The 37% Rule

There are many problems where computer scientists employ interesting algorithms to solve them. One such problem which is often seen in real life is the problem of Optimal Stopping.

Also known as The Secretary problem (GFG article on the same- here), say you’re interviewing a group of applicants for a position, how do you maximize the chances of hiring the single best applicant in the pool? (Once a candidate is rejected, they are gone forever and cannot be recalled.)

Interestingly the dating variant of the problem asks how many people should you date before truly finding the one or deciding to settle down with? Tricky question but surprisingly probability has an answer for this- \(\dfrac{1}{e} \) or approximately 37%.

• Let’s say you want to date \( n\) people (idk how you’d do that though)
• First date \( \dfrac{n}{e}\) without commiting to anyone of them, (here e is the base of the natural logarithm)
• And then ask the rest, one by one
• Now select the person outranking the candidates you’ve seen so far
• Thus maximizing the probability of going out with the best person
• Marry that person, ‘cause they are the best match for you (according to probability)

By the way, do check out The 37% Rule verse by Ernest Davis. Man’s got an enitre page of his amazing verses here- Verses for the Information Age (found this awesome piece of literature accidentally)

Won’t be going into details of this thing but you can check out this for a proof, or this paper for a more detailed historical outlook to the problem.