Freeform thoughts from here:
1/e is the probability of failing (every time) if you try a 1/n chance n times, where n is large.
To get the optimal choice, there are two (generously defined) requirements:
- #1 does not occur in the discarded group
- #1 occurs before everyone else who was not discarded, but exceeds the maximum of the discarded group
The second one seems hairy to me, so I'll wrap things up here. ;p
> As for real-world applications, the only one that comes readily to mind is rolling up a D&D character
This was introduced to me as a marriage problem, and wikipedia also notes it by that name. The analogy never seemed inaccurate to me; it's frowned upon to evaluate candidates simultaneously and rare to accept someone other than the latest candidate.
As for real-world applications, the only one that comes readily to mind is rolling up a D&D character, supposing one has only the patience for some predetermined n rolls. Somewhat ironically it is not a realistic fit for hiring, as there is seldom a need to accept or eliminate candidates immediately, interviewing more than 5-6 people for a role is torturous, and an interviewer uses his experience interviewing and interacting with people generally to have no mathematical prejudice against hiring the very first pretty-good option.