The candidate problem with unknown population size
Will T. Rasmussen, Herbert E. Robbins · Journal of Applied Probability · 1975
The familiar problem of maximizing the probability of choosing the best from a group of N candidates, where N is known, is extended to the case of N unknown. An a priori distribution is assumed for N, and the case of a uniform distribution is examined. Let VN denote the probability of choosing the best from a group of at most N candidates, then it is shown that lim N→∞ VN = 2e –2.