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Difference between revisions of "Novemtrigintillion"
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*[http://mathworld.wolfram.com/Chess.html Mathematics and chess] | *[http://mathworld.wolfram.com/Chess.html Mathematics and chess] | ||
*[http://www.chessbox.de/Compu/schachzahl2_e.html The biggest number of simultaneous possible legal moves : the composition of Nenad Petrovic by Reinhard A. Scharnagl] | *[http://www.chessbox.de/Compu/schachzahl2_e.html The biggest number of simultaneous possible legal moves : the composition of Nenad Petrovic by Reinhard A. Scharnagl] | ||
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[[Category:Large numbers]] | [[Category:Large numbers]] | ||
Revision as of 21:03, 10 February 2006
The Shannon number, one novemtrigintillion, 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=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). 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.
