Claude Shannon, an American information theorist, estimated the number of theoretical chess positions to be of the general order of roughly 1043. This includes some illegal positions (e.g., pawns on the first rank, both kings in check) and excludes legal positions following captures and promotions.
|The number of possible chess positions is
~ 2 x 1040
Taking these into account, Victor Allis calculated an upper bound of 5×1052 for the number of possible positions, and estimated the true number to be about 1050. Recent results improve that estimate, by proving an upper bound of only 2155, which is less than 1046.7 and showing an upper bound to actually be around 2×1040 in the absence of promotions. WOW!!!