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 A048987 Number of possible chess games at the end of the n-th ply. 17
 1, 20, 400, 8902, 197281, 4865609, 119060324, 3195901860, 84998978956, 2439530234167, 69352859712417, 2097651003696806, 62854969236701747, 1981066775000396239, 61885021521585529237, 2015099950053364471960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Does not include games which end in fewer than n plies. According to the laws of chess, the "50-move rule" and "draw by 3-fold repetition" do not prevent infinite games because they require an appeal by one of the players, but the "75-move rule" introduced on Jul 01 2014 is automatic and makes chess finite. - François Labelle, Mar 30 2015 LINKS Table of n, a(n) for n=0..15. A. Bertilsson, Distributed Perft Project [also found a(11)] James Grime and Brady Haran, How many chess games are possible? (Numberphile video), 2015. Jakub Kowalski, Marek Szykuła, Experimental Studies in General Game Playing: An Experience Report, University of Wrocław, (Poland, 2020). F. Labelle, Statistics on chess games T. Sillke, number of legal chess positions R. P. Stanley, Extremal [Chess] Problems Wikipedia, Shannon number Index entries for sequences related to number of chess games CROSSREFS Cf. A006494, A079485, A083276, A019319, A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king). Sequence in context: A009964 A285874 A007577 * A006494 A007545 A055476 Adjacent sequences: A048984 A048985 A048986 * A048988 A048989 A048990 KEYWORD nonn,nice,hard,more,fini AUTHOR S. J. Edwards EXTENSIONS a(10) from Richard Bean, Jun 02 2003 a(11) from François Labelle, Jul 25 2004, who thanks Joost de Heer for providing computer time a(12) from Paul Byrne on Oct 24 2006, verified by S. J. Edwards on Apr 25 2011 a(13) from Paul Byrne on Nov 08 2011, verified by S. J. Edwards on Oct 03 2012 a(14) from Richard Bean on Jul 24 2018, value from Peter Osterlund and Ankan Banerjee a(15) from Paul Barnett on Jul 04 2022, value from wikipedia page "Shannon number" STATUS approved

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Last modified December 8 13:46 EST 2023. Contains 367679 sequences. (Running on oeis4.)