%I #22 Nov 10 2018 09:31:15
%S 8,1,0,7,1,0,3,7,5,0,8,4,7,6,8,2,3,7,3,9,7,6,0,5,3,0,6,6,3,4,7,2,5,7,
%T 5,7,8,3,3,0,3,3,8,3,8,1,5,6,9,5,3,6,6,1,0,7,7,9,0,9,8,3,7,8,2,3,7,8,
%U 2,4,4,9,1,5,2,6,0,0,7,1,4,2,5,2,4,4,4,8,9,0,0,1,7,7,5,5,4,2,3,1,4,8,0,4,3,5,5
%N Decimal expansion of solution of -x*log_2(x) - (1-x)*log_2(1-x) + (1-x)*log_2(3) = 1.
%C Two people playing "online matching pennies" can get as close as they want to this fraction of success.
%D Peter Winkler, "Mathematical Mind-Benders", ISBN 978-1-56881-336-3 (the number is given as "about 0.8016").
%H Olivier Gossner, Penelope Hernandez, Abraham Neyman, <a href="http://ratio.huji.ac.il/sites/default/files/publications/dp316.pdf">Online Matching Pennies</a>, 2003, Discussion Paper Series dp316, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
%e 0.810710375084768237...
%p evalf(solve(-x*log[2](x)-(1-x)*log[2](1-x)+(1-x)*log[2](3)=1,x),120); # _Muniru A Asiru_, Oct 05 2018
%o (PARI) solve(x=0.1, 0.9, -x*log(x) - (1-x)*log(1-x) + (1-x)*log(3) - log(2)); \\ _Michel Marcus_, Oct 06 2018
%K nonn,cons
%O 0,1
%A _Jack Zhang_, Oct 05 2018