Optimal Stopping: The Secretary Problem

You must hire the best candidate from N applicants seen in random order, one at a time. You can only accept or reject immediately — no going back. The 1/e strategy: skip the first ⌊N/e⌋ candidates, then hire the next one better than all previous. This gives a ≈37% chance of finding the absolute best.

Parameters

Win probability:
Expected rank:
Optimal cutoff 1/e·N:
Last result:
P(win) ≈ (r/N)·Σᵢ₌ᵣ^{N-1} 1/i
Maximum at r = ⌊N/e⌋, P → 1/e ≈ 0.368
as N → ∞ (asymptotically optimal)