The Secretary Problem#
The one week this semester where the answer is exact
Three ideas, before anything else#
- optimal stopping
- the 1/e rule
- no recall
Get these three straight now — the scenario in a minute uses all of them.
Optimal stopping#
You’re not choosing the best person you’ll ever meet. You’re choosing when to stop meeting new people and commit to one, knowing you can’t go back to someone you already passed on.
Economists call that decision optimal stopping: the problem isn’t who to pick, it’s when to stop looking.
No recall#
Once you’ve moved on from someone — stopped replying, let the moment pass — you don’t get to circle back and choose them later. They’ve moved on too.
That constraint is no recall, and it’s what makes the problem hard: you can’t sample now and decide later.
The 1/e rule#
Given no recall and no idea how good later options will be, there’s an exact answer: spend the first ~37% of your expected dating life purely gathering information — reject everyone, on principle — then commit to the next person who beats everyone you’ve seen so far.
That threshold is the 1/e rule (37% ≈ 1/e). It’s not a guess. It’s the provably best strategy against an unknown distribution.
Now, back to the point#
You expect to date roughly 20 people before settling down. Person #8 is the best one yet. Do you commit?
Running the rule#
| Step | What happens |
|---|---|
| Expected pool | 20 people |
| Information-only phase | first ~7-8 (37% of 20) — reject everyone, just calibrate |
| Commit phase | from #8 onward, accept the first person who beats everyone seen so far |
| Person #8 | is inside the commit phase, and the best so far — the rule says yes |
Why “you’ll know when you know” fails#
Gut instinct has no phase boundary — it says commit the moment someone feels right, which might be person #2, before you’ve seen enough of the distribution to know what “right” should even mean relative to.
The 1/e rule beats intuition specifically by making the calibration phase mandatory, not optional.
The rule doesn’t tell you who to pick. It tells you how much looking is enough before an opinion means anything.
Tutorial 6#
Run the simulator against your own gut strategy first, then against the 1/e rule. The gap between the two is the actual content of the week.
What today doesn’t settle#
The rule optimizes your stopping decision alone. It has no term for whether the person you stop on would also stop on you — every guarantee here quietly assumes the choice only runs one way.
Week 8 starts answering that. Week 12 is where this, and Weeks 1, 3, 4, and 5’s gaps, all come back at once.
See you next week#
Week 7: The Cost of Asking