A048987 Number of possible chess games at the end of the n-th ply.

1, 20, 400, 8902, 197281, 4865609, 119060324, 3195901860, 84998978956, 2439530234167, 69352859712417, 2097651003696806, 62854969236701747, 1981066775000396239, 61885021521585529237, 2015099950053364471960

Offset: 0

Author

S. J. Edwards

Keywords

• nonn
• nice
• hard
• more
• fini

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

• 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).

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"