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.

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

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), 297-312.

L. A. Shepp, Explicit solutions to some problems of optimal stopping, Ann. Math. Statist. 40 (1969) 993-1010.

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