# Fwd: Re: [Retros] Math aspects of Retro from Yefim Treger 08/21/2004

**Michael Niermann-Rossi**
mniermannrossi at yahoo.de

*Mon Aug 23 10:28:10 EDT 2004*

Sorry, if you already got this mail, but I think my first attempt didn't

work.

>* Hi folks,
*

>*
*

>* > "Positions ... are considered the same, if the same player has the move,
*

>* > pieces of the same kind and colour occupy the same squares, and the
*

>* > possible moves of all the pieces of both players are the same.
*

>*
*

>* IMO this is a correct definition, esp. from a mathematical point of view,
*

>* if
*

>* "possible moves" applies to all possible future positions.
*

>*
*

>* > Positions are not the same if a pawn that could have been captured en
*

>* > passant can no longer be captured or if the right to castle has been
*

>* > changed temporarily or permanently."
*

>*
*

>* But this statement tries to clarify the definition and starts the trouble.
*

>* It should be simply removed.
*

>*
*

>* Indeed for the first example (castling/Pe2) the first definition says that
*

>* the Positions are the same, but after 1. - Pe2 castling is prevented
*

>* temporarily (Rule 3.8.ii) and after moving the rook it is illegal (Rule
*

>* 3.8.ii). So IMO the right to castle is changed permanently and the
*

>* positions
*

>* are not the same due to the second "definition".
*

>*
*

>* I think the first definition is exactly what Yefim had in mind, it means
*

>* that
*

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

>* identical. I suppose that the second "definition" was added to make it more
*

>* transparent for the non-mathematicians, but unfortunately there is a
*

>* contradiction between them, only in artificial examples, but a
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>* contradiction.
*

>*
*

>* BTW, if we would consider "claiming a draw" to be a "move" there occurs a
*

>* funny paradoxon:
*

>* When there is the same position the third time, the player who has to move
*

>* gets the right to claim a draw. But this right changes the position. So it
*

>* is
*

>* not the same position. But then he can't claim a draw. So it is the same
*

>* position ...
*

>*
*

>* But I agree that this doesn't affect the existence of positions, which
*

>* cannot
*

>* be proven to be legal or illegal. Yefim has found a contradiction in the
*

>* FIDE
*

>* rules by constructing two positions which can be proven to be "the same"
*

>* and
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>* "not the same".
*

>*
*

>* Another point comes to my mind: The longer I think about the definition
*

>* > "Positions ... are considered the same, if the same player has the move,
*

>* > pieces of the same kind and colour occupy the same squares, and the
*

>* > possible moves of all the pieces of both players are the same.
*

>* the more problems I see:
*

>* Consider e.g.
*

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

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

>*
*

>* Of course these positions cannot occur both in one single game, so it
*

>* doesn't
*

>* affect 5.2.d, but anyway we can apply these "definitions". Are these
*

>* positions the same or not the same?
*

>*
*

>* Or even better:
*

>* 4k1nr/8/8/1p6/1P1P4/KPp5/P1P5/8 w k - 0 1 and
*

>* 4k1nr/8/8/1p6/1P1P4/KPp5/P1P5/8 w - - 0 1
*

>*
*

>* Regards, Michael
*

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