How many possible positions are there in chess? Please be exact.
Shannon estimated the number of possible positions roughly 10^43. 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 5×10^52 for the number of positions, and estimated the true number to be about 10^50.
Recent results improve that estimate, by proving an upper bound of only 2^155, which is less than 10^46.7 and showing an upper bound 2×10^40 in the absence of promotions.