**Claude Shannon**, an American information theorist, estimated the number of **theoretical**** chess positions** to be of the general order of **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.

The number of possible chess positions is ~ 2 x 10^{40} |

Taking these into account, **Victor Allis** calculated an upper bound of 5×10^{52} for the number of **possible 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 to actually be around **2×10 ^{40}** in the absence of promotions. WOW!!!