The Hiring Game
The Paradox
The Rules
- Interview n candidates one at a time
- After each, you must immediately decide
- If you reject, you can never recall them
- Goal: Select the single BEST candidate
The Dilemma
Too eager? You might hire someone good, missing the best who comes later.
Too patient? You might reject the best, settling for a worse candidate.
The magic threshold
Monte Carlo Verification
Optimal (37%)
Random
First One
Why 1/e?
Let P(r) = probability of success when rejecting first r candidates.
P(r) = (r/n) × [1/r + 1/(r+1) + ... + 1/(n-1)]
As n→∞, maximizing P(r) gives r = n/e
And P(n/e) → 1/e ≈ 36.79%
The Beautiful Coincidence
The optimal threshold is 1/e of the candidates.
The success probability is also 1/e.
The same transcendental number appears in both!
Real-World Applications
Dating & Marriage
If you plan to date ~10 people seriously, the 37% rule says: date the first 3-4 without committing, then marry the next person who's better than all of them.
House Hunting
Viewing 20 houses? Look at the first 7 to calibrate your expectations, then make an offer on the first one that beats them all.
Hiring Employees
The original problem! With 100 applicants, interview 37 to set your benchmark, then hire the next standout.
Parking Spots
Looking for parking? Pass the first 37% of spots to learn what's typical, then take the first good one.
Selling Your House
Expecting 20 offers? Use the first 7 to gauge the market, then accept the first offer that beats them all.
When to Stop Searching
Any optimal stopping problem! Whether it's job offers, college choices, or vacation rentals—the 37% rule applies.
The Deeper Insight
The secretary problem reveals that gathering information has value, but so does acting on it. The 37% rule perfectly balances exploration and exploitation.
"Look at 37% of your options, then leap at the first one that exceeds your benchmark."