Shannon number
From Wikipedia, the free encyclopedia
The Shannon number is an estimation of the game-tree complexity of chess. It was first calculated by Claude Shannon, the father of information theory. According to him, on average, 40 moves are played in a chess game and each player chooses one move among 30. In fact, there may be as few as zero — in the case of checkmate or stalemate — or as many as 218.[1] However, his approximation is at least plausible. Therefore, (30×30)40 = 90040 chess games are possible. This number is about 10118, or a billion billion googol, as the solution of the equation 90040 = 10x is x = 40 log 900.
The game-tree complexity of chess is now evaluated at approximately 10123 (the number of legal positions in the game of chess is estimated to be between 1043 and 1050).[2] As a comparison, the number of atoms in the Universe, to which it is often compared, is estimated to be between 4x1079 and 1081.[3][4]
Another comparison is to the game of Go; the number of possible Go positions is calculated at 2.1×10170.
[edit] See also
[edit] External links
- Mathematics and chess
- The biggest number of simultaneous possible legal moves : the composition of Nenad Petrovic by Reinhard A. Scharnagl
 |
This chess-related article is a stub. You can help Wikipedia by expanding it. |
