| MadSci Network: Other |
My first guess is chess. It has two sides with 16 pieces each. A typical game lasts thirty or so moves. Once the game opens up, most of the non-pawn pieces can move to roughly eight or more squares. Maybe the keepers at IBM of Deep Thought or Big Blue (or whatever its name was) could give you a reasonable numerical estimate for the possibilities. The bidding phase of bridge lasts three or four rounds. The play lasts 13 rounds. The possibilities become sharply restricted as play proceeds. What may complicate this analysis is the variability inherent in the hands dealt. If I rember my combinatorial math correctly, the number of possible different hands is 52!/(some number which is suspect is on the order of 13!) (!=factorial). Now I'm changing my mind, maybe it's bridge. 52!/13! is an enormous number. Probably larger than chess's possibilities. What has intrigued game theorists about chess is that is a complete information game. Both players have equal knowledge at any point. No probability issues should exist in a complete analysis. It therefore has an optimal solution according to game-theoretic proofs. It is just so difficult to analyze that no one has come up with a solution and the game continues to attract new players. Bridge is more probabilistic... decisions within complete knowledge, guesswork are at the core of the game. Probably why I could never "get it." David Winsemius, MD
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