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.
Taking Shannon's numbers into account, Victor Allis calculated an upper bound of 5×1052 for the number of positions, and estimated the true number to be about 1050.[2] Recent results[3] improve that estimate, by proving an upper bound below 2155, which is less than 1046.7 and showing[4] an upper bound 2×1040 in the absence of promotions.
Allis also estimated the game-tree complexity to be at least 10123, "based on an average branching factor of 35 and an average game length of 80". As a comparison, the number of atoms in the observable universe, to which it is often compared, is roughly estimated to be 1080.