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February 14, 2022

How Many Frogs You Should Kiss

A mathematical guide to finding true love – or to consolation after horrendous dates.

How Many Frogs You Should Kiss

Love may be irrational, even illogical at times, but finding it does not have to be. Whether you are a scientist or not, mathematics comes to romantic rescue: Following a simple algorithm spares you not only endless and awkward dating but also gives you the highest chance of finding Miss or Mister Perfect.

At Valentine’s Day, this mysterious thing called love is omnipresent, so why not tackle the struggling search for the notorious One with something else that is everywhere to be found? Yes, Mathematics. “When it comes to the mathematics of decision making, game theory is the field of choice,” confirms Laura Schmid, investigating it at the Institute of Science and Technology Austria (ISTA). “It is also concerned with finding strategies that maximize the player’s benefit, even in environments where people can have differing preferences.” In fact, one may not only solve the marriage problem but most of the essential life questions with this piece of statistical thinking, whether it is buying the ideal apartment, getting the optimal job, or simply finding the best second-hand bicycle.

The obstacles of kissing the right frog

In dating, you lack complete knowledge of the existing options. You never know whether your McDreamy is still somewhere out there waiting to be found; or worse that you have already met and dumped them hoping for someone better. What complicates matters further, you date consecutively and must decide instantly, whether to opt for the present candidate or advance to the next one.

It is unlikely that you meet the perfect match at the very first rendezvous of your life. But it is also quite likely that waiting forever could lead to despair. Then, you are running out of options and time. Instead of staying alone, you may feel obliged to pick no – matter how ugly the frog. Therefore, knowing when to commit is the golden key of dating – and mathematics is handing it to you.

How to find your prince:ss

This strategy, laid out by Neil Beardon in 2006, is deduced from optimal stopping theory and goes as follows:

  • Step 1: Set the number of people n that you can date in your life.
  • Step 2: Take the square root of it, √n. (If necessary, buy a calculator between Step 1 and 2.)
  • Step 3: Date √n people and reject all of them, no matter their charms or wits. The best candidate will henceforth set the benchmark.
  • Step 4: Continue dating and settle with the first person to exceed this benchmark.
  • Happy End – or not?

The chances of success

Let´s say you want to settle in the next two years. You are therefore (eagerly) dating one person every week, resulting in n = 100. After two and a half months you have met the first ten people, rejected all of them – some gladly, some sadly. You developed an intuition for the pool of people out there. Assuming one could straightforwardly rank them, the best candidate sets your future threshold. By committing to the next person better than this, regardless of whether it is date number eleven or one hundred, you will on average find someone ranking in the top ten, meaning someone 90 percent perfect.

With an initial n as low as n = 10, you obviously have to date less, but on average you will only end up with a 75 percent perfect match. Of course, a possibility always remains that you end up finding no one – which you can hardly avoid when being as niggling (you call it “demanding”) as you are. But what if you are an outright perfectionist and you are solely happy with the ultimate best?

Love perfection

The question goes back to the “The Secretary Problem”. British statistician Dennis Lindley proved in 1961 that finding the perfect secretary for the job involved interviewing not √n, but 1⁄e = 0.37 of the candidates, with e = 2.718… being Euler’s number. This 37-percent-method is the best approach, if and only if you consider it a success to get the best person and deem it failure picking anyone slightly inferior. The chances of you finding this one optimal match lies closely below 40 percent, meaning that 6 out of 10 people following the strategy will end up being miserable.

“In real life, though, people can have hidden motives or personal beliefs that do not correspond with the ‘average’, and situations cannot always be framed exactly with models,” adds game theoretician Schmid, who knows the boundaries of her theoretical field. “Human decision making is complex, and many mathematical models are abstract simplifications that leave particular quirks of human psychology out of the equation.”

Now, before you start gaming through all available dating apps to quickly reject your first 37 percent, let`s estimate what a realistic value of n is in the first place.

How many are there?

It may surprise you, this question puzzled astronomers. Potentially, how many alien species are there in the Milky Way? Instead of making one wild guess, Frank Drake employed many little educated assumptions on the possibility of life that – added together – became the notorious Drake Equation. Let´s apply the same approach to potential dating partners.

As a local, you are fishing in the pool of 1.9 million people in Vienna, of which roughly 50 percent are your preferred gender. Since you do not know TikTok but still have your own teeth, the group 8 years above and below your age reduces the whole pool to one in four. Be it paycheck or intellectual profundity, you may search for someone with higher education, limiting the number to another fourth – of which only 80 percent are vaccinated, which could be another of your conditions, leaving you with 47.500 individuals. From your experience, only 1 in 25 of your peer group is smoking hot – at least to your eyes and that counts. Yet, you need a single (40 percent), which leaves you at the end with a somewhat relieving and yet intimidating number of 760 candidates. No need to fear rejection, use the algorithm and start dating!

Further reading

Peter Backus (2010): Why I don´t have a girlfriend.

Matt Parker (2014): Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More.

Hannah Fry (2015): The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation (TED Books)


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