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%I #32 Apr 30 2015 20:54:32
%S 1,3,4,6,7,8,9,11,12,13,14,15,17,18,19,20,21,22,24,25,26,27,28,29,30,
%T 31,33,34,35,36,37,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,55,56,
%U 57,58,59,60,61,62,63,64,65,66,67,69,70,71
%N a(n) = maximum number of minus balls for which it is better not to quit when you have n plus balls in the Shepp Urn game.
%H W. M. Boyce, <a href="http://dx.doi.org/10.1016/0012-365X(73)90123-4">On a simple optimal stopping problem</a>, Discr. Math., 5 (1973), 297-312.
%H L. A. Shepp, <a href="http://dx.doi.org/10.1214/aoms/1177697604">Explicit solutions to some problems of optimal stopping</a>, Ann. Math. Statist. 40 (1969) 993-1010.
%e a(5)=7 since if you have 5 plus balls and 7 minus balls, your expected gain in the Shepp Urn game is still positive, namely 0.15, but if you have 8 minus balls, the expectation is zero, so you quit.
%K nonn
%O 1,2
%A _Kafung Mok_, Apr 24 2015
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