I believe this problem is a lot closer to the Secretary Problem http://en.wikipedia.org/wiki/Secretary_problem http://en.wikipedia.org/wiki/Secretary_problem As

I believe this problem is a lot closer to the Secretary Problem http://en.wikipedia.org/wiki/Secretary_problem http://en.wikipedia.org/wiki/Secretary_problem As he notes however, he does not try to choose "the very best candidate", for which the optimal solution is to pass on the first 1/e candidates. Instead, he tries to maximize the "goodness" of his wife selection. In short : maximum likelihood soultion is to pass on (1/e)*N, minimum mean squared error solution is to pass on sqrt(N). This of course assumes you can estimate N well.