[pge]

I would add that (having simulated this problem in code myself), the reason you have bad outcomes is that you run out of candidates and take a bad one because you have no choice. In real life, at some point you would grab a decent candidate even if s/he were not as good as a prior passed candidate. It is also true that even under the original assumptions, there is a wide range of thresholds around 1/e that yield a similar outcome.