Mathematical proof on optimizing your selection for a partner!

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.

The intuition:

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.

The Proof:

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:

(K/N)((1/K)+(1/(K+1))+(1/(K+2))+...)

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.

P(K)≈Xln(1/X)

P(K)≈-Xln(X)

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.

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• Very nice! though don't be too hasty to use the log estimation, most people only expect to go through around 5 relationships in their life, not 5000 😂, so you'd better off noting that P (K) only has a single peak for K going from 0 to N-1, so you find the cutoff by finding K such that P (K) > P (K-1) and P (K) > P (K+1), then you can have something like 1/(K+1) + ... + 1/(N-1) < 1 < 1/K + ... + 1/(N-1), solve for K is very easy for small values of N. (If someone expects to go though 1000 partners I would suggest this person does the log estimate 🤔 to find that they should start thinking about settling down with the next best one after 368 lovers, that is, if you could remember the number of your current lover in the queue 🤔🤔, I suggest keep a diary )

Also fair warning, once you follow this strategy, the chance of finding the best person you could've dated, is also 1/e 😂

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• I mean 1/e, that's still better odds then just the random tactic people use.

• Wait, to calculate P (ideal being in position K+1), where 1 <= K+1 <= n, don't we first consider that there are n choices, so each has a probability of 1/n, which means that the probability of NOT being the ideal person is (1-1/n). Then after that, we consider that order is important so we want the probability that we get the specific arrangement:

~(ideal), ~(ideal), ..., ~(ideal), ideal,

where "~(ideal)" means "Not ideal", and there are precisely K of these terms before the ideal person in the (K+1) th spot. So isn't P (ideal in position K+1) equal to:

P (ideal in position K+1) = (1-1/n)^{K}*(1/n)?

And then after that, we'd want to find K that optimizes this probability?

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• In the first paragraph I mean to say that because there are n choices but only ONE is the ideal, then that ideal person has a 1/n probability of being chosen, and hence the rest will have a (1-1/n) chance of occurring in the string of date partners in the person's life.

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• Hm, I guess applied Math ain't really my thing 😅

• Thanks for MHO :D

• Interesting take but love shouldn't feel this complicated HAHA!!

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• People say guys are simple... Look what's happening in some of there head.. Might as well be defusing a bomb... Lmaooo.. I know the feeling.

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• Oh my! I just noticed you're 16, I mixed up your age with J_question. That was so inappropriate for me to suggest a date lol! Sorry!

• It's fine.

• Wow. I’m gonna show this to my sister. She loves math problems.

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• Let me know her reaction.

• Thanks!!

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What Girls & Guys Said

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• *Reads a quarter way down...*
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Nope...
I won't pretend, all this is just confusing for me, what looks like some horrible algebra and then it all went tits up... T__T

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• Just remember the 37% rule. Reject the first 37%, then choose the next best.

• Lol i think i would fail this class. I can't math for shit (:

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• It's interesting... lol

• thank you for putting all that together!!! then i failed terribly... since i failed math...
i want easy and fun relationships... no more math pls!!!

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• The conclusion makes little sense... so the whole thing is pointless
Say I meet 1000 people... take 37% is 370 ok... then reject 37% of 370 so reject the first 140 and choose the 141th person?

Lol... makes no sense

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• So reject the first 37%, then choose the next best one.

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• @coachTanthony Well this equation isn't telling you who is the ideal partner. In fact, you can never be certain if this partner is ideal or not, because there could be somebody else that is even better.

This is saying, given some n amount of partners you will estimate to date [which you could actually calculate what you would expect], let's rank everyone 1st to nth.

Now, listen carefully. The order in which you meet them will be random. Based off of this, what is the ideal strategy of getting the best partner. Because what if you propose to somebody, but you could've met someone even better? Or what if you reject too many people, and you're running out of time and options?

And actually, if I want to figure out how to attract someone, technically one could study how relationship forms and figure out how to use that knowledge for one's own relationships. The only thing that's really stopping it is that sociology and psychology is relatively young.

• Alright kid... fair enough.. I am getting a headache with all the math.

• Your calculations are based on P (Event) but life doesn't function that way, its much more subtle , complicated and conditions change from moment to moment. Its constantly P (Event radndom Event) or in English possibility that event will happen if other event already happened.

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• It is random. You don't know if your ideal partner is someone you've rejected or somebody that you could've met. This is just trying to maximize your odds.

• This gave me war flashbacks from every math class i've been in. Great take nonetheless.

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• I prefer the crazy/hot matrix.

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• From How I Met Your Mother? This is a classic

But why put all redheads in the Danger Zone? That's not fair. Some of us are only crazy if you really piss us off lol

Better to have casual relationship, not expecting anything for the first 37% relationships. And then only commit with someone who's better than the previous.
Rejecting right away makes comparisons harder.

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• Hmmm... keeping people around to use them... that's quite Machiavellian...

Me like it.👍

• I wouldn't say you're using them. There's always the possibility that the first relationship is the best possible. So if you notice it's better than any other person describe a relationship, that is the one to keep, no need to try others.

• Selection quotient:

Nice tits x 2 + nice ass + nice legs x 2 + pretty face +’not overweight = hot to the 26th power.

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• Nice equation, but it all does still hinge on a guess of the number of people you will meet in a lifetime.

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• Well we could estimate it using a bit of information. You would probably date between age 20-40. You could also look up and find that the average length of a relationship in the US in the modern day is 2 years and 9 months. Based off of this, you could say you would have roughly 7 relationships.

• Actually, that's very accurate in my case :- )

• I was never this good in math but it's definitely something to think about! Good take my man!

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• Ok how the fuck does this work because after reading all this i can't understand a shit :D

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• What? The proof or what you're suppose to do?

• Wow, I didn't know there was a formula for this

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• People said I can use math to determine love, turns out you can.

• Come on man dating is already hard enough now I gotta do fucking math

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• You implicitly assume every person has an equal chance of being an ideal one, though this is a convenient simplification and isn't much of a problem.
If we assume P (ideal is n-th) = 1/n then you will have assumed the order in which you date them, matters.

The log estimate you use will work satisfactorily only if the ideal K is large enough.

What you have shown is that your probability of meeting an ideal partner is bounded above by 1/e. In practice, you will not date sufficiently many girls, therefore if we assume the argument is valid, then you will almost surely never meet your ideal partner. Thus, it's advisable to look through the arguments, again :)

Interesting read, none the less, well done. Let's just not take this as a serious mathematical result :)

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• Interesting

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• I'm actually testing it out using a google random number generator, and so far, 2/3 times, it gives you 1, although I would need to run more trials.

• That’s interesting

• Cool. I haven't started trying, but I hope I end up finding a partner.

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• Where exactly did you get 37%?

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• If you do 1/e, it's approximately 37%.

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• @IamLisaSmith yes. I hope you don't mind. I was trying to be funny but I failed.. Lol

• @J_question Well Mr. Joke guy what exactly was the joke you were trying to get across? wink

• Got to love math and enthusiasm!

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my poor brain

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• Thank you

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• Good take.

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• I'll just say hi to a dude I like, how's that?

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• I mean is it the optimal way?

This proof relies on the fact that if you accepted these axioms to be true, that's what the logical result is. Reject the first 37%, then choose the next best one.

Your chances of an ideal partner by saying hi, assuming he would definitely like you, is 1/(the expected number of partner). Which I estimate is going to be a 1/7 chance.

• Good enough for me. I live on the edge

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• You lost me.

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• Interesting

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• aye, you're 16 an know math very well

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• Cool take! One part I don't get: Why is the probability of NOT considering the K+2th person equal to 1/(K+1)?

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• I don’t like math

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• Can you define P (K)
P (K)=ΣP (being in position n)*P (being selected given position n)

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• Well it's a function that takes in a value of K and spits out the value of the probability of finding the ideal partner.

• How do you get this
P (K)=ΣP (being in position n)*P (being selected given position n)

Like why do you sum those likeliness probabilities from K to N? I mean can you give me a picture how do you get that?

• Well here's the thing, everything at K and before get ignored. The idea is that We're summing the probability of the ideal person being in any given position, which is 1/n, but we also have to multiply it by the probability we even consider that position since we might considering going with a person, even though the ideal person is further ahead.

The summing is actually starting at the K+1 position all the way to the nth person. But when you intergrate, if you know about intergral, you're actually going to intergrate from K to N.

• Is there formula that can assist in my chances to stay forever single? >_<

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• Yes. Multiply each term by 0.

• Wow interesting

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• And if we’re the K?

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• The Kth person and everyone before is rejected.

So I assume you are worried if you are the Kth person for your partner.

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• Well does he even know about the 37% rule. Otherwise, if he had a lot of partners before, then reject you, he may be coming to the age when he won't date anymore.

• There’s always a different story what I’ve gotten