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A320084
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Decimal expansion of solution of -x*log_2(x) - (1-x)*log_2(1-x) + (1-x)*log_2(3) = 1.
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0
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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Two people playing "online matching pennies" can get as close as they want to this fraction of success.
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REFERENCES
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Peter Winkler, "Mathematical Mind-Benders", ISBN 978-1-56881-336-3 (the number is given as "about 0.8016").
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LINKS
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Olivier Gossner, Penelope Hernandez, Abraham Neyman, Online Matching Pennies, 2003, Discussion Paper Series dp316, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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EXAMPLE
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0.810710375084768237...
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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