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What are the best proved upper and lower bounds for the Shannon number, i.e. number of possible positions of chess? Is the upper bound 7728772977965919677164873487685453137329736522 given in http://homepages.cwi.nl/~tromp/chess/chess.html generally accepted?

chessmath
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  • I wouldn't accept that number.

    First step -- calculate the number of possible pawn positions. For each position, have a minimum number of captures required to reach that position. Also, calculate which pieces are nonmobile in a given position.

    Second step -- for each pawn position, calculate the number of legal positions for the remaining mobile pieces. Not all positions will be reachable, but that doesn't matter for estimates.

    Exercise -- no pawns moved or captured. How many positions are possible?

     – Ed Pegg Sep 25 '14 at 15:21
  • Do you have a particular reason for not accepting the number? – Deedlit Apr 13 '15 at 12:01

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