Options arrive one at a time in random order. You must accept or reject each on the spot — no going back, no recall. You can only judge each candidate relative to those you've already seen, and you want the single best. The answer is the 37% ruleAlso called the secretary problem or the marriage problem. Assumes: random arrival order, no going back once rejected, only relative ranks known, goal is the single best outcome — not 'good enough'.: reject a first batch to learn the field, then take the next one who beats everyone in that batch.
Skipping the first 9 and then taking the next candidate who beats them all gives you a 38.1% chance of landing the single best option. That's the optimal cutoff — you can't do better without knowing the future.
Skip too few and you commit to an early mediocre option before you've learned what "good" means. Skip too many and the best has probably already gone by, leaving no one left who beats your now-too-high bar. The curve peaks at roughly n ÷ e ≈ 9 and is flat near the top — being roughly right barely costs you compared to being exactly right.
| Skip | P(best) |
|---|---|
| 0 | 4% |
| 3 | 27.3% |
| 9n ÷ eyou | 38.1% |
| 13 | 35% |
| 24 | 4% |
The probability curve is shallow near the peak: skipping one or two away from the optimum costs almost nothing. But the tails are steep — commit after seeing zero candidates, or wait until the very last one is your only option, and your odds collapse to 1 in 25. The 37% rule is robust; extremes are not.