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." ;-) 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
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
participants (4)
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Adam Lake -
collins＠newton.apple.com -
Eli Brandt -
Jim choate