Shannon number

From Chesspedia, the Free Chess Encyclopedia.

The Shannon number, 10¹²⁰, 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 (but in fact, there may be as few as zero -in the case of checkmate or stalemate- or as many as 218). Therefore, (30×30)⁴⁰, i.e. 900⁴⁰ chess games are possible. This number is about 10¹²⁰, as the solution of the equation 900⁴⁰=10^x 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). As a comparison, the number of atoms in the Universe, to which it is often compared, is estimated to be between 4×10⁷⁸ and 6×10⁷⁹.

See also

• Chess (programming)
• Solved board games
• Fairy chess

External links

• Mathematics and chess
• The biggest number of simultaneous possible legal moves : the composition of Nenad Petrovic by Reinhard A. Scharnagl

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