Shannon number

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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 = 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).[2]. This is approximately equal to the factorial of the number 82, which is more precisely equal to 4.75364334... × 10¹²². 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]