# [Retros] Math aspects from Yefim Treger and the 5-th example! 08/23/2004

Michael Niermann-Rossi mniermannrossi at yahoo.de
Tue Aug 24 02:50:27 EDT 2004

--- TregerYefim at aol.com schrieb:

> Thank you, thank you, thank you for catching the following idea: There is a

>

> contradiction between definition of Position in chess rules and Math (which

> is:

> two positions are the same if sets of all games emerging from them are the

> same, not paying attention to numbers of moves; also good is graph

> definition:

> if trees are the same then Positions are equal.).

I don't agree. You should add "and all squares are occupied by the same
pieces and the same player has to move". Otherwise all positions in which
White (resp. Black) is mated or stalemated are the same, since the tree is
always empty. :) And of course there are examples like Francois' ones.

And I see it slightly different:
The definitions in the chess rules are unclear (or better incomplete?) and on
the other hand we have two definitions for "two positions being the same" and
for "two positions being not the same". First, this is principially very
strange from a mathematician's point of view. Second, I can't see how to
specify the unclear terms in these definitions such that
pos. A and B "are not the same" <=> not (pos. A and B "are the same")
i.e. such that the "not" in the definition suits to the logical not-Operator.

> PS. for Michael: For some reasons I cannot read (type) positions you gave:

> Would you please give them in other way?

No, sorry, please follow Francois' hints to get a good program to view chess
positions or do as follows with your board:

> 4k2r/5p2/3P4/8/8/1q6/8/K7 w k - 0 1 and

It means
8th rank: 4 empty squares, black king, 2 empty squares, black rook
7th rank: 5 empty squares, black pawn, 2 empty squares
6th rank: 3 empty squares, white pawn, 4 empty squares
...

White to move

Legal castlings:
White: none
Black: king's side
(e.g. Kkq would mean: White king's side, Black both)

no en passant possible
(otherwise the passed square would be given)

0 halfmoves after the last pawn advance or capture

1st move in the game

Or look at e.g. http://www.wordiq.com/definition/Forsyth-Edwards_Notation for
a detailed explanation or google for "FEN chess notation". It's a compressed,
but human readable notation with all (or almost all after this discussion
here) necessary informations to describe the position. Of course in the
example 4k2r5p5P21q14K would be much more compressed than
4k2r/5p2/3P4/8/8/1q6/8/K7, but harder to read. And I don't want to compare
its size with your gifs :)

IMO everyone should use FEN and PGN in emails!!!

Regards, Michael

___________________________________________________________
Gesendet von Yahoo! Mail - Jetzt mit 100MB Speicher kostenlos - Hier anmelden: http://mail.yahoo.de