# [Retros] Castling and repetition

TregerYefim at aol.com TregerYefim at aol.com
Tue Oct 23 22:11:10 EDT 2007

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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