It is worth noting that the 1/e secretary problem solution is optimal only if your goal is to maximize the probability of choosing the single best secretary. I

It is worth noting that the 1/e secretary problem solution is optimal only if your goal is to maximize the probability of choosing the single best secretary. If your goal is to do expectimax optimization, as decision theory would dictate, you should make a decision after reviewing sqrt(n) applicants. That's assuming a uniform distribution of utility among secretary choices. If the distribution is non-uniform, another heuristic might be better.