Secretary Problem

You know the "secretary problem"—the one that involves logarithms?

If there are 37 total applicants, where does the 37% mark fall?

I’ve sent out resumes to 37 companies so far, and I’ve been rejected by 15 of them. Applying the logic of the secretary problem in reverse, I’m thinking: maybe an offer is coming soon?

I mean—if I look at the situation in a purely positive light—I could just assume that the first 14 companies were "misses," and that the 15th company (or one of the ones following it) might be the one that hires me. Just trying to stay positive, you know!

Haha! Well, even if you do get an offer, you have the right to choose too, right? By the way, in the secretary problem, the probability of the best candidate appearing is highest at the 14th person, and then it gradually drops off—is that right?

Haha, exactly! But here’s a little trick: you can actually shift that 15th-company mark further down the line. You do that by simply increasing the total number of applications. You just keep adding more, timing it so that you hit that "logarithmic sweet spot" where you’re most likely to encounter the absolute best company. That’s how it works!