science of us

# I’m Plagued by This Decades-Old Dating Equation

Photo: Courtesy of HBO

Toward the end of this horrifying and fun episode of the Gimlet podcast Science Vs, in which the host and an array of experts use math to solve love by way of online dating, there’s this fascinating bit about something called the Optimal Stopping Theory. [Editor’s Note: Gimlet also produces the Cut’s podcast.]

As host Wendy Zukerman explains, the OST is useful for “hiring someone, picking apartments, and, yes, even picking your person.”

This theory is, according to American Scientist, “a simple rule that will guarantee you will marry the absolute best [person] more than one-third of the time.”

Okay, go on.

According to the show’s mathematician guest Hannah Fry, this “special number works out to be about 37 percent.” (Fry also wrote a book on the topic.) That is, you should “stop” when you’re 37 percent of the way through with something — whether that’s hiring an assistant, looking for an apartment, or whiling away fertile years — and commit to the next option you come across that’s better than all the ones you’ve already seen. Doing this will apparently give you the highest odds (also 37 percent) of ending up with the “best” option available.

This led me on a rabbit hunt through the internet to understand where that number (the 37 percent) came from. Mathematician Matt Parker’s summary, in this Slate excerpt from his book Things to Make and Do in the Fourth Dimension, is my favorite: 37 percent is the result of 1/e, where e is the special exponential number and fundamental mathematical constant 2.718281828 […], which was discovered in 1683 by mathematician Jacob Bernoulli and is, in Parker’s words, “linked to estimating where the best candidate could be in [a] queue.” (It is also, per Wikipedia, “of eminent importance in mathematics, alongside 0, 1, π and i.”). This is also where the concept of e started to go a little over my head and I stopped Googling.

I did enjoy this simplified example of the setup, though, which is also called the Secretary Problem, from Scientific American in 1960:

Ask someone to take as many slips of paper as he pleases, and on each slip write a different positive number. The numbers may range from small fractions of 1 to a number the size of a googol (1 followed by a hundred 0s) or even larger. These slips are turned face down and shuffled over the top of a table. One at a time you turn the slips face up. The aim is to stop turning when you come to the number that you guess to be the largest of the series. You cannot go back and pick a previously turned slip. If you turn over all the slips, then of course you must pick the last one turned.

Back to dating.

To demonstrate this Optimal Stopping Theory, the Science Vs team lays out an example: If a 15-year-old would like to be married by age 35, she would therefore have 20 years of dating ahead of her. If she applied the Optimal Stopping Theory to this number (20), at 37 percent of the way through — or, at age 22 — she should settle down with the next guy she meets who’s better than all the other guys she’s already dated. (Or a 25-year-old in a new dating scene might want to shift gears at 28.7, in preparation for the gates to come down at 35.)

This all presumes that the other person would also want to marry you, too, which seems like a fairly large hole in the theory. Zukerman and Fry joke about this (it’s a “slight flaw,” Fry says) before revealing that the 37 percent commitment shift is more or less what happened to them in their own relationships:

Zukerman: I caught myself doing some calculations, and without knowing [about] this theory, this [pattern] is actually what I did.

Fry: Is it? Because it’s sort of what I did as well, actually, to be honest with you. I think a lot of us do this quite naturally.

Well, I’m not sure what to do with this newfound knowledge, although I’m glad I don’t drink anymore, because I can see myself trying to explain this theory loudly at parties.

Sort of related to that, but I wonder if this same kind of math could also apply to more specific phases of life, like after getting divorced, moving to a new country, or getting sober. For more application of math to love and dating, see also: the numbers behind having sex with 500 people.

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I’m Plagued by This Decades-Old Dating Equation