secretary problem
when should you stop looking?
You're hiring. N candidates arrive in random order. After each interview, you must hire or pass — no callbacks. The optimal strategy: reject the first 37%, then hire the next candidate who's better than everyone you've seen.
optimal threshold = N/e ≈ 37% P(best) ≈ 1/e ≈ 36.8%
This is the optimal stopping problem. The 1/e rule maximizes your chance of picking the single best candidate. Play the game below, then run the simulation to see the peak at 37%.
references
Ferguson. "Who solved the secretary problem?" Statistical Science, 1989.
Bearden. "A new secretary problem with rank-based selection." Journal of Mathematical Psychology, 2006.
monte carlo simulation
For each rejection threshold (0%–100%), simulate thousands of hiring rounds. The peak reveals the optimal stopping point.