The Secretary Problem

The problem
100 candidates · random order · hire on the spot#1#100no callbacks

You're hiring for one role. 100 candidates apply. You interview them one at a time, in random order. After each interview you must decide: hire now, or pass forever — no callbacks.

What strategy maximizes your chance of picking the actual best candidate?

Tempting (but wrong)
common guesses50%?2/3?none of these is optimal

The intuitive answers tend to be:

  • "Sample half, then hire anyone better than what you've seen."
  • "Sample two-thirds."
  • "Just hire the first one who feels exceptional."

These all feel reasonable. None of them are optimal. The math points to a single, specific number — and it's not 50%.