The Secretary Problem Says Men Should Lock In a Partner by 24.3
Let's start with the conclusion: elders who urge you to marry can never explain clearly why you should do it before 25. I'll do the math for them.
Set the window for "a guy seriously considering relationships" roughly at ages 18–35, a total of 17 years.
Apply the optimal solution to the "secretary problem," proposed by mathematician Merrill Flood in 1960 — colloquially known as the 37% rule — you should spend the first 37% of the time only observing, not choosing, and remember the best candidate you encounter during that period. Then, starting from the 37% mark, the moment you meet someone better than everyone before, commit immediately.
Observation period = 17 × 0.37 ≈ 6.3 years
Inflection point = 18 + 6.3 ≈ 24.3 years old
In other words:
- Before 24: In the sample-collecting, standard-building phase. No matter how good someone is, you shouldn't lock in.
- After 24.3: Enter the decision window. When you meet someone who surpasses everyone from the past 6 years, commit immediately.
- If you're still looking for someone better at 30: You'll likely be forced to accept the last person who appears — the "last straw" within the window.
The phrase "find a partner before 25" translates to: by 25, you should have finished observing and started choosing seriously.
How math nails down the number 25
To make this credible, I did both the calculations and simulations. All data comes from an interactive simulator I wrote:
🔗 https://numfeel.996.ninja/pages/optimal-stopping/ (You can open it and run it yourself)
Step 1: Plug N=17 into the formula
The formula for the optimal number to skip in the secretary problem:
I calculated it directly using theoreticalOptimalR(17) in the demo:
| Parameter | Value |
|---|---|
| N (window years) | 17 |
| Optimal skip r | 6 years |
| Proportion | 35.3% (close to the theoretical 1/e ≈ 36.8%) |
| Corresponding age inflection point | 18 + 6 = 24 years old |
| Theoretical probability of picking the "best" | 38.73% |
Note the third row. N is a discrete integer, so the result of 35.3% is slightly smaller than 36.8%, and the corresponding inflection point lands exactly on 24 — this is the mathematical version of the "before 25" saying on Zhihu/Weibo. If you're willing to extend the window to 18–36 (17→18 years), the inflection point pushes precisely to 24.6 years. No matter how you tweak it, it stays around the magnitude of 25.
Step 2: Run twenty thousand simulations to see the real success rate
Formulas aren't enough. I used Tab 2 of the simulator to run N=20, twenty thousand Monte Carlo trials.
Results:
| Strategy | Probability of picking the best |
|---|---|
| 37% rule | 38.52% |
| Pick one randomly | 5.15% |
| Pick the first one immediately | 5.04% |
| Wait until the end and forced to pick | 5.12% |
The 37% rule's hit rate is about 7.5 times that of the other three "winging it" strategies.
If you think N=20 is too many, pull N down to 10 (only seriously considering 10 people in a lifetime), the results are equally valid:
| Strategy (N=10, 20000 trials) | Success Rate |
|---|---|
| 37% rule | 40.16% |
| Random pick | 9.78% |
| Pick the first | 9.93% |
| Wait until the end | 9.84% |
Note that when N=10, the observation period r=4, and the inflection point is also at 18+(4⁄10)×17 ≈ 24.8 years old, still between 24–25.
Step 3: Use parameter scanning to verify that the "24–25 years old" line is no coincidence
Tab 3 of the simulator scans the skip ratio from 0% to 100% and draws a success rate curve.
I ran a scan with N=17, 5000 trials per point, and extracted key ratios:
| Skip Ratio | Measured Success Rate |
|---|---|
| 0% (pick immediately) | 5.8% |
| 10% | 28.0% |
| 20% | 32.5% |
| 30% | 36.5% |
| 36% (theoretical optimum) | 39.1% |
| 40% | 38.5% |
| 50% | 35.4% |
| 60% | 32.4% |
| 80% | 16.4% |
The peak falls precisely in the 36–42% interval, and the curve collapses quickly at both ends. Skip too little, and you haven't even established a baseline — your standard is just a wild guess. Skip too much, and the best one has already passed; you can only pick from the leftovers.
Compare this curve with "24–25 years old": starting from 18, 36% corresponds to 24.1 years, 40% to 24.8 years. The plateau around the peak of the curve exactly covers the "mid-twenties" everyone talks about.
Why 1/e, not 1/2?
Many people's first reaction is "just look at half and then choose." The problem is, I ran the 50% case too — the success rate drops to 35.4%.
If the observation period is too short, the baseline is too low, and you easily mistake "the 7th best person" for "the best overall." If the observation period is too long, the "best overall" likely already appeared during your observation phase, and you'll never meet anyone better afterward, forcing you to default to the last one — the trash can. Comparing this to reality, it's painfully accurate.
The 1/e line equalizes the risks on both sides. The optimal strategy this model ultimately gives is just this one — telling you the best switching point between information gathering and action.
But! Here comes the "but," reality check: Which assumptions will make "24.3 years old" drift?
Ideals are full, reality is bare.
Candidates don't appear uniformly. The overall quality distribution of the campus pool and the workplace pool is completely different. Changing environments itself changes N and your sample distribution — this is why some people meet the right one at 22, while others are still waiting at 32.
"No going back" is a hard assumption. In reality, exes can get back together, and people you skipped might still be waiting. So the 24.3-year-old line isn't a hard deadline. But it tells you one thing: the longer you drag it out, the lower your chance of going back.
Is the goal the "best" or "good enough"? Economist Herbert Simon proposed satisficing. If you accept an 80-point person instead of a 100-point one, the optimal observation period shortens — you should probably start deciding around 22. So people who "would rather go without than settle" actually need to wait until 24–25. The higher your standards, the more time you need to leave for the observation period.
N is your guess. No one knows how many people they'll seriously consider in a lifetime. But as long as N falls within a reasonable range of 5–30, the skip ratio hovers between 33%–40%, and the inflection point is locked between 23–25 years old. This interval is uncomfortably rigid.
If you're currently under 24?
Then you can evaluate using the following methods:
- Truly build your scoring dimensions. Looks, height, income are surface features. What really determines long-term compatibility is "after spending a year with this person, did I become better or worse?" This requires time samples.
- Broaden sample diversity. A homogeneous pool distorts your baseline. Date in school, in clubs, through friends, and after starting work — each relationship calibrates your ruler.
- Seriously review. For every person you dated for more than 3 months, write down afterward "what they taught me" and "what I can't accept." This is your training data before the 24-year-old dividing line.
After 24.3, the rules change:
- When you see someone who makes you feel "more right than anyone in the past few years" — stop dragging your feet.
- "Let's see if there's someone better" is the most classic failure mode in this model. The simulator tells you that the later you wait, the lower the probability of meeting someone better than your current best, and you'll likely be forced to pick the last one at the end.
The probability of a naive, rich, beautiful girl falling for a poor boy, or a Saudi Arabian prince falling for a poor girl working as a cleaner, is extremely low in reality.
Finally, come play with the demo yourself to see how effective this law really is
I added a "mate selection scenario" switch that can toggle to "view women / view men" mode. Candidates display as 12 styles of cartoon avatars + a "heartthrob index," making the experience closer to a real dating scenario. But the underlying algorithm and math are the same set — a different skin on the same bones, because while players might lie, math doesn't.
🔗 https://numfeel.996.ninja/pages/optimal-stopping
Top 1 from juejin.cn, machine-translated. The original thread is authoritative.
e is everywhere [onlooker eating melon]