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

[Michael Niermann-Rossi]

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

> 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

> "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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