The 37% Stopping Rule

👨‍🔬 E. Regnath · 📆 Jun. 2023 · 🧪 v-0.2

How to choose wisely if you know little: Observe 25%–37% of options, then select the next best.

The optimal strategy for selecting the best car, phone, or romantic partner is easy to follow and proven by math – yet known by few. If $N$ is the number of options, $T$ the maximum time to decide, and $P$ the probability that you get the option if you select it, we can derive the optimal strategies that are shown in the following table.

Condition	Problem	Strategy
Known $N,P=1$	Interviews	Observe 37% of $N$, choose next best
Known $T,P=1$	Purchasing	Observe 37% of $T$, choose next best
Known $T,P=0.5$	Marriage	Observe 25% of $T$, choose next best

• Known $N$ and $P=1$: This is called the secretary problem in which you interview $N$ applicants for a secretary position and need to decide to reject or accept each applicant directly after the interview. $P=1$ means that an applicant will take the job if you make an offer. The optimal strategy to maximize the chance for selecting the best candidate
• Known $T$ and $P=1$: If the number of options is unknown, we can apply the same rule to the timeframe we have: Observe options (as they come in) for 37% of the time, then select.

Good Choice Variant:

If the goal is to maximize the chance for a good selection instead of the chance of hitting the best choice, a shorter observation ratio of 25% is better.

📚 References

• Algorithms to Live By: The Computer Science of Human Decisions, 2017
• Up and Atom: “When to Quit”, YouTube