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.
Citation
Alexander V. Gnedin. "A Solution to the Game of Googol." Ann. Probab. 22 (3) 1588 - 1595, July, 1994. https://doi.org/10.1214/aop/1176988613
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