When should you stop dating? The 37% rule solved step by step

Problem. You will meet potential partners one at a time over the ages 18 to 35 (17 years), and you can rank each one only against those you have already met. Once you reject someone you cannot go back, and you want the best chance of ending up with the single best partner of all.

Step by step

1. Model this as the secretary problem: candidates arrive in random order, you see each one only once, you must accept or reject on the spot, and you win only if you pick the very best of all.

2. The best strategy has a simple form: reject everyone in an initial phase, then accept the first person who is better than everyone you have seen so far.

3. The ideal length of the rejection phase is a fraction 1/e of the whole search, where e ≈ 2.718. So 1 ÷ 2.718 ≈ 0.37, or about 37%.

4. With this rule, the chance of ending up with the best partner is also about 1/e ≈ 37%. No other strategy does better under these assumptions.

5. Your search lasts from 18 to 35, which is 35 − 18 = 17 years.

6. The rejection phase lasts 0.37 × 17 ≈ 6.3 years.

7. Add this to your starting age: 18 + 6.3 = 24.3, so about age 24.

8. From about 24 on, commit to the first person who is better than everyone you dated before that point.

Answer: Look without committing for the first 37% (1/e) of your dating years, then pick the next person better than all before: 18 + 0.37 × 17 ≈ 24.

This assumes a fixed search window, a random order of partners, no going back, and that you can rank people only relative to those already met, so real life will differ and even the best rule fails about 63% of the time.