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 | "You say that so often. I wonder what your basis 408.862.0540 | for comparison is." -- Goblin King ................|.................................................... BUSINESS. fax:974.6094 R254(IL5-2N) collins@newton.apple.com Apple Computer, Inc. 5 Infinite Loop, MS 305-2D Cupertino, CA 95014 ..................................................................... PERSONAL. 408.257.1746 1024:669687 catalyst@netcom.com