How Many Games of Chess: Exact answer given!

[collins@newton.apple.com (Scott Collins)]

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." ;-)


Scott Collins   | "That's not fair!"                         -- Sarah
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