

A256827


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.


0



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, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..62.
W. M. Boyce, On a simple optimal stopping problem, Discr. Math., 5 (1973), 297312.
L. A. Shepp, Explicit solutions to some problems of optimal stopping, Ann. Math. Statist. 40 (1969) 9931010.


EXAMPLE

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.


CROSSREFS

Sequence in context: A164386 A111909 A184010 * A175139 A182835 A058654
Adjacent sequences: A256824 A256825 A256826 * A256828 A256829 A256830


KEYWORD

nonn


AUTHOR

Kafung Mok, Apr 24 2015


STATUS

approved



