How To Mathematically Optimise Dating
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- Опубліковано 22 лип 2024
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This video was sponsored by Brilliant
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Huge thanks to Abulafia for help with the coding as always making these videos possible. On top of that, thanks to Lathurshaan with proof-reading of the script and checks of the animations. Honorable mentions go to Burhan, Sophie and Aiyush for helping with new ideas and methods of explaining.
This was a slightly weirder topic to go into and the maths is definitely much harder than normal although I liked the challenged posed by the man himself - FreddieColes738. There were a lot of animations which actually got cut which I may post depending on if people want it although I'd likely just post it for member only.
0:00 The Problem
2:05 Simplifying
7:35 Benefits of Brilliant
8:47 Adding Some Numbers To It
13:37 One Last Trick
18:03 The Solution
![The Most Useful Curve in Mathematics [Logarithms]](/img/n.gif)
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/Viks/ . The first 200 of you will get 20% off Brilliant’s annual premium subscription.
Sponsorship with 1.7K subs?
@@x2damnI was wondering the same thing wth
Has this dude never heard of the stable marriage problem?
@x2damn yeah I somehow got the sponsorship at like 700 subs. No idea how lol but I'm not complaining
Good for you bro, grow more@@viks3864
so all I have to do is find 100 willing girls, take them all out on a date, then compare, reject or accept based on "simple" calculations... sounds easy enough.
As always, the situation I make is completely real and usable.
this but unironically
isnt that just how tinder works
@@bloodakoosyou ain't wrong tho
The real point is what strats to use to find the best person
There are 2 main problems with this in applying to the real world:
1. The population dating size is unknown or might be too large
2. That solution is assuming the other person always accepts you...
There's more, the entire setup doesn't really mirror dating in reality. You can talk to people multiple times, and it's not guaranteed that a person with maximum compatibility even exists. But this isn't about applicability anyway, it's just for fun.
It's the same when teaching stable matchings from Graph theory, it's not really dating advice either.
Even bigger problem: The solution assumes that you always know the absolute compatibility of a person, which is very, very hard to know in real life.
@@marzipancutter8144 how is it not guaranteed that person with maximum compatibility exists?
@@jimmcneal5292 Of course, if you could represent dating compatibility with a number then some number is logically always bound to be the maximum.
I guess what I'm trying to say is that compatibility in real life isn't cleanly ordered, and likely cannot be represented like that, so there may not even be such a thing as an objective best.
Another one you're too op
I feel like the scariest thing is that this optimisation can be sucessifully applied to recruitment of employees.
Why scariest? Isn't it good for the employers to hire the best possible talent?
@@patryk6769 imagine being rejected just because you are part of the comparison group, doing everything possible in order to show how great you are but in reality it doesn't matter because you will be rejected regardless.
@@hiu4086wouldn't it be more unfair for someone to not get a job if they were better qualified because of a lack of a good recruitment system
It can be, but in that situation, I don't think it's the best strategy. The company doesn't have to reject a potential employee before interviewing the next. They can (and probably do) interview all applicants, then choose the best of all interviewed applicants. In this hypothetical scenario, the best employees can be selected with 100% accuracy. They wouldn't settle for 37%.
@@hiu4086 I mean that's fine. Chances for that are low and you never interview at a single place only.
As someone who loves both biology and maths I see this as an absolute win
50% cool, 50% lame person 🤣
i hate both.
@@myonlylovejesus887 my antagonist...
Found the person with the 1 value
@@myonlylovejesus887why are you here
I wonder if looking to maximize the expected value of compatibility, rather than just looking for the best would lead to a more useful result as well
@@Fouriersuirno the thing being maximized is definitely the probability of picking the absolute best person, the strategy happens to also make it likely to get someone pretty good but it's not being optimized for that
His result only maximizes the probability of hitting a singular result 1/n and treats not getting it as a miss. If there were a way to instead of looking for the singular best 1/n look to see which method maximizes the probability of getting something good or maximizes the “expected value” it could be more useful. I think that this is what op was trying to say.
I think we’d need a probability distribution on the compatibility values to even do that. What’s neat about this approach is that it doesn’t even need compatibility to have a value, only that it can be compared.
Well the strategy doesn't depend on what your metric is, whether that's best looking or most compatible or most knowledgeable about star wars
I would love to see that!
I decided to write a python code to test the results of rejecting 37 at the beginning and seeing how likely you are to get a perfect, and I got the expected ~37% result. I also would like to note I had it also find the average result it gets (whether that be higher than all rejected but found before perfect, or the last because 100 was in the forced rejections) and got the average result for this was about 81% compatibility, so the odds really are pretty in your favor
share the code
The assumption in that average-analysis is that the compatibility score is evenly distributed, right?
@michaeldesanta749 I wouldn't mind sharing the code, but before I do, I need to mention I am not a programmer or software engineer in any way, I have just picked up a bit of python here and there and it might be pretty unoptimized
@brujua7 It isn't, although I could probably find a way to make it. It factors in the 100s that were encountered which being about a 37% chance, skews it pretty heavily in favor of higher numbers
Could you still share it?
One of the only math videos I've been able to kinda keep up with. Honestly just love math being used for obtuse situations like this
lol I'm glad you liked it :D
Obtuse? 🤨
This is as astute as it can ever get.
your feelings are irrational
@@Fire_Axus all feelings are irrational
@@user-dm2kp3vo2u Neither the way "Obtuse" was used nor the way you used "Astute" really made much sense in this situation
Thanks for this, I was just about to blind date 100 people before this video and this will be so helpful!
Oh yeah, as always my methods always work and never fail guaranteed. Good luck.
@@viks3864 except when they fail 37% of the time, of course
@@gr.4380 they fail to get the best mate at 63% of the time not 37
@gr.4380 lol we don't talk about that. 37 literally rounds to 0 so
@@gr.4380as I understand the chance of failure is more like 63%
As a biology student, I don't even think I need to make up a comeback to all the jokes he made about us, this video is proof enough that I'm not gonna have problems outcompeting this guy in the dating market
💀💀💀
This comment is def the proof u won’t
guys how is this comment not censored, this is so scary and disturbing, how can any one be a biology student
@@Nihalthegreat well I lied it's actually life scienes
This video gave me more tingles than a ASMR one. I’m 15 and, more than ever, I can’t wait to finally do real math stuff in class.
When you consider that you have to choose them, and they would have to also randomly choose you using the same maths, it’s incredibly unlikely that anyone gets together at all. In my friend group and wider group, there’s tons of crushes going around, yet there are no partners, because people keep developing crushes on other people who aren’t the person whose crushing on them, in some super complicated love polygon.
A love network, as it were
I was thinking the same, but you have to consider that the numbers we are using to evaluate the 100 people are NOT the grade we gave them, those numbers are the compatibility between us and them!
If you can redefine the methodology, you can change the problem. If you're allowed to talk to people more than once you can ask what the minimum number of conversations is to find the best match. Assuming you do 2 1:1 conversations, such that you can compare 2 people, this is a 2-way Alternative Forced Choice (AFC) comparison. At an internship I worked on an algorithm to find the highest ranking test subject
1. using as few comparisons as possible. For example, you do not want to tire from too much dating.
2. with as much distance between subjects. For example, you do not want the other person to tire from too much you.
The result was to use merge-sort, which gives O(n log n) comparisons unlike trivial O(n^2) sorts, and doesn't use a sentinel (ex. comparing every person to 1 person, causing you to have a lot of conversations with that 1 person over and over). Even better is that as you approach the end of the study the rankings are pretty much already set before you finish. So you can end early with a "good idea" of a "group" of the highest ranks. Or, you can continue on and find the highest rank. The number of times each person would be compared is ~ log(n), so in the 100 person example, 10 times. Which isn't the end of the world for finding a soul mate.
If you want to get really risky, you can up your AFC factor from 2. Comparing 2, 4, 5, .... partners at a time makes things significantly faster. Just be prepared for them to not like it.
Definitely trying to apply this.
tinder please take freaking notes
But what if the "scoring" follows a normal distribution curve instead of a linear randomness? And what if one wanted the highest mean score (you are ok with 99 or 98) instead of the absolute best? How would one optimize the outcome then?
I actually have no idea and it is something a lot of people mentioned. I'm sure you could develop a method which would like guarantee something like a 90%+ as opposed to only the best. Please give it a try and lmk if it works :D
Normalizing scores... doesn't do much here at least on in itself because it preserves scores(a.k.a. the absolute best is still the absolute best... and everyone's still compares the same with that person).
But the "maybe get K people but go for top T instead of top 1" could change the game.
As you increase T you increase your tolerance... or reduce your "good enough" threshold.
It would increase your "success" chance... not in the sense you would get the top 1... but the top T;
It probably reduces the chance of getting the absolute because you sometimes may settle early.
But... it also reduces the chance of rejecting everyone when the top 1 is in the benchmark set.
@@matheusjahnke8643 yeah you could still count from 1th percentile to 99th percentile
Stochastic dynamic programming
it is interesting that for such quality, the video has less than 50 views now. You deserve more. Fun video. Honestly had me more gripped than most math videos on youtube that is some of 3b1b included. Good job man!
Honestly thanks. I'm glad that you liked the video but I'm not 100% sure how the new style will be received lol. Thanks :D
@@viks3864 What new style are you referring to? Either way, regardless of reception, in absolute terms, the video is good. Keep going. Thanks to you I have solved optimisation problems fed from chat gpt and it was fun. Your effort must be appreciated.
@scienc-ification2539 I normally keep the video completely driven by the topic of the video, not really involving myself or random jokes. I thought I'd make this more light hearted to see how it would be recieved.
@scienc-ification2539 Again though appreciate the feedback :D
The video blew up less than 24 hours later
I really enjoy when you take a moment to explain that a certain part is difficult to understand and to try to replay it or think it over. As someone with ADHD I often find myself losing my focus half way through the video and ending up not understanding the explanations by the end, so your disclaimers really help me fully grasp the ideas! Great job, I really enjoyed it.
I'm glad to have helped, and I'm glad you enjoyed it
broooo same
actually, the best way to find the 100% compatibility partner is to ask your current date its favorite number. if she/he says 7 or 42, you must choose that one partner.
or 420@yt45204
Actually based
@yt45204test it out and lmk how it goes
in reality she'll say 6'2 because that's her favorite height😂
Not a number @FloppaTheBased
At first i didn't understand conditions.
Basically task sounds like this:
1) You have set of unknown numbers
2) you have to choose biggest number
3) you can create a set of numbers to compare from which you cannot choose
4) you can compare any number to numbers in created set, but if you don't choose it, it goes to compare set and you cannot choose it anymore
Pretty much yeah. It's important to remember none of this proof actually requires someone to be represented by a number. Its more that one person is 'more' or 'less' - or comparative compatibilities. Numbers just make it easier to quantify that visually and intuitively but we wouldn't know what each person would mean to us in the moment. Hope that helped.
Great video! We are really going to need a Mathematical Dating Advice Pt. 2 where we optimise for probabilistic expected value. My go to method would be running Monte Carlo sims but I am curious to see if you can derive a purely symbolic expression as you did here.
Things i learned:
1. Be absolutely sure about your ideal partner.
2. Don't reject someone unless you are sure they aren't the one.
3. Have a good understanding about people and dating. (To minimise rejection)
4. This was a good video to understand statistics, calculus, combination and comparison.
my probability lecturer actually talked about this 1/e portion on optimizing choice with proof. but u explain these without requiring the audience to have all the prerequisite knowledge is amazing!
Next can you do a video on how to mathematically calculate the size of your mother?
I did, it's infinite cuz your mum can be modelled by the harmonic series as the number of terms tends to infinity. On an unrelated note your mum is a Saint and I'm not sure how the apple fell so far from the tree.
@@viks3864 Bro got cooked.
@@viks3864 i got ratiod by Viks, my life is over
I think highest average is a more substantial thing to optimize. Since 37% the best is cool, but what if the other 63% is the worst, obviously this isnt the case but it shows the importance of the highest average selection.
It's actually a great point. In reality this probably isn't very useful but I liked the maths of this quite a bit. I may look into a way of optimising to get a greater average instead but I have no idea how it would work.
Computer simulations show that the EV is maximized by rejecting 8%, which gives an EV of 91.4 out of 100, whereas 37% gives 80.6
Great video. I was just thinking about the fact that there is way more applications for this compared to the ideas discussed in your other videos. I saw quite a similar video by numberphile about this, but I found this a lot easier to understand. Nice video.
Yeah I actually found the numberphile video as inspiration for this one but I tried to expand on their method to try and make it more clear. I'm glad you liked it.
19:24 You absolutely should mention that you bring around a calculator and ask their favorite number if you think that represents you. They will have a better idea of who you are, and if they reject you, then they weren’t meant for you. Great video :)
Lol if only I felt that way before xD (and by 'I', I obviously me a friend which isn't me, I wish lol)
100% agreed. It's better to get people who don't fit you out as quickly as possible. Pretending to be who you are not is just a waste of time
Yes. Wasting time with people that definitely aren't compatible is 0% efficient.
The stock market would be another (maybe even better) application: say you're trying to find the best time to buy a stock over a certain time period (say 100 days for simplicity). The stock price varies randomly over time. You can't go back in time to pick the best stock price; at any point, you have 2 choices: buy the stock now or later. This optimal stopping problem also works for finding the best time to sell a stock.
Honestly, with the sponsorship, the quality and the didatics, I was surprised to see the channel has less than 2k subscribers and the video, less than 6k views. Keep up the good work!
lol, I am in the process of trying to improve the quality of my videos but my upload schedule is still non-existant.
This is a nice video on the optimal stopping theorem, would love to see more :3
Great quality stuff. I have always admired UA-camrs who have their standards high from day 1.
Subscribed. Keep it up!
Hey thanks :D. I'm glad you liked the video :)
The content and production of this video were both spectacular. Really great work.
Thanks, I appreciate it :D
I genuinely did not know that this wasn’t one of the huge math UA-camrs that I watch until I went to like it! Why don’t more people watch you!!???
lol my animations still need a bit of work. Honestly I do appreciate comments like these and I'm glad you liked it :D
Great video as usual except the biology slander >:(
Tbf at least it isn't geology... yuck. Thanks for the help with proof reading for this video :)
@@viks3864Hey come talk to me, I promise i’m not a biogeo major,,,,
Always happy to find new math channels! Great and fun video
Great video! By the way, on 16:57 I noticed you used \frac{}{} to write the fraction inside the ln, but if you use \dfrac{}{} instead the parenthesis become the size of what’s inside!
didnt know that either, thanks
Oh that's quite interesting, I didn't know about that. Thanks!
I just use \left( tall stuff
ight) to get nice parentheses
I really loved every part of this. The problem itself seems unrealistic, saying you're randomly and blindly dating people, but it can truly be applied in some problem in real life, albeit strange. The simplification, which I find to be a necessary step in most problems, was done very carefully, the expansion into the greater problem, in order to generalise, was also very smooth and comprehensive. The mathematics are basically just simple calculus knowledge, and if anybody knows calculus this was very easy to understand, and the methods to reach the solution were confusing, but that's normal and you did your best to explain the reason behind what you did. It was very fascinating.
Happy new year? Have a great time.
It's being applied to job interviews I think. I haven't fully watched the video yet though.
Nice stuff! My only two notes would be that 1: The fact that there’s an approximation in calculating that sum means that there’s should really be an asterisk after anything saying “this is the optimized value” adding that “this number is slightly off, but gets more accurate the higher n gets.” Or something to that effect. And 2, which is a bit more substantial: I think it would make far more sense to maximize for the best expectation value rather than maximize for hitting the best person. With this method there is a substantial chance of the best person being in the comparison group, in which case the odds of who you end up with are the same for everyone (except the most compatible person whom in this scenario is *always* rejected) regardless of compatibility, which seems to me a flaw
They're all the same except for the best one, who has a 0% chance of being gotten, as in the situation they are in the trial group and rejected automatically
@@derpinator4912 yes, I thought that was implied but I guess it may not be immediately clear so ill just edit that previously unmentioned bit in
I was thinking the same, in fact by this strategy 37% is also the probability of the best person to be in the first group and therefore to reject everyone
@@lucanina8221 well you wouldn’t reject *everyone* you’d just always settle for whoever is last
@@frimi8593 yeah you are right it still an option
I find it so cool that the final result ended up being a form of informational entropy. Makes sense if you think about it.
I always did this, but rounded to 1/3 instead of using integrals and stuff, although it decreases the chance of me getting the absolutely best result it increases the chance of me actually picking something(I don't use this for dating but in general like choosing from different job offers)
props for the last bit
I am like overjoyed you made this lmao
i remember finding that comment so funny, and even better you took the ask seriously and turned it into a really cool math video !!
please keep up the wonderful content !!! :)
Your content looks leagues above mine. Honestly its an honour to have so many people watch my video. I'm so glad you enjoyed it and good luck with your videos too :D
@@viks3864 I'm not sure about that one haha
regardless, I'm certain this is only the beginning of your journey here !!!
your content deserves many more eyes than you're getting at the moment, and I'm excited to see how your channel grows over time !!
Fantastic video and great quality. Keep up the good work!
Wow thank you so so much. I wasn't expecting any donations but I appreciate it more than you know. I'm so glad you enjoyed the video and again thanks - I'll try my best to not upload once a decade xD
@@viks3864 take your time! I'll be ready when you upload the next video even if it takes a decade xd
You deserve so, so, so many more views. Keep up the good work brother ❤
Thank you so much :D. I'm glad you liked it.
I heard of this concept from my econ teacher when in high school. The quality of this video is unparalleled. Thank you!
That's so cool - I don't think we cover this in school but I think it is really interesting. I'm glad you liked it :D
I simulated how the expected rank of the chosen partner varies with r (with n=100 and 1e5 rank orders per simulated r). the maximum of the expected value is way earlier than the maximum for choosing the best partner, at r=8 or r=9 (8-9% of the pool of people). Expected rank of the chosen partner is 91 vs 81 when using r=37.
How does this have that few views especially with a sponsor (even though that doesn't determine anything). You're doing good work
Thank you so much :D. At the end of the day my video is still maths so the audience is slightly smaller but I really like the audience who watch so I'm more than happy to make them. Also the quality of my videos still has some ways to go but I think the quality has been gradually improving. Anyways thanks again
i tried this and ur my ideal partner …
That was really great man keep up the good work it will pay off!
Excellent video. I first read about optimal stopping problems in a book called "Algorithms to Live By." Others should look this up if they like topics like this. The problem with the practical applications of this approach (especially in dating) is that you must have a predetermined finite amount of variables. In dating, this means you have to tell yourself, "I will only accept or reject up to 100 people" and you must absolutely abide by this. If you don't like the 100th person and don't commit, you can't just say "okay, well now the first 38 people are my comparison group" and keep going. Still a fun thing to think about, and might be more applicable to situations like selling a house.
Having not watched it, I imagine you'd speak to 33% of the people available, decide on one to be the benchmark, and then keep talking to the rest until one comes along at or above the benchmark, immediately choose that person and you're done.
Honestly not a bad guess - it's actually 37% but I'm sure 33% would work quite well.
I think it would make more sense to maximize average compatibility, since there is surely a better strategy than one that gets an optimal match 37% of the time and a completely random match 63% of the time. A video on more possible strategies, like optimizing the median, average, or 25th percentile would be very cool.
no way this hasn’t blown up yet 10/10 video it has everything i love
lmao maths and relationships - what else is there xD
First video of yours I watched, and I really liked it. Subscribed.
At 16:49 you replaced the summation with an integral.
I obviously get where the general I tuition for that came from but was this done with the supposition that r tends to infinity? (for it to be approximately equal)
Or are we just taking a good enough approximation.
Yep exactly - the probability of success and percentage we reject is only 1 over e as r and n tend to infinity. It makes sense that the number of people we reject was always bound to be some percentage of n as opposed to an absolute value like 7 so in the formal proof, they just tended n to infinity.
"WhO iS 3BlUe1bRoWn?" Got me
unforgivable sin
Saw something similar to this a few years back in relation to job hiring but the presentation here is so much better!
Lol thanks - glad you liked it :D
Mans wasn't joking, what a ride. This was a fun watch, I zoned out on most of it but I rewind until I understood it. Thank you.
I got a notification from someone I didn't even remember I was subscribed to but I am so pleasantly surprised by this! Great job!
Glad you liked it lol
Interesting video explaining the Optimal Stopping Theory in the context of dating (where you reject about 37% of the people you meet and then accept the next person you think is better than everyone else you've previously met) in the fact that even in dating, math can help you out with optimizing your experience to give you the best chance of success. I've seen this talked about from other UA-camrs and before that I didn't know that you could use a math to help you out in this specific scenario.
The issue with this is that you do have to have set some sort of quantitative limit on how many people you meet so that you can use this strategy (i.e.: 100 people), otherwise it's much harder to judge when you've rejected 37% of the people you met then pick the next one that's better than everyone else you met previously. Regardless of this, it's still lovely that math gives you a helping hand in the dating world even if you despise the subject itself.
Watching the demonstration that E is the solution to love was definitely worth my time.
This is genuinely an amazing video and best one i have seen in a long time. I remember being a kid watching such videos and not understanding anything. Now i am in my last year of highschool and i pretty much understood everything in this video! such an amazing explanation. the number e is defnitely one of a kind!
EDIT: I just got to know that you are 17, is that true? Cuz if it is, then thats very impressive for you to make such vids at this age!
Yep although I actually turned 18 last month so I probably need to change my bio but I do appreciate the enthusiasm :D
6:02 my ex was a biology student. this video hits hard…
Sorry for bringing up those memories :((( Hope you feel better
Haha same looks like we dodged a bullet
Nice video, I like the more personality driven style of video. Good job!
Thanks, I have no idea how the new style will be taken although I'm glad you liked it.
i really like the emphasis on a large personality for compatibility.
i prefer the old numberphile analogy of trying to find the best festival toilet, but your visualisation was really nice (as much as i like their animations, manim is heaven)
Lots of assumptions:
1. Sample size
2. People remain same
3. Can't meet the same person twice. Etc.
Still very impressive.
Although this strategy does maximize the chance you get the best partner, I wonder if that means it's actually the best strategy? For instance, there is a 37% chance the best person (100) is in the comparison group. If this is the case, you are stuck with whatever the last number is (would this just be 50 on average? hm). Perhaps with lower comparisons you would reduce this likelihood, and therefore increase the *overall* result? Genuinly have no idea, I'm not a very smart person so maybe this was covered and I was confused by it lol
by overall result do you mean that you are trying to maximize the expected value? like the average compatibility?
Yeah I get exactly what you mean. Most people would be happy with a compatibility of 90% + in reality. It's obviously possible to account for this into our method but it's a lot more difficult as we would need to extrapolate from our sample to figure out what 90% + really means. It's a great question though and I was going to mention it but the video was getting way longer than I wanted to as is, so I decided to leave it.
@@auriga05 I'm guessing exactly that.
it won't be 50 on average, it will be lower.
In the case where 100 is not in the first n/e people, you're bound to choose him or a maximum before him.
So in the case where you went all the way to the end, that must mean the best people are at the start, and all of the people afterwards are worse than the maximum of the first n/e people, OR specific edge cases such as 100 is the last person.
I didn't study statistics yet so I don't know the exact value, but be sure it can't and won't be 50, but less.
I think an intuitively optimal solution would be to look for the best partner for some number of people but at some point switch up your strategie to also accept the secound best and a bit after that the third best and so on. Until the second to last person, which you should choose if they are over avarage.
It would be nice to see how the dynamics would change if other people are also applying the same method at the same time
Yeah I know it becomes way more complicated. The issue seems to be that a lot of people tend to find the same person as their ideal partner meaning there is a lot of cross over. I know modern dating apps have ways of dealing with this but I am nowhere near smart enough to understand it xD.
Pre filter with clustering algorithms and only match within a cluster or cluster pair. At least that's my initial guess. Bipartite matching algorithms may be O(n^2), but when n is somewhere beyond the thousands and "computation" time takes hours, you still have an interest in reducing the size of the solution space.
This does assume people are told where they rank within the pool of applicants, which I'm certain dating apps don't do
We actually learned this method at my University! good content, awesome explanation, keep it up!
Oh nice :D I'm glad you liked it!
awesome video keep up the cool animations and coherent explanations
Incredible explanation! 🎉
1 question: What if you dont know the exact number of those who you rejected. Like in life you wouldn‘t know that 1 out of the 37 was a 99, you would know it was nearly perfect (chances are, you wouldnt realise its a 99 and not 100 later in life😂. But a few early 90+ numbers will skew the continued rating for how far away a higher number would be. Is there a mathematical way to calculate the same question but with the uncertainty around the exact number included? :D
Hey glad you liked the video! First thing is that I would recommend never using this in the real world lol. Its more a funny way to let me ramble and make the maths feel more intuitive. Also to answer your question - we actually don't need to know the number of each person - for example that someone is 99. All we need to do is compare people - we are looking for the first person better than whatever the best was - the best could be 210 or 12 or in this case 99. Adding numbers to it just makes the comparisons clearer. I hope that made sense although feel free to ask any other questions you had.
3:00 caught me off-guard lol
Yeah I should really learn to draw lol
@@viks3864 i was talking about what was said there but
whatever floats your boat?????
Oh lol - yeah I went a couple of weird tangents in this video xD
@@viks3864 understandable
Great video! Was wondering though, although this seems great for picking high numbers out of a pile, would this actually work in a context more like dating? If you had a matching problem with two groups of 100 people, where everyone could talk to all members of the other group once etc and everyone adopted this strategy, would it still hold or fall apart? Intuitively this method seems to hinge on your best pick accepting you and it might fail if they don't. But if you are the ideal partner of your ideal partner it might hold?
Yeah exactly right. In the real world, holding out for the best person probably isn't the best approach but I felt like this helped make the situation feel more intuitive and helped me complain about how awkward I am. In reality, dating apps use much more complex methods to ensure you get partners who are quite good as opposed to the best.
The best math video i have watched on this platform in a long time.
lol I'm glad you liked the video :D
Great video! I have two questions. What happens if the most ideal partner is within the initial rejection region? Do you reject all of the others until the very last option, which you accept? Also, you said that this integral approximation holds for large values. Is the success equation still decently accurate for small samples? Keep them coming! I loved this!
Came to the comments to ask this. Seems like there would be a greater than 1/3 chance that the 100 would be in the first 37
Yep exactly, if the ideal partner was in the rejection region, you would reject everyone until the last person. And again you said it perfectly - for large values success rates and percentage of people rejected get closer and closer to 37% although it is still relatively close for smaller values of n too. Glad you enjoyed it!
@@viks3864That makes sense! Thanks for taking the time to respond.
I think I saw this same problem on QI or Numberphile or something like that. The objective was to find the cleanest public toilet instead of finding the ideal partner.
Oh yeah numberphile made a pretty good video on it and actually gave me some inspiration for this.
This is a nice approach but it could use some improvements:
1. Aiming at maximising the expected value rather than going for the maximum possible value
2. Including probability of YOU being rejected
3. Assuming a normal distribution instead of linear (as someone else suggested)
4. Giving some extra score to finding your partner earlier.
The best math video that gets recommended to me. Awesome.
For reference, women in the US, UK and Europe have an average of 7 sexual partners over their lifetime, and men have an average of 8 (according to the first result on Google, I'm no scholar). Making a naïve assumption that the average is a perfect distribution based on people traversing their respective arrays of partners, the total number of partners x in the array would be found by the equation .37x + (.63x)/2 = 8. Hence, x = 8/.685, or around 12. (10 for women.)
As such, practically speaking, you should reject around four (maybe five, as a man) sexual partners for use as your test set before you even consider settling down with anyone. After that, any person who makes a better match than all four is a keeper.
Yep exactly - if only life turned out that easily xD
Girl: " I have to go now, that was a nice date. Wanna meet again maybe next week?"
Absolute dating master: "Well, actually, if you look right here, * takes out noteblock * the rating I've given to you is pretty good, but not better than the best rating in my comparison group, so- hey, where are you going?!"
lmao that's actually so good. Someone was saying I should make merch out of that xD. Imagine
"Absolute dating master" I'm dying here 😂😂😂
Thank you for enlightening me cant wait to use this in the real world and binge on the remaining videos.🙏🙏
Very well made video. Bravo
I wonder how much more complicated this would get if you added the real 2 party system. (not politic), where a girl is also simultaneously going after people that SHE is trying to maximally date, so you could also be rejected. Supposing there's a 'soulmate' for every person, it's also possible that you accidentally reject your soulmate since they are in the initial 37%. Wack
Problem with this is you would need to create a model on how the other party would react/strategize, which I don't see a clear way of doing beyond "make them maximally rational" which I think would result in behaviour that doesn't track well to the real world.
The issue with real life dating apps is that loads of people's ideal partner will be one specific person. Not to get too deep into it since no-one cares but it has been shown that in samples of 100, women and men tend to choose only around 10 as their top pick which makes it difficult for apps. With that tangent over, give it a try yourself and let me know if you figure anything out - it's always nice to test your hypothesis.
bluds talking about finding ideal partners but i cant find A partner
The real hardest mathematical problem
14:15, the sum of reciprocals of the first n natural numbers is proportional to log(n), so that might have been a good estimate (with a deviation of around 0.57)
This is best method of optimization only given that you know what's the exact size of the set you're choosing from. It's great when it comes to looking for a parking spot but when it comes to dating you are clueless about how many there will be.
Compatability... I just want someone... anyone...
You will always have me sninja332
@@viks3864 😘
trying to find out if i’m viks 1 2 or 3 because i almost exclusively watch math videos but im also a biology student 😓
lol at least it's biology and not... geology. yuck. Nah I'm joking - its good to be passionate about things and if you are passionate about a lot - it just shows you have motivation which can never be a bad thing. You can be a 4 :D
Catchy title of the video, but I think it's worth mentioning that this method can be used for optimising in all problems where you need to choose from a sequential flow of offers, not only for partner finding purposes :)
For example, search for accomodation, recruiting etc.
If you have already given up with dating, this method is valid too for choosing how many spotify songs you skip before the free version stops you
Not gonna lie, I thought I had it down to an art at this point. But nope, once again viks has blown me away with top notch quality content. New style of video is 100/10. Do recommend not being as cool as u r tho cos then gonna be no women left for the rest of us.
Who is cooler, the man who gets a C in maths or the man who made the space poo???
@@viks3864 lad u never got a C 👀
You guys are talking to girls😳
Seems like you could take this a step further by finding a Nash Equilibrium between your own payoffs and those of potential partners. The most ideal is probably out of your league for instance, so they might have better options/not be as keen/dedicated to the relationship/amenable/etc. Of course this introduces some ambiguity as to whether it's universal scoring or if utility function vary greatly among players.
5:02 in and this sounds like the Monty Hall Problem. After watching the rest of the video, I still can't get that out of my mind. I'm also wondering what the probability is for getting at least 90 or at least 95 or at least 97, and which number is best for lowest diminishing returns if you don't care about getting the absolute best but you still want to keep high standards. Although I imagine that these would all change the math quite a bit...
I do not need this in my watch history lmao
"I'm just watching for the maths, I swear!"
I just know this viks guy is a handsome chap.
All I know is this dhruv fella is leng and has too much rizz.
I don't know what video animation you're using, but at 16:55 the brackets aren't tall enough. In latex, you would use /left( and /right) to autosize for contents or, specifically in this case, /Big( /Big)
wow, i actually unconsciously used this method before watching this analysis, although i had this video put into my watch later playlist, that's crazy
That's why it makes sense not to reject people but to put on them "on hold" for a while for a chance of finding a better match. Friend zone invented!
Waa waaa what a sob story
Nice video
If the best outcome was in the sample group then do you not pick anyone? How would you optimize success rate if success is proportional to the number you choose relative to the best outcome? (so that you end up choosing an outcome close to the best even if the best option is the the sample, and you end up choosing someone no matter what)
criminally underrated, despite the great editing and amazing execution.
Thanks :D Glad you liked it