## The Annals of Probability

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

### A Solution to the Game of Googol

#### 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.