It seems like a preposterous claim at first to state that we can use ideas derived from mathematics to analyze love relationships in a very principled way; after all, love is mostly irrational and falling “head over heels” over someone else rarely involves a proper and logical decision-making process.  Fortunately for the clueless, there is indeed a way to analyze courtship with a branch of applied mathematics that can capture the essence of the problem and dramatically change the way we look at our relationships.

The discovery of Game Theory by John von Neumann and Oskar Morgenstern revolutionized the way individuals think about how they should react in the best possible way in situations when it is unclear what their opponents are thinking about. Since then, Game Theory has been applied to a wide range of topics and fields that spans across evolutionary biology, prisoners facing time and even countries involved in missile standoffs. And in my opinion, the most interesting applications of game theory often incorporate ideas from these areas of biology, psychology and sociology.

It seems extremely apt to be applying analysis from Game Theory to go about understanding courtship. After all, neither males nor females seem to know exactly what is going on in their partner’s mind while both parties tend to lose or win substantially if they happen to make the wrong decision.  However, the caveat of using Game Theory to analyze courtships is that we have to first simplify the “complications” of a relationship before we can carry out any meaningful analysis.

According to the ‘True Love Game Model’ presented by Presh Talwalkar, there are some ground rules to the game which captures some of the dynamics of the dating world.

1. You only date one person at a time.

2. A relationship either ends with you “rejecting” or “selecting” the other person.

3. If you “reject” someone, the person is gone forever. (Old flames cannot be rekindled.)

4. You plan on dating some fixed number of people (N) during your lifetime.

5. As you date people, you can only tell relative rank and not true rank. This means you can tell the second person was better than the first person, but you cannot judge whether the second person is your true love. After all, there are people you have not dated yet.

The ultimate aim of the game is to achieve an optimal strategy which will allow you to balance between playing the field and holding out for ideal partner. After all, if you pick someone too early you might be missing out on a better option that might appear later. Or if you choose to check out your options and wait, you might leave yourself with fewer candidates to pick from towards the end. Either way, both extremes are risky decisions. According to the math presented, what would be the best strategy to execute then?

The best strategy for any general case would be to reject some number of people first and then choose a partner who is deemed to be better than all of the previous ones. The main idea behind this model is to always be in the playing field before finally settling on a good catch when it comes along and to reject a certain number of people that is proportional to the number of people you intend to date.

Bearing these assumptions and the general strategy in mind, the article provides an analysis of the model using the example of an individual who plans to be involved in three relationships over his/her lifetime.

When N=3, what is the probability that the first person is the best partner? It seems that according to statistics, there is an equal chance for the first person to be first best, second best or third best. Hence, the odds of meeting your true love in the initial relationship is going to be 1/3. Similarly, the chances of picking the second best person or last person are also 1/3.

 However, there is a chance to beat pure luck and this is possible by adopting the following strategy: get to know–but always reject–the first person. Then, select the next person judged to be better than the first person.

Why is this so? In this particular example, there are a total of 6 possible dating cases and the following results prove that by adopting this strategy, the person would have a 50% chance of ending up with their most ideal partner:

(The notation 3 1 2 means you dated the worst person first, then the best, and then the second best. I marked the person that the strategy would pick in bold and indicated a win if the strategy picked the best candidate overall.)

1 2 3 Lose

1 3 2 Lose

2 1 3 Win

2 3 1 Win

3 1 2 Win

3 2 1 Lose

Hence, this strategy is effective for 3 out of the 6 cases and sticking to this strategy would be seem like a good way to find your ideal partner.  Based on the mathematical proof presented here, the odds do not change as you date more people as the percentage of people you would want to reject before settling down approximately tends towards 37% for all cases. The conclusion?  It is always good to not be overly-committed to a serious relationship especially when you first started dating. And for those had their hearts broken by their first love, don’t worry because you are one step closer (out of the 37%) towards finding your true love.