Shannon number

Shannon also estimated the number of possible positions, of the general order of

After each player has moved a piece 5 times each (10 ply) there are 69,352,859,712,417 possible games that could have been played.

As a comparison, the number of atoms in the observable universe, to which it is often compared, is roughly estimated to be 1080.

John Tromp and Peter Österlund estimated the number of legal chess positions with a 95% confidence level at

, based on an efficiently computable bijection between integers and chess positions.

[5] As a comparison to the Shannon number, if chess is analyzed for the number of "sensible" games that can be played (not counting ridiculous or obvious game-losing moves such as moving a queen to be immediately captured by a pawn without compensation), then the result is closer to around 1040 games.