Postprint version. Published in International Journal of Game Theory, Volume 21, Issue 2, June 1, 1992, pages 151-160.
Copyright © 1992 Springer.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1007/BF01245458.
In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson — 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). We extend this to the case where the number of items is unknown with a known upper bound. Corollary 3 extends one of the main results in [HK] to all randomized stopping times. We also include a modified, somewhat more formal argument for Ferguson's result.