A · Too EarlySkip 10%
Impatient.
You commit to the second decent face you see. You never met the best.
OutcomeRank 2 · Settled
Trials
0
One hundred candidates arrive in random order. You see each one, once. You must commit instantly, with no going back. At what point do you stop observing, and take the next one better than all before? Mathematics answers with a single, astonishing number.
Reject the first 37% of options you see, then pick the next one that's better than everything you've rejected so far.
You are apartment hunting in New York. Twenty viewings. One month. After each viewing you must decide on the spot — take it, or walk away. Once you leave, it's gone. You want the very best one.
What's your strategy?
What is the optimal stopping strategy that maximises the probability of selecting the best candidate from a sequentially observed pool of n candidates, where each rejected candidate cannot be recalled and the decision must be made immediately upon observation?
You commit to the second decent face you see. You never met the best.
You observe without deciding. Then, the first to surpass them all is yours.
You watched forever, and the last face left is the face you get.
Observe the first 37% of candidates without choosing anyone — use them to calibrate your sense of quality. Then select the very next candidate who beats every single one you have already seen. This strategy maximises your probability of finding the best option at exactly 36.79% — the mathematical ceiling, provably unbeatable.
You'll tour listings one at a time. You see the price, layout and square footage — but you'll only know how each one ranks against the ones you've already viewed.
Do not sign a lease for the first 37%. After that, take the first unit that beats every one you've seen.
Treat 37% of your window as exploration. After the switch age, commit to the next partner who surpasses everyone before.
Like all mathematical models, the 37% rule rests on precise assumptions. Understanding where those assumptions hold — and where they break down — is essential for applying it responsibly.
Candidates must arrive in a uniformly random order. In practice, rental listings sorted by price, recruitment agencies filtering candidates, and dating apps using recommendation algorithms all introduce systematic ordering that violates this assumption.
The total number of candidates must be known up front. When apartment hunting you may not know how many listings will appear over the next month. Poisson-arrival extensions address unknown n, but the clean 1/e result no longer holds exactly.
Once a candidate is passed, they cannot be recalled. Many real-world situations allow for negotiation or return — a landlord may still accept your application, an employer may reopen a position. When recall is possible, a less aggressive threshold is optimal.
You can always rank the current candidate perfectly against all previous ones. In reality, noise, incomplete information, and changing preferences make consistent ranking unreliable — especially over long horizons such as a multi-year search for a life partner.
It tightens only as n grows large. For small pools, the exact optimal threshold k can differ from ⌊n/e⌋, and the success probability is meaningfully above 36.8%.
| n | k · 37% rule | k · exact optimum | P(best) · 37% | P(best) · exact |
|---|---|---|---|---|
| 3 | 1 | 1 | 50.0% | 50.0% |
| 5 | 1 | 2 | 41.7% | 43.3% |
| 10 | 3 | 3 | 39.9% | 39.9% |
| 20 | 7 | 7 | 38.4% | 38.4% |
| ∞ | ⌊n/e⌋ | ⌊n/e⌋ | 36.8% | 36.8% |
Highlighted: for n = 5, the 37% rule selects k = 1 (41.7% success), while the exact optimum of k = 2 yields 43.3% — a real gap the asymptotic formula misses.
The classic model requires knowing n in advance. Two natural extensions relax this requirement:
Known horizon T, unknown count. If candidates arrive uniformly over a known interval [0, T] and you do not know how many will appear, the optimal strategy is to observe until time t* and then commit to the next record-setter:
The 37% threshold re-emerges, now in units of time rather than candidate count — the mathematical structure is identical.
Unknown T and n (geometric prior). If even the horizon is unknown and the number of candidates follows a geometric distribution, the optimal cutoff rises above 1/e:
The 1/e result is a robust anchor: moderate uncertainty in n shifts the optimal threshold by only a few percentage points, so the 37% rule remains a useful heuristic even when the pool size is approximately — but not exactly — known.
The secretary problem forbids recall: reject a candidate and they vanish forever. Few real decisions work that way. Apartments get re-listed. People stay reachable. Jobs reopen. The rule's discipline (commit and never look back) solves a problem most of us don't actually have.
The formula takes N as given. In practice you don't know how many apartments you'll tour, how many candidates you'll meet, how many years you have left. The 37% of what? The rule degrades gracefully under uncertainty, but it degrades.
The theorem assumes a total order on candidates: any two can be compared, and the comparison is reliable. Real preferences are noisy, multi-dimensional, and revised in hindsight. The number you thought was a 9 at 25 can look like a 6 at 40, and vice versa.
37% maximizes the probability of picking the single best option. It makes no promise about the expected quality of your pick, and those are different problems with different answers. If a very-good outcome is nearly as good as the best, the optimal strategy shifts. Most lives are graded on expected quality, not on whether you caught the global maximum.
The win rate is 36.8%. Which means roughly two-thirds of the time, you don't get the best, and a meaningful fraction of the time, you walk away with nothing at all. The math treats those outcomes as uniformly "a loss." People don't.
The rule is still the best answer to the question it was asked. The quiet move is learning which questions it was asked, and which ones it wasn't.
Mathematics has a habit of finding the same profound truth from completely different directions.