The Annals of Probability

A Solution to the Game of Googol

Alexander V. Gnedin

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Abstract

For any $n > 2$ we construct an exchangeable sequence of positive continuous random variables, $X_1, \ldots, X_n$, for which, among all stopping rules, $\tau$, based on the $X$'s, $\sup_\tau P\{X_{\tau} = X_1 \vee \cdots \vee X_n\}$ is achieved by a rule based only on the relative ranks of the $X$'s.

Article information

Source
Ann. Probab. Volume 22, Number 3 (1994), 1588-1595.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176988613

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176988613

Mathematical Reviews number (MathSciNet)
MR1303655

Zentralblatt MATH identifier
0815.60038

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Googol best-choice problem secretary problem

Citation

Gnedin, Alexander V. A Solution to the Game of Googol. Ann. Probab. 22 (1994), no. 3, 1588--1595. doi:10.1214/aop/1176988613. http://projecteuclid.org/euclid.aop/1176988613.


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