What is Monte Carlo?

Here's a video describing programming magic: Monte Carlo integration!
It's a super cool algorithm that is used all the time (in physics at least), so it was good to cover it here. We'll have more algorithms coming up, so be sure to check them out as they come along!
Information on the Batman Curve:
mathworld.wolfram.com/BatmanCu...
math.stackexchange.com/questio...
I also did a small write-up on integrating the Batman Curve:
leios.github.io/Batman_Montecarlo
As always, the simulations were done live on:
/ leioslabs
/ @leioslabslive
Feel free to follow me on Twitter!

The code is available here:
github.com/leios/simuleios/bl...
And the music is from Josh Woodward (sped up 1.5 times):
www.joshwoodward.com/
Thanks for watching!
Also, discord:
/ discord

[@LeiosLabs]

Since making this video, we have created a new project called the Algorithm Archive and have added a chapter on Monte Carlo: www.algorithm-archive.org/chapters/monte_carlo/monte_carlo.html Please go there for information on how to code this up yourself!

[@ananyapamde4514]

Thank you sir

[@yolofapper9668]

this is the best mathematical education video I ever saw,short,simple,no overcomplicated shit,just straight to the point

[@LeiosLabs]

That is exactly how I want the videos to be: As short as possible while still conveying the point. It takes forever to make 3 minutes of content, but that's alright.

[@raqueloliveiramotivacional2348]

Yolo Fapper Monte Carlo

[@J_46]

Totally!

[@AdnanKhan-so1ey]

After wasting an hour trying to understand an algorithm that shouldnt take more than 3 minutes to understand, I finally came across your video. You explained it perfectly. Thanks a lot

[@LeiosLabs]

I'm glad it was helpful! =)

[@AnujGupta-wp2ww]

Einstein once said "If you can't explain it to a 6 year old kid, your education about that topic in incomplete". Great explanation

[@phythematics2188]

Einstein himself couldn't make understand scientists the Theory of relativity let alone a 6 years old kid.

[@samuraijosh1595]

@@phythematics2188 Lol.

[@jameshuang9568]

I've been running through all youtube videos about his topic for hours and even the professor from MIT didn't answer my question. You are brilliant

[@jrwkc]

Keep it up, you will hit youtube fame soon. Probably one of the best educators out there.

[@LeiosLabs]

Thanks! I really appreciate it!

[@rishabtirupathi9431]

I was so scared that this video would be too complicated. Thank you so much for making it simple.

[@victoriagee1059]

This is one of the best explanations for Monte Carlo I have found. Good job, James!

[@DanielDuesentrieb86]

Monte Carlo methods are also very handy in game theory where it is easy to state the game rules, yet hard to precisely calculate the probability to win.

[@AbuSayed-er9vs]

A lots of thanks for giving a valuable information.Please keep going on to do more and more videos with your amazing information.

[@harkirehal258]

This is an excellent explanation of a complex concept. I was glued to the video and understood every word. I wish I had you for my teacher when I was younger. I subscribed to your channel. I now want to learn everything you teach even if it just for fun. Its rare to find a teacher that explais a concpet to the core in a way that a layman understands.

[@naveenchandrakumar480]

Very Nice. This is first time I understood Monte Carlo method clearly. Thanks for the video

[@Aa11qq]

This is an amazing explanation. Thank you!

[@forgettd]

This is the best explanation of anything I've ever seen on youtube. Thank you!

[@corporalwaffles]

You earned a sub today, keep up these vids (along with algorithms) :D

[@kamruzzamankanon4794]

Concise+informative+to the point+easy example = My subscription!

[@charlesasmr7242]

you are amazing, and also very vivid ways to tell others the simulation process.

[@TheRach995]

My grandfathers research on Monte Carlo numbers was actually pretty important. Look up Martin J Berger, his world is all available online and his obituary is achieved by the Washington post, is available through a simple search. I’m so proud of him.

[@Tom-sp3gy]

This is absolutely brilliant ! What a simple and short explanation ! Thankyou so much

[@robertpretorius7627]

Short, simple, clear. Wow! Great video! I finally understand Monte Carlo simulations!

[@LeiosLabs]

Yeah, it's crazy how random numbers can be so useful!

[@vladscp6579]

this is the coolest algorithm videos I've ever seen, better than most stuff in my uni

[@filiphradil95]

Awesome explanation! Finaly some non-boring video for numeric methods! :)

[@LeiosLabs]

haha, I'm glad you liked it! I actually really like Monte Carlo. It was one of the first integration methods I learned and really helped me understand integration.

[@snackbob100]

you are going places my dude, keep it coming!

[@PrettyMuchPhysics]

It's amazing how many modern application use Monte Carlo! Great introduction video :D

[@lerneninverschiedenenforme7513]

Awesome! The only video, that can deliver 4 minute content in around 4 minutes (and not 10, 20 or 50, like the other videos)

[@jennis493]

Great Video! After a one semester course on computational science and still not quite getting what this was all about your video really cleared things up! Thank you!

[@LeiosLabs]

Woo! I'm glad it was helpful! =)

[@kemfic]

This is the best explanation I've seen on Monte Carlo so far

[@tudorversoiu8138]

Never seen a better explanation on anything, ever. Amazing videos, just found your channel :)

[@LeiosLabs]

I'm glad it was useful! =)

[@ferdousadnan5814]

An excellent excellent video, excellent explanation. Both liked and subscribed.

[@AashishMishra_Nygma]

This channel is gonna touch the skies! I am happy that I am such an early subscriber!

[@shakilmasud]

Thank you. Searching for so many sites but here I cleared my conception :)

[@kaarla2805]

Omg i just discover your videos and they’re amazing, thanks for share.

[@ashishbastola8412]

Short, sweet & amazing!

[@handlenotprovided]

Very concise and straightforward explanation of monte carlo integration. Thank you

[@abdulelahaljeffery6234]

omg!! dude you are definitely one of them! a rare bread of human beings who know how to explain things really well, congrats! (clapping)

[@LeiosLabs]

Haha, I'm glad you like the content! =) Let me know if you have any questions!

[@abdulelahaljeffery6234]

I most certainly will ..

[@SamiyuruSenarathna]

You conveyed the point very clearly.

[@prateekverma6873]

Nice video!. the explanation was easy and understandable.

[@prathameshpradipdatar2003]

Simple, elegant and impactful!

[@bondmanu]

Very much liked it....explained the complex definition very simply ...keep up the good work! :)

[@LeiosLabs]

I'm super glad it was useful! =)

[@ProXicT]

This is the best explanation on the internet, thanks a lot!!

[@LeiosLabs]

I'm glad it was helpful!

[@ujjayantabhaumik3109]

This was really cool. You explained it so nicely. Gracias :)

[@OOnestly]

Dude, you explained such a concept in 3 minutes. That was amazing!

[@LeiosLabs]

I'm glad it was helpful!

[@qiuzhishu2583]

Really nice! Easy to understand!

[@greenowski]

This is exactly what I was looking for! thanks :)

[@JoannaBalasbas]

thank you so much for explaining so well and concisely to beginners like us!

[@LeiosLabs]

I'm glad it helped! =)

[@khudhurm7709]

Amazing explanation! Subscribed :)

[@srik24]

A thorough explanation. Thanks!!

[@harshavardhan9660]

Thanks a lot bro;Atlast I've found the platform for visualizing the concepts clear.Keep it up..

[@LeiosLabs]

I'm glad it was useful! I've been trying to get more videos out, but with work and everything, it takes a little longer then I'd like...

[@kshitijkulkarni8698]

Thank you for making this video!!

[@yassertalebi1026]

Many thanks Sir, you made as easy as could have been possible, I was watching MIT 's course for 55 min wasn't that clear as you were

[@ozzyfromspace]

Wow, you did that in less than 4 minutes. Bravo!

[@LoserHands]

I've always wanted to integrate odd shapes into a shooter videogame, for shotgun chokes. Maybe percent-error per shot can be used for boosting the unlucky shots, or the area-of-circumscribed-shape can be used to find the effectiveness of a shotgun choke, so the better ones cost more in a borderlands-style procgen. Also sometimes your videos make certain terms like integral wayyy less scary for someone like me, who has a lot of math left on their plate following high school and dropping college once. It's hard getting back into crowded class and math is totally smthn I don't want to fail. Ty

[@LeiosLabs]

I'm happy this was useful! I'm interested to see how you work this out for your game. It could be really cool!

[@peter9910]

Great explanation, thanks!

[@aminsn779]

great, easy, and fast explanation. exactly what I needed :)) Thank you.

[@LeiosLabs]

Great to hear!

[@aashmavlogs5512]

Thank you so much. You explained it with simplicity.

[@cameronmiller4144]

concise and entertaining. thanks!

[@saitaro]

Best Monte Carlo advertisement I've ever seen. The slogan @ 3:26 is great

[@LeiosLabs]

I like my videos to advertise algorithms. It's better to motivate people to learn.

[@scose]

The Batman example showed how to use Monte Carlo methods to find the area of a complex domain. More generally, we can think of integrating f(x) * p(x) where p(x) is a probability distribution. In your example f(x) is the indicator function of the batman logo and p(x) is the uniform distribution on the ellipse. But we could also extend this to something more complicated e.g. if f(x) = x and p(x) is the uniform distribution over the logo itself, we can find the center of mass of the logo. Or, if p(x) is not a uniform distribution, we can use importance sampling or Markov Chain Monte Carlo methods to compute the expected value of a function of a random variable. (commenting for other viewers - as a physicist I guess you already know this)

[@LeiosLabs]

Yeah. I want to cover some of this stuff in the future soon (tm)!

[@matt9912]

Very nicely done!

[@LeiosLabs]

Glad it was helpful!

[@tusharkush7]

Great Explaination!

[@locopepele]

Great explanation! Thank you!

[@bluecpp2059]

Thank you for this great video. I will read more about it.

[@HKHasty]

Greatest explanation of Monte Carlo I've ever seen!

[@LeiosLabs]

I'm glad you found it useful!

[@ashish6114]

You sir should have more subs. The presentation of the concepts is super intuitive and easy to absorb thanks to the proper and simple explanations provided unlike the majority of college professors who unnecessarily complicate the matter due to their inadequate teaching skills. Sometimes I think that they became professors simply because they held 'PhDs'.

[@ashish6114]

I've seen the other videos of yours too. It'd be amazing if you were a professor. We need more people who teach in such simple and intuitive ways.

[@LeiosLabs]

Honestly, I would love to be a professor. It's one of my dream jobs!

[@deeptivirgo2009]

Very nice Explanation ! Thanks a lot!

[@LeiosLabs]

Thanks! I am glad it was useful!

[@TheFitAuto]

I understand exactly about Monte Carlo calculation after seeing this video..many thanks!!

[@LeiosLabs]

Great! I am glad it was helpful! =)

[@ElMakk_Med]

hey there, thanks for this awesome work, i just wanna ask what is the software you used to make the simulation in the video?

[@jackyxue7885]

I was out there reading papers and falling sleep. You saved my day. Simply and elegant ~~~

[@LeiosLabs]

I'm glad you liked it! When I saw this for the first time, I thought it was magic!

[@Rotwh7]

Sir, I hope you read this comment. You are brilliant and kind. GOD bless You! Keep educating us like this Sir!

[@thyagtubes]

Very well done

[@aming.alhashim-ou6032]

Well done! You are a great teacher.

[@LeiosLabs]

I'm glad you found it useful!

[@Aa-tf1li]

I made a long research to understand this topic and I can't reach to the nut... your video is very helpful , it summarise whole idea in simple concepts, thanx for ur efforts

[@LeiosLabs]

Yeah, there are a lot of concepts that seem super complicated at first glance, but are much easier after you get used to them a little.

[@arturotorreslopez4283]

And that's another precious way of calculating pi :D

[@GBWF1984]

I just want to thank you for this great video. Also, I took sometime to visit the Arcane Algorithm Archive, very nice work!! Congratulation!!

[@theinstigatorr]

Nice video. I'm surprised it doesn't have more views

[@abubakerbarenis]

very nice explanation, appreciated..

[@LeiosLabs]

I'm glad it was helpful!

[@FamMeierundCo]

Oh my god awesome video!

I should've found this video several hours ago! Nice!

[@LeiosLabs]

I'm glad it was helpful!

[@Ravikumar_Sharma]

Excellent!

[@IanFarias00]

Amazing video! ^^

[@aln447]

Brilliant!

[@karimaelouahmani7078]

i am soooo thankful

[@AhmedHatem1996]

Awesome Explanation .. Thank you so much

[@LeiosLabs]

I'm glad it was useful!

[@kishangovind8499]

Thanks a lot . Nicely explained

[@LeiosLabs]

I'm glad it was useful!

[@bharatkukreti8449]

Very well explained the Jargon.

[@LeiosLabs]

I'm glad it was useful!

[@reinia127]

Thank you so much sir!!

[@md.abdullahal-alamin8059]

At last I understood monte carlo simulation. Thanks :)

[@LeiosLabs]

I'm glad it was helpful!

[@pman-codes]

short and awesome

[@kenroyadams2762]

Thank you! Liked and subbed

[@Rightwing789]

I love this!!!!!

[@NERMIENKH]

very useful thank you!

[@Manu-sz4mo]

Simply AWESOME

[@LeiosLabs]

Yeah, batman took a while...

[@GeorgeSandle]

Very well explained :)

[@LeiosLabs]

Thanks! The point is to provide quick, intuitive descriptions of things.

[@Foba_Bett]

Cool Video, Thank you :)

[@MrZouzan]

2 sec of this vid and u got a new suscriber !

[@vincenthuang5228]

So how does the program know whether a random point is in the region we what to integrate over?

[@walidwalid9991]

Thank you so much for this explanation. your student from Algeria

[@cupofkoa]

You're one of the few that don't say 'click like and subscribe'. Its because you don't need to because you're stuff is good. Hitting that subscribe button now.

[@LeiosLabs]

Ah, thanks man! I don't tell people to like and subscribe because I hate watching people who say that. People know what to do. I don't need / want to tell them. I would honestly feel bad if people only subscribed to me because I told them to.

[@ProCipher]

you are a hero :)

[@juusokorhonen1628]

I have one question. If thinking about more complex function (still in xy-plane for simplicity) how do we know if the randomly selected dot is under the curve or over it? Like ofc we as humans can see it, but how to tell computer about it, how to code it in? Probably it is a stupid question, but it just popped into my head