Overview
Hiring, dating, apartment hunting, choosing a parking space: any search where you must commit on the spot and cannot go back is this problem in disguise.
How to solve The Secretary Problem
- Any sensible strategy has two phases: learn the field, then commit to the next thing that beats everything seen.
- If you stop looking after r candidates, the chance of landing the best is (r/n) · Σ 1/(i−1) over i > r.
- Maximising that sum over r gives r ≈ n/e, and the winning probability tends to 1/e ≈ 37%.
The key insight
37% is both the fraction you should sacrifice and the odds you end up with — the same 1/e appears twice. Sacrificing that much information is what buys you a calibrated bar, and no strategy can do better under these rules.
Variations & echoes
- If you only want a good candidate rather than the very best, the optimal cutoff drops to √n and success rises sharply.
- Allowing recalls, ties, or a known score distribution all change the answer — the 37% rule is specific to rank-only, no-going-back decisions.
Frequently asked questions
What if the best candidate is in the first 37%?
Then you lose — and that happens 37% of the time. The strategy is optimal on average, not lucky every time.