How Many Games of Chess: Exact answer given!

Based on new information I have at last answered the question of `How many
games of Chess' with finality.  Here is the quote that woke me up to the
reality of this problem in combinatorics.

Jim choate writes:
  >The fact is that the end game is what defines a game of chess and
  >not the infinitude of possible paths between the first and last move.


The natural conclusion is that the complexity of the problem depends on how
much of the game you consider to be the `endgame'.  Thus, the actual number
of different chess games: 5

 2) White mates
 1) Black resigns
 0) Stalemate
-1) White resigns
-2) Black mates

Happily, this agrees with observed behavior.  In fact, this is the way
posterity remembers them, e.g., "Oh, yes, Spasky won." ;-)


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> 
> 
> The natural conclusion is that the complexity of the problem depends on how
> much of the game you consider to be the `endgame'.  Thus, the actual number
> of different chess games: 5
> 
>  2) White mates
>  1) Black resigns
>  0) Stalemate
> -1) White resigns
> -2) Black mates
> 
i am not sure this is a very reasonable question without any 
restrictions.  while this answer is humerous, i don't think anybody has 
addressed the fact that i can move a king back and forth between 3 
squares infinitely many times.  

POSSIBLE answer: uncoutably infinite?

lake@uenics.evansville.edu
----------------------------------------------------------------------------
Isn't it nice to have only one simple question.....
Zero or One.
----------------------------------------------------------------------------

> 
> > 
> > 
> > The natural conclusion is that the complexity of the problem depends on how
> > much of the game you consider to be the `endgame'.  Thus, the actual number
> > of different chess games: 5
> > 
> >  2) White mates
> >  1) Black resigns
> >  0) Stalemate
> > -1) White resigns
> > -2) Black mates
> > 
> i am not sure this is a very reasonable question without any 
> restrictions.  while this answer is humerous, i don't think anybody has 
> addressed the fact that i can move a king back and forth between 3 
> squares infinitely many times.  
> 
> POSSIBLE answer: uncoutably infinite?
> 
> lake@uenics.evansville.edu
> ----------------------------------------------------------------------------
> Isn't it nice to have only one simple question.....
> Zero or One.
> ----------------------------------------------------------------------------
> 
> 
I would counter that this was a single game irrispective of how many times it
could be moved since the outcome is the same.

> I would counter that this was a single game irrispective of how many times it
> could be moved since the outcome is the same.

This would really simplify the strategy of chess...
	Smirnov		Jagermeister
1.	Wn !!		Rsgn
Commentary: Smirnov's "White wins" opening gave him an early and
dramatic tactical advantage.  Jagermeister showed foresight and
played "Black resigns".

This whole argument is getting rather weird, its topicality aside.
There are a finite number of legal positions in chess.  If any
shows up a third time, the game is over.  Thus we have a bound on
the length of a legal chess game.  Hence the number of games is
finite, and we don't have to quibble about whether it's countably
or uncountably infinite.

   Eli   ebrandt@hmc.edu