> The basic problem is this: there are N applicants for a secretarial position. The applicants are interviewed in random order, and you must accept or reject a candidate immediately after interviewing them. After you reject someone, there's no way to bring them back. There is only one position available, so as soon as you accept a candidate you are done. What strategy should you pursue in order to maximize the likelihood of hiring the best candidate out of the N applicants?
> It turns out that the best strategy is to look at the first N/e applicants (i.e. the first ~37%), reject all of them, then accept the first applicant that is better than all of the initial rejects. It turns out this strategy has a ~37% (1/e) chance of picking the best candidate, regardless of how large N is. This is counterintuitive. It means that even if you have one billion applicants in some random order, you will find the very best one ~37% of the time with this strategy, even though you will (on average) make your choice without meeting the last few hundred million candidates.
> I think this has some interesting practical implications. For example, as a VC, one possible strategy that I can pursue is to look for interesting sectors (3D printing, drones, bitcoin, etc.) and try to invest in the very best startup in each of those sectors. The Secretary Problem is a decent approximation of this. I can go on AngelList and see that there are thirty 3D printing startups in LA/NYC/SF, which are the markets I'm interested in. One way to pick the best one of these 30 would be to meet 11 of these startups, pass on all of them, then invest in the next 3D printing startup I meet that's better than all of those. Of course, this would be a jerk move. I'd be wasting the time of a lot of founders if I knew I was planning to pass on their startups no matter what. However, if I happened to pass on a dozen 3D printing startups by chance, and I knew that there were ~30 in total, then if the 14th one was better than the first dozen, I would know there was a pretty good chance it was the best one out of all 30 even though I had yet to see the last 16.
[1] https://www.quora.com/Mathematics/What-are-the-most-interest...