Many people are in disappointing relationships. About half of all relationships end in divorce. But I have a solution. A proof that increase your odds of finding a successful significant other.
Before getting into the proof, it's a good idea to understand what I'm communicating. Let's have n equal to the expected number of partner you will date in your lifetime. Now the underlying assumption is once your reject someone, you can't go back to them. We want to date some number of people, reject then at some point [which we'll call K], then pick the best person after the Kth person. But, we don't want K to be too large, since that'll mean we don't have much options left. But a small K means we don't meet many people, so the ideal partner may be out there. The goal is to find the ideal K, reject everyone before and the Kth person, then begin our search.
P(ideal being in position n)=1/n
P(K)=ΣP(being in position n)*P(being selected given position n)
Now you should notice something. Since we reject the Kth person and everyone before it, all the terms Kth and before is 0 since we won't choose it.
Now let us consider the K+1 person. We will definitely come across this person since it's the first person we consider. The people before K+1 are not considered. So now, what is the probability of considering K+2? Well the probability of not considering K+2 is 1/(K+1). So the probability of considering it is K/K+1. And you continue doing that for all the remaining people until you've reached the nth person.
So now we have (1/n)*1+(1/n)*(K/(K+1))+(1/n)*(K/(K+2))+....
Now we can factor out K/N to get:
Now that inside part is an approximation for f(x)=1/x. So what you do now is you take the intergral of 1/x from K to N and you get ln(N)-ln(K) which is equal to ln(N/K).
So now P(K)≈(K/N)ln(N/K). Now let X equal K/N.
Now we want to find the maxima of this function. To do that, take the derivative of -Xln(X). You get out -ln(X)-1=0. Now using basic algerbra, you could show ln(x)=-1. Therefore x=1/e≈37%
So to conclude, in order to maximize your odds of finding an ideal partner, find the estimated amount of people you will meet in your life, calculate what 37% of it is, reject the first 37% of people, then choose the next best one you meet.