Secretary Problem, explained.
The secretary problem is an optimal stopping problem: when should you stop searching and accept an option if rejected options cannot be recalled?
Why it happens
An observation period gives you a benchmark, but waiting consumes opportunities. With randomly ordered candidates and a goal of choosing the single best, an effective rule is to observe first, then accept the next candidate who beats everything observed.
A stopping rule trades learning about the field against the risk of letting the best option go.
Read the result
Compare different observation periods over many runs. A successful hire in one round does not establish a better policy; compare the frequency of finding the best candidate under the same rules.
A worked example
A search with no second chances
You must choose from 20 candidates interviewed in random order, and cannot return to anyone rejected.
Observe the first seven without hiring. Then accept the first later candidate who beats your previous benchmark.
You exchange some missed early opportunities for a more informed stopping rule. Sometimes the best candidate was in the observation group.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Twenty candidate qualities are shuffled without replacement. Observe the first skip candidates, then accept the first later candidate better than all observed; if none appears, accept the last. The plotted exact success rate enumerates each possible location of the best candidate and the best earlier rank.
Where this idea is useful
A practical use
Interviewing applicants one by one when rejected applicants cannot be recalled.
A common misconception
“Always reject exactly 37% of real opportunities.”
The familiar approximate rule depends on random order, a known horizon, no recall, and a very specific objective. Real hiring rarely satisfies all four.
What this explanation leaves out
- The classic rule assumes random order, independent rankings and no recall; real hiring seldom does.
What changes if I can return to earlier options?
Recall changes the cost of waiting and therefore the stopping problem. The benchmark policy here is designed for irreversible rejection.
What would make further searching worth more than accepting the best option available now?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.