same result regardless of the order in which we apply them and regardless of the ordering of the questions being answered through their application."

In addition, there is the issue mentioned several times already that relying on such a castling convention leads to an artificial narrowing of the retroanalytical possibilities considered. Thus there is no reason, as Sabey has said, why the diagram position of Ceriani's problem might not have arisen through a sequence of moves that prevents both sides from castling.

Finally, Eriksson says "Most retro experts do not share Alexander Georges opinions about the castling convention." That may be; I don't know. But perhaps it is worth noting that T.R. Dawson had this to say:

"Problems which prove only partially some retrograde fact cannot be held to prove the fact absolutely. Given that IF White may O-O-O, then Black may NOT play O-O-O --- from retro reasoning --- and vice-versa, does not give evidence that White may start 1.O-O-O and so prevent O-O-O in reply." [_Fairy Chess Review_, February 1950]

For some other relevant quotations, see again my article (copies of which are available upon request).

Inspired by the current discussion on castling and partial retrograde analysis, let me point out some examples of the confusion that arises when changes are made in definitions and conventions.

The equihopper and the non-stop equihopper are two slightly different fairy pieces. Yet, according to the FIDE Album 1986-88, when you write equihopper under a diagram, you really mean non-stop equihopper.

Is the imitator a fairy piece? If so, pawns may promote to imitator by the convention that promotions to fairy pieces present in the diagram position are allowed. The excellent solving program Popeye is slightly inconsistent in this matter; it treats the presence of imitator(s) as a fairy condition, yet it allows promotion to imitator. (In fairness to Popeye it should be added that it has another fairy condition, which forbids such promotions).

Under the fairy condition of anticirce, may you capture on the home square of the capturing man? For instance, is black in check in the position wKe2, wNe8, bKe1? The original definition was unclear on this point, so now there exist some anticirce problems where such captures are allowed and others where they are forbidden. Sometimes type Cheylan is added to the condition to indicate that these captures are forbidden, but what is a solver supposed to do without this addition?

In the current controversy I support Henrik Erikson in his defense of the traditionalist view for pragmatic reasons, although I am not completely happy with the logical implications.

Richard Sabey's statement is correct: a PRA solution involves splitting the set of proof games intelligently. Is such a convention workable, he asks. Well, it has produced several wonderful problems, and for me that's the only criterion.

AG> "This suggestion is not satisfactory, however, for according to it AG> what follows from the [convention] is sensitive to one's decision AG> as to whether to apply the convention first to White or to Black. AG> Its rulings are inappropriately sensitive to the ordering of the AG> questions one employs it to answer (e.g., in this case, "Can White AG> castle?" vs. "Can Black castle?")."

My own understanding of the priority convention for mutually exclusive castlings is different. So that it is not sensitive to one's choice of ordering the 2 "can W (resp. B) castle ?" questions. Really, the question can only be asked when (and if) a given side does effectively castle. Thus the ordering is given by actual moves.

Here are my two cents worth on 'conventions', hoping to give further fuel to this interesting debate:

In general, conventions are not satisfactory only when

1) they are ambiguously stated so that e.g. you cannot implement them in a computer, or you cannot decide whether a problem is sound or not, or

2) they rule out previous well-known problems ("classics").

Any rule is OK if it is not ambiguous. But it can be an heterodox/fairy rule. A convention is a default rule, so that it defines orthodox problems (slightly different from "real chess").

Usually conventions are never ambiguous, except when you try to broaden their scope and apply them to some weirder fairy genre. What must be clear is that in such cases the difficulty arises from the broader scope, not from the convention itself.

The priority convention for mutually exclusive castlings is perfectly non-ambiguous when it is applied to direct #n, h#n, s#n, ... even if it is combined the convention for en-passant capture. In that sense it is a perfectly valid rule, allowing very interesting problems with a nice castle-forbidding strategy. Other conventions can be suggested but I am not aware of some which would have inspired composers.

Agreed, the priority convention becomes ambiguous if you step out of the direct #n framework. E.g. use a stipulation like "White plays his move then changes his mind, retracts and plays something else, mating in two" where the 1st "try" move is O-O forbidding Bl's further 1 ... O-O after the real key move. Is this a valide interpretation of the priority convention ? I don't know, and the convention does not claim to know !! The difficulty here arises from applying a rule outside of its domain. Here experts will gather and finally come to a consensus on how to extend the convention. It will be an extension because we want to preserve our classics.

If somebody suggests a crystal-clear rule that applies non-ambiguously to all situations but conflicts with earlier narrower conventions, then it is very likely that this rule will be a rule, not a convention.

My bottom line: I agree that the priority rule for mutually exclusive castlings must be refined when you step out of its basic application domain. But this does not make it a bad convention.

Philippe Schnoebelen says:

"My own understanding of the priority convention for mutually exclusive castlings is different. So that it is not sensitive to one's choice of ordering the 2 "can W (resp. B) castle ?" questions. Really, the question can only be asked when (and if) a given side does effectively castle."

I don't understand this: if we have a convention to determine who can legally castle, then we have to apply it before someone castles. Its application cannot wait until *after* a castling has taken place.

A number of people (Erikkson, Juel, Schnoebelen) have indicated that what is decisive for them is that preserving the Common Convention for Castling preserves the classics. It is true that the position I advocate (outlined in "Paradox and Partiality in Retroanalysis") would have us declare many great works unsound. But if that is the cost of increased clarity and precision, then perhaps it is worth paying. It also bears noting that these works, should we consider them unsound, are not for that reason any less great. They retain their historical, constructional and even aesthetic significance, perhaps in the way that some of the (what we now consider) flawed problems of the great pioneers of the nineteenth century do.

On a different note entirely: does anyone have any recommendations regarding chess problem archiving and desktop publishing software? Is SmartChess the best around (in spite of its being oriented for game analysis)?

My opinion on it: If black can't prove white may not castle, white can castle. If white proves that black can't castle, if white can, black may not castle, unless the first move was not white's castling.

AG> A number of people (Erikkson, Juel, Schnoebelen) have indicated AG> that what is decisive for them is that preserving the Common AG> Convention for Castling preserves the classics. It is true that AG> the position I advocate (outlined in "Paradox and Partiality AG> in Retroanalysis") would have us declare many great works unsound. AG> But if that is the cost of increased clarity and precision, then AG> perhaps it is worth paying. It also bears noting that these works, AG> should we consider them unsound, are not for that reason any less AG> great. They retain their historical, constructional and even AG> aesthetic significance, perhaps in the way that some of the AG> (what we now consider) flawed problems of the great pioneers AG> of the nineteenth century do.

A further example: should composers of endgame studies declare a convention that a Knight can draw against two Bishops if it can reach the Kling-Horwitz "fortress", or that R+B generally draw against B+N even in the case of opposite colors, etc., when exhaustive but incomprehensible (or nearly so) computer analysis *proves* that these conventions are wrong? A.J.Roycroft has in fact proposed that a composer should have the option of making such a declaration, as long as it is intuitively plausible and consistent over the entire study -- not only to preserve unsound classics, but because composition is an art made by and for humans. But it is a radical and controversial proposal, and the endgame community does not advocate sweeping the problem under the rug, which seems to be what the retrograde convention is trying to do.

Alexander George is a proponent of some new castling convention. New conventions, new rules, new ideas are always welcome if they can inspire composers to great works. I assume that Alexander can show us interesting problems based upon his new rules. Please do!

Regarding that problem by Ceriani, I wrote

The solver has to choose how to split the set of proof games. If you split the set of proof games one way, the problem works; if you split it another way, it doesn't.

Henrik Eriksson replied:

Richard Sabey's statement is correct: a PRA solution involves splitting the set of proof games intelligently.

That is not what I meant. My point was that, in that problem by Ceriani, the solver has to decide how to split the set of proof games, and the soundness of the problem depends on how the solver split that set. It was intended as an argument against conventions which force the solver to do this, and I used that problem by Ceriani as an example.

In contrast, a PRA problem does not allow the solver to decide how to split the set of proof games: RA *determines* how that set is to be split.

As I see it, a diagram position represents a set of possible game states which differ in the hidden state (castling and en passant ability, move clock, who is to move). The CCC is in effect saying that if one of these positions has strictly less castling ability than another, then you don't have to provide a solution for it. This is sensible, for otherwise every problem which did involve castling would have to be provided with a solution for the non-castling case. (If a diagram position includes any state in which castling is possible, it also includes all "less-castling" states too.)

In the case of RA-type problems with mutually exclusive castlings etc., there will be some problems where an interesting "less-castling" solution exists and some where there is none. I think that rather than imposing some "rule" which disallows one or other category of problem, we should simply agree on a notation which enables us to distinguish between them.

Richard Sabey disagrees with my statement that the solution of a partial retroanalysis problem involves splitting the set of proof games intelligently and finding a solution for each part.

In contrast, a PRA problem does not allow the solver to decide how to split the set of proof games: RA *determines* how that set is to be split.

I guess that is true for those who reject the castling convention. But for all PRA problems based on the castling convention, it is clear that the set of proof games must be split intelligently. For there are always some proof games disallowing castling.

Colin Hogben said, of the CCC,

if one of these positions has strictly less castling ability than another, then you don't have to provide a solution for it.

The CCC does, though, allow for RA: castling is supposed to be legal unless RA can prove it illegal.

The trouble is this. There are various phenomena where the set of valid solutions depends on the answer to some question, and one answer indicates that the situation is more advantageous to White than the other answer indicates. For the sake of argument, let us phrase the question so that Yes indicates a better situation for White than No does. Then any solution for the No situation is also a solution for the Yes situation. So if you have solved the No situation, then you needn't look at the Yes situation.

Examples of such questions, pertinent to that Ceriani problem, are:

"Is White kingside castle legal?" "Is Black queenside castling illegal?" "May White capture Black's b-pawn en passant?"

Note that the first of these questions is phrased in a "positive" way, and the second in a "negative" way.

If RA doesn't answer the question, the CCC says "you only need to provide a solution where castling is legal" and I say "you only need to provide a solution if the answer is No". We agree in regard to Black castling, but not in regard to White castling.

Apply this to the Ceriani problem. There is no trouble if Black may castle. So suppose that Black may not castle. If there had been a solution where no castling is legal, you needn't seek a solution where White may and Black may not. But there is no solution where no castling is legal.