# [Retros] Example 4 (better version of E.P.) Yefim 08/23/2004

Michael Niermann-Rossi mniermannrossi at yahoo.de
Tue Aug 24 10:16:13 EDT 2004

> Kuhlmann's criteria for comparing two positions is

> essentially the same as that mentioned by Michael Niermann-Rossi:

>

> > two positions are the same, if the trees starting from the positions are

> > identical.

But then you run into the paradox I mentioned.

Take the positions after 1.Nf3 Nf6 and 1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6
In the first position after 2.Ng1 Black can't claim a draw.

The positions are the same.
In the second position after 4.Ng1 Black may claim a draw.
So the trees are different and the positions are not the same.
So in the second position after 4.Ng1 Black can't claim a draw.
So the positions are the same.
etc.

> Here is my attempt to tranlate this rather mathematical definition

> into a more non-mathematical language:

>

> Two positions are the same, if

>

> (1) the same player has the move,

> (2) pieces of the same kind and colour occupy the same squares,

> (3) the set of all legal moves of the side to move is the same

> in both positions

> and

> (4) the future castling capabilities of both sides are the same

> in both positions.

>

> Where "future castling capabilities" is defined as follows:

>

> In a given position, a side has the future castling capability

> to castle king-side (resp. queen-side), if neither his king

> nor his king-side rook (resp. queen-side rook) has ever moved

>

> AND

>

> there exists at least one sequence of moves from the given position,

> in which the castling can actually be executed.

You can remove the first statement since it is implied by the second one.

And what about the 50 moves rule? The repetition rule? I think in the
mathematical definition they should explicitly be excluded as a part of the
position.

Regards, Michael

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