

A048987


Number of possible chess games at the end of the nth ply.


15



1, 20, 400, 8902, 197281, 4865609, 119060324, 3195901860, 84998978956, 2439530234167, 69352859712417, 2097651003696806, 62854969236701747, 1981066775000396239
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OFFSET

0,2


COMMENTS

Does not include games which end in fewer than n plies.
According to the laws of chess, the "50move rule" and "draw by 3fold repetition" do not prevent infinite games because they require an appeal by one of the players, but the "75move 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..13.
A. Bertilsson, Distributed Perft Project [also found a(11)]
James Grime and Brady Haran, How many chess games are possible? (Numberphile video), 2015.
F. Labelle, Statistics on chess games
T. Sillke, number of legal chess positions
R. P. Stanley, Extremal [Chess] Problems
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 (rwb(AT)eskimo.com), 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


STATUS

approved



