The Problem
You’ve just been through a tough breakup and are ready to start dating again. Over the next year, you’ll meet 100 potential romantic partners one by one. After meeting each person, you must immediately decide whether to commit to them or move on forever. Once you pass on someone, you can never go back to them.
You want to maximize your chances of finding your best match. How should you approach this decision problem? Is there an optimal strategy that balances exploration (meeting enough people to understand your options) with commitment (not waiting too long and missing out on great partners)?
This is a classic mathematical challenge known as “The Secretary Problem” or “The Optimal Stopping Problem,” reimagined for the dating world.
Second-Chance Romance Strategy Simulator
Not started (0/100 candidates)
Click “Start Simulation” to begin your dating journey!
Simulation Complete
Statistics
Total Candidates: 100
Candidates Seen: 0
Current Candidate Rank: –
Best Candidate So Far: –
Chosen Candidate Rank: Not chosen yet
Mathematical Solution
The optimal strategy, mathematically proven, is surprisingly simple:
- Observe phase: Reject the first 37% of candidates (about 37 out of 100)
- Selection phase: Choose the first candidate who is better than everyone you’ve seen so far
This 37% rule (sometimes called the 1/e rule, where e is Euler’s number) balances the risk of rejecting the best match early against the risk of waiting too long and ending up with someone suboptimal.
Why does this work? The observation phase helps you establish a “baseline” of what’s available. Then in the selection phase, you have enough information to make better decisions while still having plenty of candidates left.
The probability of success (finding the absolute best match) with this strategy approaches 1/e ≈ 37% as the number of candidates approaches infinity. While this might seem low, it’s mathematically proven to be the best possible strategy for this constraint.
Discussion Questions
- How would your strategy change if you could go back to previously rejected candidates, but each time you reject someone, there’s a 10% chance they become unavailable?
- What if the quality of candidates isn’t randomly distributed, but follows patterns (like better candidates appearing in certain social circles or seasons)?
- In real life, we assess potential partners on multiple dimensions, not just a single score. How would you adapt the secretary problem to handle multiple attributes?
I’ll reveal the best reader solutions next week. Good luck with your dating strategy!
