You may find more optimism in the fact that as we increase the range of our dating life with N, the optimal probability of finding Mr/Mrs

There are some interesting observations here: as we increase the number of candidates N that we consider, not only does the optimal probability decreases and see to converge, so does the optimal ratio M/N. 37.

You may wonder: “Hang on a minute, won’t I achieve the highest probability of finding the best person at a very small value of N?” That’s partially right. Based on the simulation, at N = 3, we can achieve the probability of success of up to 66% by simply choosing the third person every time. So does that mean we should always aim to date at most 3 people and settle on the third?

Well, you could. The problem is that this strategy will only maximize the chance of finding the best among these 3 people, which, for some cases, is enough. But most of us probably want to consider a wider range of option than the first 3 viable options that enter our life. This is essentially the same reason why we are encouraged to go on multiple dates when we are young: to find out the type of people we attract and are attracted to, to gain some good understanding of dating and living with a partner, and to learn more about ourselves along the process.

Perfect does not decay to zero. As long as we stick to our strategy, we can prove a threshold exists below which the optimal probability cannot fall. Our next task is to prove the optimality of our strategy and find that minimum threshold.

Let O_best be the arrival order of the best candidate (Mr/Mrs. Perfect, The One, X, the candidate whose rank is 1, etc.) We do not know when this person will arrive in our life, but we know for sure that out of the next, pre-determined N people we will see, X will arrive at order O_best = i.