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The Maths Behind Dating: Optimal Stopping Theory

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I am a former maths teacher and owner of Doingmaths. I love writing about maths, its applications and fun mathematical facts.

Which Date is the Best?

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How Many Dates Should You Go On Before You Choose?

You've joined a dating site and started going on dates, looking for love and that special person to settle down with. You've had some good dates and some bad dates—but even after the good ones, you might wonder if they are actually the one or if will there be an even better option further down the dating road?

This is where maths can help us find the optimal solution. Surprisingly enough, using something called Optimal Stopping Theory, the maths states that given a set number of dates, you should 'stop' when you're 37% of the way through and then pick the next date who is better than all of the previous ones.

For example, if you have 100 dates lined up, you should work your way through the first 37 of them without committing and then commit to the first date after this who is better than any that came before.

Obviously this could lead to problems if the best possible match was one of the first 37%. In this case you would either have to settle for date number 100 or end up alone, but overall, this tactic gives you the highest chance of ending up with the best option (incidentally, this chance is also 37%). But why is this the case? Let's look at the maths.

Some Assumptions to Make Before We Look More Closely at the Numbers

For all of the scenarios here we will assume that once you have dated a person and then dumped them, there is no going back, even if you decide later on that they were the one. We will also assume that the dates are a good representation of how well the resulting relationship would work i.e. an excellent date means the relationship will be great, while a poor date means the relationship would not work either.

Where Does 37% Come From?

First of all we will start with the small numbers. If you have just one date, then obviously that person will be the best of your dates, hence you are guaranteed to pick the best date.

If you increase this to two dates then you have a 50% chance of picking the right candidate whatever strategy for choosing you decide to use.

If you go on three dates, things start to get interesting. If you randomly pick one person, then the probability that they are the one is 1/3 ≈ 33%. However, suppose we skip the first person and then choose. If date two was better than the first date, stick with person two. If date two was worse than the first date, move onto date three and hope that they are better than both of the previous dates.

Looking at this in a diagram where 1 is the strongest date and 3 is the worst, we can see that are six possible scenarios.

Six Combinations of Three Dates

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In scenarios a and b, we have skipped the best date (in red) and ended up empty-handed. In scenario f we have skipped the worst date, but because this is followed up by the second-best date we end up with them. However, we have ended up with the best date in all three of the remaining scenarios meaning success 3/6 = 50% of the time; an improvement on picking randomly.

By similar logic, it can be seen that ditching the first two dates and sticking with date three if they are better would give you the best option 2/6 ≈ 33% of the time (scenarios d and f).

What About Four Dates?

If you have four dates lined up, there are 24 possible combinations of order of quality of dates. Picking a date at random would give you a 1/4 = 25% chance of picking the best person. If you skipped the first date and picked the next date who was better than person one, you would pick the best choice 11/24 ≈ 46% of the time.

If you ditched the first two dates and then picked the first person better than them, you would be successful 10/24 ≈ 42% of the time and ditching the first three would give you a 25% success rate again. Hence for four dates, ditching person number one and the choosing the next superior date is the best scenario.

More Than Four Dates

This carries on. For five dates, ditching the first two means you end up with the best choice 43% of the time. For six dates, ditching the first two is again the best strategy with a success rate of 43%.

As we keep on increasing the number of dates, the percentage you should ditch at the beginning and the percentage success rate of that strategy both tend towards 37%.

The Mathematical World

So in the perfect mathematical world, there you have it. Once you have a set number of dates lined up, you should work your way through the first 37%, ditching each one as you go, and then settle down with the first date after that who is better than all that came before them. This way you have a 37% chance of ending up with the best option.

The Real World

Obviously, this model has its limits. Date one may be so great that you can't possibly imagine a better match and hence you stop there. An early ditched date may be so good that you never better it and end up without anybody. It may even be that you make your choice using this method, but your choice isn't interested in you.

Despite it's limits however, this method does give you a rough guide if you are mathematically minded and can even be used in other hunts for the best choice, whether that be searching for a new employee, a new car or even a new house.

© 2020 David

Comments

David (author) from West Midlands, England on September 29, 2020:

Thank you. I'm glad you liked it.

Judy Vargas Bongala from Tabaco City, Albay, Philippines on September 29, 2020:

Wow! An artistic way of illustrating probability. Thanks for writing this article.

David (author) from West Midlands, England on September 28, 2020:

Thank you. I'm glad you liked it.

Binoy from Delhi on September 24, 2020:

Interesting article. Jesus Loves You