18.03.2022

How many frogs should you kiss?

Mathematical advice for finding true love – and coping with terrible dates. Love can be irrational, even illogical, but finding it doesn't have to be. Whether you're a scientist or not, mathematics can save your romantic quest: Follow this simple algorithm and you'll not only save yourself endless and awkward dates, but also have the best chance of finding Miss Perfect or your Prince Charming.

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On Valentine's Day, the mystery of love is ever-present. So why not tackle the arduous search for "true love" with something equally ubiquitous? Exactly, mathematics. "When it comes to decision-making, game theory is the field of choice," confirms Laura Schmid, who studies it at the Institute of Science and Technology Austria (ISTA). "It deals with strategies that maximize a person's utility, even in scenarios where participants have different priorities." In fact, not only the marriage problem, but many essential life questions can be solved with a statistical approach; whether it's buying the ideal apartment, getting the perfect job, or simply finding the best used bicycle.

The Difficulties of Kissing the Right Frog

When looking for a partner, you're groping in the dark: you never know if your McDreamy is still out there somewhere, waiting to be found; or worse, that you've already met him and dumped him in the hope of something better. To make matters worse, you'd have to date one person at a time and decide immediately whether the current date is a good match or not.

It's unlikely you'll find the perfect relationship on your very first date. But it's also possible that waiting forever will lead to unhappiness. Then you'll run out of options and time. Instead of remaining single, you might feel compelled to make a choice, no matter how unattractive the frog is. When to make a decision—this question is the holy grail of dating—and mathematics provides the answer.

How to Find Your Prince Charming

This strategy, introduced by Neil Beardon in 2006, is derived from the theory of optimal stopping and goes as follows:

Step 1: Determine the number n of people you can date in your lifetime.
Step 2: Take the square root of this number, √n. (If necessary, buy a calculator between steps 1 and 2.)
Step 3: Meet √n people and reject them all, no matter how charming or intelligent they are. The best candidate sets your benchmark.
Step 4: Continue dating and marry the first person who exceeds this benchmark.
Happy ending—or not?

The prospects for success

Let's assume you want to settle down within the next two years. So you (eagerly) go on dates with one person every week, which gives n = 100. After two and a half months, you've met the first ten people and rejected them all—some reassured, some regretfully. You've developed a feel for the people out there. Assuming you could create a ranking, the person you've met so far will set your future threshold. If you settle for the next person who's better than your initial threshold, whether that's the eleventh or the hundredth, you'll find, on average, someone who's among the top ten, meaning they're 90 percent perfect.

With an initial n of 10, you'll have to date fewer people, but on average, you'll only find someone who's 75 percent perfect. Of course, there's always the possibility that you won't find anyone in the end—which is almost unavoidable if you're so picky (you call it "demanding"). But what if you're a perfectionist and only settle for the very best?

Expecting perfect love

This question stems from the "secretary problem." In 1961, the British statistician Dennis Lindley demonstrated that to find the perfect person for a job, one needs to interview not √n, but 1/e = 0.37 of the candidates, where e = 2,718… is Euler's number. This 37 percent method is the best approach if you consider only finding the best person a success and falling for someone slightly less suitable a failure. The probability of finding the ideal person in the crowd is just under 40 percent. Six out of ten people who follow this strategy will therefore end up unhappy.

"In real life, people can have hidden motives or personal beliefs that don't exactly match the situation in the 'models,'" adds game theorist Schmid, who is aware of the limitations of her field. "Human decision-making is complex, and many mathematical models are abstract simplifications that ignore the quirks of human psychology."

Before you start tweaking every available dating app to quickly reject your first 37 percent, let's estimate what a realistic value for n is.

The number of potential heartbreakers

Let's say you live in Vienna. You're fishing in a pool of 1.9 million Viennese, of whom about 50 percent are your preferred gender. Since you're unfamiliar with TikTok or Caterina Valente, the group of people of a suitable age (your own age +/- eight years) reduces the entire pool to a quarter. Whether it's salary or intellect, you might prefer academics, which limits the number to another quarter – of whom only 80 percent are vaccinated, which could be another requirement. So, in the end, you're left with 47,500 people. Experience shows that only 1 in 25 is a looker – at least in your eyes, and that's what counts. However, he or she must be single (40 percent).

In the end, you're left with a somewhat reassuring, yet simultaneously intimidating number of 760 candidates. So don't worry about a broken heart; just follow the algorithm, and you can count on love!