What's the best way to find the ideal partner? Use the optimal stopping strategy to significantly increase your chances of doing it right!🧐
Number of dates
I want to find ideal partner in
yrs
I'll go on
dates a
mo
Max number of dates
We assume that each date is with a different person.
The optimal stopping problem
First, you'll need to reject a given number of potential partners. It doesn't matter how wonderful they are, reject them all. Then continue meeting with other people, and the first person that is better than all previously rejected people is the one for you. See the text for an example!
I want
the best partner
Rejection chance
0%

In this era of the Internet, meeting new people is much easier than before, but paradoxically, finding the proper partner is still a challenge. How do you know that the person sitting across from you at dinner is right for you? It can be tough to know for certain, but you can remarkably increase your chances of finding your ideal companion using... math.

Romantic, we know.

Mathematicians developed a theory called the optimal stopping rule, the primary purpose of which is to find the most effective strategy of maximizing an expected payoff. In our dating theory calculator, we use it to finally solve (or at least help to solve) the eternal problem of finding the right lifetime partner. What's more, we further improved it to make it more realistic and practical. Take some time to explore it in detail, and find out why love is often called a numbers game!

Maths and love on one picture

What is the optimal stopping problem?

The optimal stopping problem has many different names: the secretary problem, the sultan's dowry problem, the 37 percent rule, or the googol game... The essence of all of them is the same: find the best option from sequentially observed random variables. Sounds complicated? It's not that bad if we explain it with an example!

To stick to this calculator's topic, we'll think about choosing the ideal partner. Let's say that during your lifetime you will meet ten people that you could really love and live with. Which one should you pick? Obviously, the best one! The problem is that you cannot gather them all in a room at once, so you can find which one is right for you. Instead, you will date them one by one, in a random order, with less suitable partners thrown in. You don't know whether the person you're currently dating is your soulmate. Maybe the next one will be a much more suitable choice for you? Besides, more often than not, you cannot go back to rejected partners. So, herein lies the problem. Choose too early, and you might not even meet the perfect one - wait too long, and you will have already rejected Mr or Mrs Right.

Ten candidates to choose

So, how to find the love of your life? Well, this is where math and probability become truly helpful, even if on the surface it seems like it's all about luck. It turns out that the best strategy is, out of the total number of potential dates you will go on, to reject the first 37% of them (precisely 1/e ≈ 36.79%, where e is the base of the natural logarithm). Of our ten people, we will need to reject the first four. It doesn't matter how good they seemed, reject them. The next step is to pick the next person who is better than anyone you've ever met before. Following these instructions will give you the highest chance of meeting the very best suitor possible. In our example, the probability of choosing the best person increases to about 40%, from only 10% if you were to select randomly. Check it by yourself with our calculator!

Reject 4 candidates and take the next best one

Dating theory calculator

The optimal stopping theory doesn't just give you one number, after which you will find the right person for you. It also gives many more valuable pieces of information that you can use to find the perfect partner. This is why we created the dating theory calculator, which takes care of all the exhaustive estimations. It is based mostly on the standard optimal stopping theory, but we also included some extensions to make the calculator more handy for real-life cases. How does it work? It's straightforward! All you need to do is to follow these steps:

  1. Estimate how many dates you might have, or aim to have, during a time period.

  2. Select which extensions of the optimal stopping theory you would like to include. You can:

  3. Check the results!

    • read what your current probability is of finding the right partner, and what the risk is of remaining alone.
    • look at the first graph - the x-axis is the number of rejected candidates. The blue points show the probability of finding a candidate that fulfills your requirements, and the yellow points are the chances that you will find any partner. The optimal stopping policy may not be suitable if the latter chances are too low. Maximizing probabilities is a vital point.
    • even if you aim for the best partner, you may end up with a slightly worse option. Turn on the advanced mode, and enter how many partners are you ready to reject first. This will show you a new graph, which shows the probability of you being with each of your top 10.

That's it! Try different combinations to find the strategy that suits you most.

Remember that math can't take into account every possible factor, for example, human emotions. As the mathematician, Bobby Seagull, said 'it should be a guidance'.

People stop searching too soon

The optimal stopping problem isn't just pure mathematics. Experimental psychologists, J. Neil Bearden and Amnon Rapoport, have studied the decision behavior of actual people in their publication in Operations Research in Experimental Psychology. Each tested person (subject) had to hire one (virtual) applicant for a position where there were 40 or 80 other candidates. The subjects could either choose the current applicant, or proceed to the next one just as in optimal stopping problem. Once the best overall candidate was selected, a subject was awarded either $0.30 or $0.50. Psychologists repeated this experiment 100 times on each tested person, so the total possible payoff was relatively high. What do you think? Did subjects follow the optimal policy?

Well, Bearden and Rapoport analyzed the results and demonstrated that people tend to stop earlier than it is predicted by optimal stopping strategy. The propensity to stop too soon suggests that we don't search enough when we are faced with problems where we encounter options sequentially.

There are many problems of this kind in the real world. For example, drivers must decide which gas station along a highway they should choose to stop at for gas. According to the above research, they might pay more than if they had searched for a longer time. Another example is selling a house. You don't know the value of the offers before they come. With each offer, you must decide whether you accept or reject it. How long should you wait for the best deal?

Love is numbers game - the risks of optimal strategy

Sadly, the optimal stopping strategy doesn't have a 100 percent success rate. As explained by the mathematician Hannah Fry, the author of The Mathematics of Love, during a Ted talk, there are some unfortunate scenarios that you may end up in.

Imagine the perfect partner is one of the first persons you date. If you follow the optimal stopping policy, you'll reject that person. Then, you'll continue to meet other people, but no one will be as good as your ideal candidate. So, unfortunately, you'll have to go on, reject everyone else and end up being forever alone (or surrounded by cats 😺).

Becoming alone forever in optimal stopping problem

Another scenario is that you start your dating life with some really terrible partners. If that's so, your expectation will be super low, and you'll marry the very first person that is marginally less boring than all of the previous losers you've met. And what about all these wonderful candidates waiting just around the corner? Such a loss...

Accepting one of the worst candidates in optimal stopping problem

Finding the right partner is a little bit like Russian roulette, and even with the use of the optimal stopping theory, sometimes things can go wrong. Yet, keep in mind that this strategy is better then any other one you could follow. Ana Swason from The Washington Post explains simply, having you choose the best out of three potential partners. She showed that the probability of finding the right one is 20% higher when using the optimal stopping strategy, and it increases even more when considering more candidates!

Dating is a numbers game for a reason. Whenever you meet someone new and go on a date, you're automatically adding to your knowledge of what you want most in a person. You should start dating to find out what are your actual expectations, and this will increase your chances of choosing the ideal person for you. Happy hunting!

Dominik Czernia, PhD candidate

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