%I
%S 1,20,400,8902,197281,4865609,119060324,3195901860,84998978956,
%T 2439530234167,69352859712417,2097651003696806,62854969236701747,
%U 1981066775000396239
%N Number of possible chess games at the end of the nth ply.
%C Does not include games which end in fewer than n plies.
%C 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
%H A. Bertilsson, <a href="http://www.albert.nu/programs/dperft/main.htm">Distributed Perft Project</a> [also found a(11)]
%H James Grime and Brady Haran, <a href="https://www.youtube.com/watch?v=Km024eldY1A">How many chess games are possible?</a> (Numberphile video), 2015.
%H F. Labelle, <a href="http://www.cs.berkeley.edu/~flab/chess/statisticsgames.html">Statistics on chess games</a>
%H T. Sillke, <a href="http://www.mathematik.unibielefeld.de/~sillke/SEQUENCES/series014">number of legal chess positions</a>
%H R. P. Stanley, <a href="http://wwwmath.mit.edu/~rstan/transparencies/iap.pdf">Extremal [Chess] Problems</a>
%H <a href="/index/Ch#chess">Index entries for sequences related to number of chess games</a>
%Y Cf. A006494, A079485, A083276, A019319, A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).
%K nonn,nice,hard,more,fini
%O 0,2
%A _S. J. Edwards_
%E a(10) from Richard Bean (rwb(AT)eskimo.com), Jun 02 2003
%E a(11) from _François Labelle_, Jul 25 2004, who thanks Joost de Heer for providing computer time
%E a(12) from _Paul Byrne_ on Oct 24 2006, verified by _S. J. Edwards_ on Apr 25 2011
%E a(13) from _Paul Byrne_ on Nov 08 2011, verified by _S. J. Edwards_ on Oct 03 2012
