On the game of googol (Q1196120)

In the classical secretary (or best-choice) problem, the decision maker observes only the relative ranks of the \(N\) items presented sequentially, and wins only if he stops with the best. Recently, \textit{T. S. Ferguson} [Stat. Sci. 4, 282-296 (1989)] --- building on ideas of Stewart --- showed that, in a game theoretic sense, there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). Ferguson's minimax result is extended here to the game of googol when \(N\) is a random variable with an unknown distribution but with known upper bound \(n\), thereby improving the result of the authors [Ann. Probab. 19, No. 1, 342-353 (1991; Zbl 0723.60043)] for the analogous secretary problem.