How many legal positions are possible in a chess game and how do we know this?
If all we know is an estimate, please explain how we get this estimate.
You’re talking about the Shannon Number, an estimation of the game-tree complexity of chess.
Its computed that the number of possible board positions is around 1×10^120. This is considerably larger than the estimated number of atoms in the univsere.
The number of legal board positions, however, is estimated to be 1×10^43 and 1×10^50.
Shannon’s initial esitimate was based that an aveage game consists of 40 moves, and during each move, the player picks from a set of 30 possible moves. = (30×30)^40 = 1×10^120.
Of course, sometimes the number of moves can be much smaller, like 1 or even 0, and sometimes the number of possible moves on a board is 200, but I guess it evesn out.
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