# [Retros] Castling and repetition

Rol, Guus G.A.Rol at umcutrecht.nl
Thu Oct 25 04:11:45 EDT 2007

Yefim, I am all in favor of presenting the issues in a mathematical setting. Fortunately mathematics is perfect, but unfortunately, the modelling of reality into mathematics is quite often suspect. Your translation immediate raises the question of what you mean by "castling right" even in a (non-composition) game environment. To explain that, I refer to your "Problem". The trivial replies to your problem are either (a) game termination as suggested by Andrey (b) impossible, since white on move can only affect his own 2 castling rights or eliminate one black rook with one white rook while destroying 1 white castling right.

Assuming that you did not attempt to tease us with a triviality I assume your formal response would be something of this nature: (response_to_a) good try, but terminating the game puts it outside the scope of the chess system and all of its subsystems including evaluations of castling rights; (response_to_b) another good analysis, but I mean something else by "castling rights'"!

The "response_to_b" returns us to the original query. Since I am confident that my reply "(b)" is precisely in line with the FIDE laws (but don''t take my word for it) I am left with the question as to what your particular interpretation of "castling right" might be here. I came up with 3 options: (1) you are referring to "the right to castle" as "the possibility to castle" (2) you are referring to "the right to castle" as the "opportunity to castle" (3) you have switched from "game mode" to "composition mode" and are referring to (what I call) the "license to castle".

In my view the "opportunity to castle" only corresponds to "temporary castling right" in FIDE vocabulary and as such is insufficient by itself to arbitrate "repetition of position" as showcased by my earlier discussion of the well-known Fisher-Najdorf game. The "possibility to castle" though corresponds to precisely NOTHING in FIDE law. It doesn't matter for any FIDE article (exept by implication for dead positions) whether or not the possibility to castle could ever arise. The Fisher-Najdorf game argument equally dismisses "opportunities" and "future possibilities" as deciders for the repetition rule.

That leaves us with the third option that your "Problem" switched from "game mode" to "composition mode". Before providing a solution to thát problem I first wish to note that this assumption invalidates your notations (1111=KQkq) and (0000). If you intend to apply a formal notation system to resolve "repetition of positions" for both games and compositions then you must first prove that it will work in both fields. Since I demonstrated the precise opposite in my composition R309 for Probleemblad I will leave it there for the moment.

In 1969, André Hazebrouck published a #3 problem in Europe Echecs with 4 licensed castling possibilities. Executing either of the white castlings (retro variants) would switch off (post factum) the 2 black castling licenses. Though the logical structure of this composition is debatable - and I will debate it in time - its retroanalytical aspect is impeccable and meets the expectations. If you are interested I can provide you with the position. But may be this third option is not the one you had in mind when posing your challenge.

Guus Rol.

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Van: retros-bounces at janko.at [mailto:retros-bounces at janko.at] Namens TregerYefim at aol.com
Verzonden: woensdag 24 oktober 2007 4:11
Aan: retros at janko.at
Onderwerp: Re: [Retros] Castling and repetition

I have read suggestions about genetic ideas for castling with a big pleasure.
They are probably good for chess composition, but they have little connections with
mathematics, which we have discussed before (below).

Each position (as diagram) has to have unique properties of castling rights which may be recorded by binary system (corresponds to EPD-FEN notation)
There are 16 of them.
0000 = no games (from the position) with any castling;
0001= q: games with Black Queen side castling;
0010 = k: games with Black King side castling;
0011= kq: games with Black King or Queen side castling;
0100 = Q: games with White Queen side castling;
0101 = Qq: games with White Queen side or Black Queen side castling;
0110 =Qk: games with White Queen side or Black King side castling;
0111=games with White Queen side or Black King side or Queen side castling;
1000=K: games with White King side castling;
1001=Kq: games with White King side or Black Queen side castling;
1010=Kk: games with White King or Black King side castling;
1011=Kkq: games with White King side or Black King or Queen side castling;
1100=KQ: games with White King side or Queen side castling;
1101=KQq: games with White King side or Queen side or Black Queen side castling;
1110=KQk: games with White King or Queen side and Black King side castling;
1111= KQkq games with all castling possible.

"Equal positions must have the same Binary Word for castling". If you add this sentence to the FIDE rules (about repetition) you do not need wierd phrases about permanent or temporary rights of castlings...

Of course, there are situations where defining the right castling Binary type is very difficult, but that is caused by complexity of Chess, not by the math classification above. There are positions with King and Rook have not been moved before, but no games from them, so they have 0000 castle type. If an arbiter decides by his judgment that castling is possible, we may accept it, but it is not math point of view.

Problem.
Create a position (White to move) with all castling rights (1111=KQkq), where after White's move all castling right will be lost (0000).

Yefim 10/23/2007

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