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.

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 10^46.7 and showing an upper bound to actually be around 2×10⁴⁰ in the absence of promotions.    WOW!!!