Something interesting happened when Tinder took away my unlimited free right swipes. For those of you who may have been living under a rock, Tinder is a dating app that matches people if they both agree the other one is attractive (by swiping right instead of left). It’s a fairly simple coordination game, which makes it fun if you’re just getting into game theory (like me).

Times are tough for your frugal Tinder user. It used to be that Tinder allowed you to swipe right for as many people as you wanted, until you developed arthritis in your thumb and your doctor told you to stop Tindering. Now, with a limited number of swipes, we have a decision to make: should I swipe right and potentially waste one of my precious swipes? Should I swipe left, saving my right swipe for another potential match? Should I just pay the $14.99 a month so I don’t have to think about this anymore? Let’s analyze this decision in further detail, using a little bit of game theory.

Game Theory refers to the mathematical theory behind decision making. To apply game theory to Tinder we should learn about normal form games and how they’re used. What normal form represents, is the possible decisions that two parties have, and their corresponding payouts. The following table is an example of Tinder in normal form. The payouts are the numerical values in the table. The girl’s payouts are the first of the pair of numbers in each cell, and the boys are the right. The boy’s decisions are the columns of the table, and the girl’s are the rows. So, for example, if the boy swipes left we look at the left column. If the girl swipes right we look at the payouts in the bottom row. So if the boy swipes left and the girl swipes right, the payouts will be in the bottom, left cell. The payouts are determined as follows: If both parties swipe left, neither of them lose a swipe, but they also don’t match. Nothing really happens, and we move on with our lives. The payouts in this case are both 0. If the girl swipes right, and the boy swipes right, it’s match! We’re both a little happier that it appears someone finds us attractive, and this is represented by a payout of 10 for each person. Now, if the girl swipes right, and the boy swipes left, she loses a precious swipe, and the boy can go on with all of his swipes to greener pastures. The payout for the girl, in this case is -1, and 0 for the boy. If the boy swipes right and the girl swipes left, he loses a swipe (payout of -1) and she doesn’t (payout of 0). All of this can be seen on the chart below, in the payoff matrix.

BOY LEFT RIGHT GIRL LEFT 0,0 0,-1 RIGHT -1,0 10,10

What does this tell us about how to Tinder? Let’s put ourselves in the boy’s perspective. If he assumes the girl will swipe left, the obvious choice is to also swipe left, so he doesn’t lose a swipe. If he assumes the girl will swipe right, the obvious choice is to also swipe right, and create a match. The same is true for the girl, she should choose to swipe the same direction as the boy. It’s obvious that both parties should either both swipe right and match, or both swipe left and not lose a future swipe. This produces two Nash equilibria, which are highlighted in green in the payoff matrix.

(Disclaimer: The following isn’t meant to be offensive at all, and hopefully won’t be. I’m just trying to have a little fun with some math.)

Now, all of this so far hasn’t taken into account what really makes Tinder interesting. It’s nice to think of this in a perfect world, where everyone finds everyone else attractive, and knows that everyone finds them attractive. The fact is, it’s not just a blind guess as to what the other party will do, and we won’t base our decision only on what we think they might do. Normally, in game theory, we say that each individual will base their decision only on the rules of the game, and assume that the other person will do the same. With Tinder, we need to take into account how attractive the other person is, and how much a match with them is worth.

Let’s say I’m on Tinder, and an extremely attractive person comes up. Way out of my league; I wouldn’t even bother in real life due to my overwhelming fear of rejection. I obviously want to match this person, and would love the opportunity to talk to her and possibly take her out. The obvious choice it to swipe right! Right? Let’s start to make some assumptions on how she will swipe. We can assume that whatever makes her attractive to me, also makes her attractive to others in the area, and that every other person who has come across this extremely attractive girl will swipe right, excited for the potential to match. That makes her potential to swipe right on me much lower, because she can afford to be picky on who she matches with. Conversely, if I come across someone not quite as attractive, the likelihood is higher that she will swipe right for me. There seems to be an inverse relationship between attractiveness and the probability that they will swipe right. The more attractive they are, the less likely they’ll swipe right for me. The less attractive, the more likely.

The next question we should ask ourselves is: what is the true payout of a match, to us? Obviously, a match with a more attractive person is worth more than one with a less attractive person. Let’s use these assumptions to make an informed swipe on Tinder. The first thing we need to do is make an estimation of the probability that the user we’re viewing will swipe right. Let’s just say that the user we’re looking at is fairly attractive, and will have a 5% probability of swiping right for us. Now, this means that the utility of a match will be relatively high compared to a user with a higher probability of swiping right, because they’re more attractive. How are we going to measure this utility? Well, we need to compare it to the negative utility of losing a swipe, because that’s what we’re gambling here. If we say a swipe has a utility of 1, we can say that our potential match is maybe worth 30 swipes to us. So, the utility of a match in this case is 30. Take the probability of the other user swiping right and creating a match (P(M) = 0.05) and multiply it by the utility of the match (U M = 30). This gives us the utility of a match weighted with it’s probability. Now, to figure out the total utility of swiping right, we need to subtract the probability that the other user swipes left, and we lose a swipe. We’ll call this P(L) for probability that we lose a swipe. P(L) will be equal to (1-P(M)), or the chances the other user swipes left. If we multiply this by the utility of a swipe (which we’ve defined as 1), we get the weighted utility of losing a swipe. When we subtract that from the utility of a match, we get the total utility of swiping right.

U R = [P(M)*U M ] - [P(L) * U S ] U R = [0.05 * 30] - [(1-(0.05)) * 1] = 0.55 U R = Utility of swiping right P(M) = Probability of a match (Other user swipes right) P(L) = (1-P(M)) = Probability of losing a swipe (Other user swipes left) U M = Utility of a match U S = Utility of a swipe

Now, let’s compare this to the utility of swiping left. If we swipe left, we know there is a 0 probability of a match. (P(M) = 0). We also won’t lose a swipe, so the probability of losing that swipe is 0. That means our utility of swiping left is effectively 0.

U L = [P(M)*U M ] - [P(L) * U S ] U L = [0 * 30] - [0 * 1] = 0

In this example, we can see that swiping right is the better option, because it’s utility is higher. If The utility of swiping right is greater than the utility of swiping left (or if it’s positive, since the utility of swiping left will always be 0), then swipe right. Let’s look at an example where one would swipe left.

Let’s say a Tinderer estimates another user’s probability of swiping right at 15%. However, maybe they’re not very interesting. Something about the user’s profile doesn’t sit well with you. So the utility of a match would only be worth, let’s say, 5 swipes. So, the utility for swiping right for us would be:

U R = [P(M)*U M ] - [P(L) * U S ] U R = [0.15 * 5] - [0.85 * 1] = -.10

In this case, the utility of swiping left is higher (0 > -.10), so the user should swipe left.

What can we observe through all of this? For one, swiping right is almost always better than swiping left. Why is this? Well, matches are usually worth much more than future swipes are. Even if you exhaust your limited supply of swipes, you get a whole new set in 12 hours. A match, even if you’re not really excited about someone, is full of potential, and definitely boosts self confidence, knowing someone finds you attractive. So even if you think that the probability is fairly low that someone will match you, the relative utility of getting that match is much greater than the utility of simply holding onto a swipe. So go out there and swipe right!

Now, this is an oversimplification in many ways. First of all, we really don’t have a good basis of judging which way the other Tinder user will swipe. Basing this off of how attractive they are is probably the best we can do to offer some insight into how we should play the game, but it’s obviously not a very good way of estimating this. Also, it’s hard to base how much a match is worth in units of future swipes. That seems like a silly way to think about how excited you are about being matched with someone. However, it’s easy to see that the vast majority of matches are going to be much more valuable than holding onto a swipe. In reality, you really shouldn’t bust out your calculator while Tindering. This analysis shouldn’t be taken too seriously, it was really just a shallow dive into game theory and decision making.

TL;DR: Unless you value matches very low, or really hate to give up swipes, you should almost always swipe right!

Questions, comments? Did I get something wrong? Email me: kdr213@gmail.com