Secretary Problem

mechanism

When options arrive one by one and rejection is irreversible, use the first roughly 37% to establish a benchmark, then select the first later option that surpasses everything observed.

To improve your chance of choosing well, you deliberately reject the first 37% of the candidates—even if one looks excellent.

Learn first, choose second

An early option is hard to judge because you have no reliable baseline. The observation period builds one: the best candidate in that sample becomes the standard the remaining candidates must beat. After the threshold, the rule switches from exploration to commitment. You accept the first new record rather than continuing to search indefinitely and risking the loss of every good option.

Where it shows up

A sequential shortlist

If ten candidates must be accepted or rejected as they appear, observe and reject roughly the first four. Record the strongest of them, then choose the first subsequent candidate who is better than that benchmark.

The rule needs a finish line

The 37% threshold fits a narrow problem: the approximate number of options is known, they arrive sequentially, rejected options cannot be recalled, and the aim is to capture the best available option. If you can revisit candidates, keep gathering useful information, or care about several dimensions of fit rather than a single ranking, the neat cutoff can mislead.

Set the cutoff before you start

For your next finite, one-pass search, estimate the total number of options and mark 37% of that number as observation-only. Write down the best result from that sample; after the cutoff, commit to the first option that clearly beats it.

Episodes that teach this

Are you a Baloo or a Bagheera? Explore vs Exploit Concept - FutureIQ · explained at 14:19 5,300 views
"reject the first 37% and then after that say yes to the first one who is better than all the previous ones"