Improving on bold play when the gambler is restricted
Jason Schweinsberg
Source: J. Appl. Probab.
Volume 42, Number 2
(2005), 321-333.
Abstract
Suppose that a gambler starts with a fortune in (0,1) and wishes
to attain a fortune of 1 by making a sequence of bets. Assume
that whenever the gambler stakes an amount s, the gambler's
fortune increases by s with probability w and decreases by s
with probability 1-w, where w<½. Dubins and Savage
showed that the optimal strategy, which they called `bold play',
is always to bet min{f,1-f}, where f is the gambler's
current fortune. Here we consider the problem in which the gambler
may stake no more than
l
at one time. We show that the bold
strategy of always betting min{
l
,f,1-f} is not optimal if
l
is irrational, extending a result of Heath, Pruitt, and
Sudderth.
Primary Subjects: 91A60
Secondary Subjects: 60G40, 60G42
Keywords: Bold play; red-and-black; gambling; supermartingale
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1118777173
Digital Object Identifier: doi:10.1239/jap/1118777173
Mathematical Reviews number (MathSciNet):
MR2145479
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