A single integer N = a complete chess game

[Maximilian Hasler]

> > > [FIDE definition of legal position elided].
>
>  I said the largest known number of plays, not plies. There is a position
> from which White can choose from 218 possible plays. The position,
>  http://www.chessbox.de/Compu/schachzahl2_e.html
>
>  is, as far as I can tell, legal.

1/ I agree that here "plays" might be more appropriate than ply.
2/ The elided definition implies that this position is not legal.

> By promoting all pawns to queens and summing the optimal number
> of moves of each piece on an open board, we arrive at 321,

For the sake of curiosity, I remember (though I still was in school
then) reading in a book by Smullyan related to retro analysis that up
to some not so remote date, promotion rules did not state that you
must chose a piece of your own color.  (There are positions in which
you can (only) mate by promoting a pawn to a piece of the opposite
color.)
Although no more possible with today's rules, this would (very
theoretically) allow to have a position with 17 white queens, and
probably(maybe?) even more than 218 "plays" (possible moves).
Needless to say, I don't consider this as relevant, since again these
positions are not legal, because they cannot occur in a real game.

Maximilian



On Apr 14, 2008, at 11:20 PM, David Wilson wrote:

> The position, shown at
>
> http://www.chessbox.de/Compu/schachzahl2_e.html
>
> is, as far as I can tell, legal.


On Apr 15, 2008, at 11:30 AM, Maximilian Hasler wrote:

> 2/ The elided definition implies that this position is not legal.


To prove that the position is legal, one need only construct a "proof  
game". This has not, as far as I am aware, been done. To prove that  
the position is not legal, one need only construct an argument showing  
that the position can not be arrived at in legal play. This also has  
not, as far as I am aware, been done.

Hans