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How many possible positions are there in chess? Please be exact.

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  • "Please be exact" = troll
    – Tony Ennis
    Apr 3, 2015 at 23:58
  • The number of legal chess positions is roughly 4x10^44: github.com/tromp/ChessPositionRanking
    – John Tromp
    Aug 10, 2021 at 14:21
  • To be more precise, it is about 4.8x10^44, as the latest research at github.com/tromp/ChessPositionRanking shows.
    – John Tromp
    Apr 2 at 12:57

1 Answer 1

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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.

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