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RV and Castling Convention

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.)"

Henrik Eriksson, 6 Dec 1995

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!  

Richard Sabey, 7 Dec 1995

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.

Henrik Eriksson, 7 Dec 1995

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. 

Richard Sabey, 7 Dec 1995

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?

Alexander George, 8 Dec 1995

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).

Henrik Juel, 8 Dec 1995

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.

Henrik Eriksson, 8 Dec 1995

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.

Philippe Schnoebelen, 8 Dec 1995

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. 

Alexander George, 8 Dec 1995

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)?

Joost de Heer, 8 Dec 1995

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.

Noam Elkies, 8 Dec 1995

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.

Henrik Eriksson, 8 Dec 1995

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!

Richard Sabey, 8 Dec 1995

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.

Colin Hogben, 11 Dec 1995

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.

Henrik Eriksson, 11 Dec 1995

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.

Richard Sabey, 11 Dec 1995

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.