When to stop searching: the 37% optimal stopping algorithm

In the book "Algorithms to Live By" the authors describe an algorithm they call "optimal stopping". This is a principle that can be applied to everyday situations where we must decide when to stop searching and make a decision.

The idea behind optimal stopping is the so-called 37% rule. According to this rule, you should dedicate the first 37% of their available time or resources to exploring different alternatives without making any decision. This is called the "looking phase". After this period, you should be ready to choose the first alternative that is better than everything seen so far.

This algorithm can be applied to everyday scenarios, for example:

• Apartment hunting: If you have 30 days to find an apartment, you should spend the first 11 days (37% of 30) looking at apartments to establish a baseline. After that, you should be ready to choose the first apartment that is better than those you saw during the first 11 days.
• Job searching: If you're interviewing for a position, you can use the same principle. Reject the first 37% of candidates and then choose the first one who is better than all previous ones.
• Partner selection: If we assume that ages 18-40 is the period when a person searches for a lifelong partner, the optimal age to "stop searching" would be around 26.1 years according to this rule.

However, this algorithm only gives a 37% probability of choosing the best alternative. The method can however be adjusted depending on the situation. If there's a possibility to go back to previous alternatives (e.g. in apartment hunting), the optimal looking phase can be extended to 61% of the time. Or if one is okay with choosing an alternative that is in the top 5%, then you should end the looking phase after 22%, which raises the probability from 37% to 57%.