A Random Walk & Monte Carlo Simulation || Python Tutorial || Learn Python Programming

[@Socratica]

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[@Socratica]

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[@sterlinglozalee9926]

Great update on an almost 3 year old video - thanks for the awesome content!

[@SagiPolaczek]

Socratica great content!

[@VashaLittleMasha]

This. Is. Amazing. I never ever saw a tutorial with such a refined artistic taste

[@SingingblissofRajat]

VashaLittleMasha Code can be used to create art. Try it. It's fascinating.

[@vulturebeast]

She is an actress , a very great actress that's why :)

[@marsrocket]

@@vulturebeast And a dancer, and a voice artist...and probably more too.

[@Socratica]

@@marsrocket And a programmer!! Ulka really is amazing.

[@rashayahya]

I agree

[@ChumX100]

As for the "even numbers get you closer" thing: Since the direction of the steps is evenly distributed, in the even case, we can expect the number of steps going up to be the same to those going down. But in the odd case, we can expect the number of steps in one direction to be one larger than the other, leading us further away from the origin. The same is true for the left/right dimension. This phenomenon should be less and less noticeable, as we increase the number of steps.

[@saraperestrelo8377]

Yes, but this is only because it was considered the result "distance = abs(x) + abs(y)", removing the influence of the sign of x and y, which can influence your distance in each direction. Interesting.

[@chukypedro818]

Yes., Also this is dependent on the number of blocks chosen, take for instance 5 blocks away from home, We expect the even number to be further aways..

[@sebastiandonickler.6715]

I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.

[@WillChaseIV]

Is it safe to say that with an even number of blocks, there are more chances of backtracking compared to an odd number of blocks?

[@saitaro]

She's my coding dominatrix now

[@ting-hsiangwang311]

Exactly the vibe I got from her. XDD

[@felixsnag9897]

Dont be rude

[@CarlosOrtiz-ht6rn]

Jeez guys, keep your pants on

[@mikefocal5770]

here name?

[@thegaminghobo4693]

mike focal I can’t tell you exactly where you are but I’m in England🤷🏼‍♂️

[@pursuitofcat]

"This concludes my gamble amble preamble" hahaha

[@elghs2001]

This channel is INSANE. Thank you for providing such an in-touch way of explaining something as complex as coding in Python.

[@hayfordadjavor18]

There's absolutely no question about it; Socratica is a winner by every measure! Keep up the excellent work!

[@CarloRizzante]

"The city of Monte Carlo... you'll never find a more wretched hive of scum and villany." ...hahaha, pretty well said :-D

[@CalifDuDad]

Again....... starwars.wikia.com/wiki/Mos_Eisley

[@bigfootpegrande]

Mos Eisley is not a real Cassino city, Canto Bight is...

[@banderilllero]

what does this mean?

[@bigfootpegrande]

These are jokes on Star Wars ("A New Hope") and The Last Jedi...

[@dirkmcnasty8585]

Well played Socratica, very well played. Throwing my kudos on using the Star wars quote as well.

[@SheepWaveMeByeBye]

Great teaching. Love the high-tech style.

[@kangjohan78]

Did you see her dress?

[@TheSatishPatel]

Please add videos for basic algorithms also. Videos on this channel are high quality and watching them is absolute satisfying.

[@clydecessna737]

"Monte Carlo: A sunny place for shady people". - Somerset Maugham

[@theexposer9483]

High class material, reminds me of Morpheus explaining the Matrix. Excellent, to the point and does not waste any time of the listener. Keep the good work.

[@tythedev9582]

How have I missed this channel?? This tutorial is superb!

[@Artonox]

this is the kind of videos i need. Just straight up describe the problem, code in a very highly excellent presentative manner.

[@peterfarrell66]

Great videos, wonderful sense of humor and quality Python content!

[@Erotemic]

"We will perform the programer's solemn duty to write a docstring." - Preach!

[@PeterManger]

Whenever I need to reset my programming thinking brain - just watch any of Socratica's programming videos!

[@Socratica]

We love this idea!! Thanks, Peter. 💜🦉

[@kalied3715]

Wow, this blew my mind. When I increased it to 5 blocks or less, the odd walk has a higher chance of being closer to home.

[@khonello]

Oh my gosh this woman is the best python programmer i know so farr

[@emmanueltondikatti8754]

As a beginner in programming this took me a bit of time to grasp, but the way you explained was phenomenal. It really boost up my confidence. Thanks for this.!

[@Socratica]

Thank you so much for telling us - this really gets us excited about making more videos! 💜🦉

[@GlauberLimaBR]

Seriously, your Python videos are the best! Many thanks for the time you spent building such a beautiful and well organized material! Top-notch!

[@amoorinet..]

This lady is not just a programmer, but she is actually a real scientist I have been searching for more than ten years for an efficient and logical way to implement Monte Carlo simulation

[@kirill_good_job]

Where's Monte Carlo ?

[@amoorinet..]

I said tool use for ​@@kirill_good_job

[@macmos1]

To answer @Benjamin Voll, my initial guess is that the odd distances (numbers) are not perfectly divisible by two like even distance(numbers). P.S. Great videos. I like the emphasis on computer science and not just "learning python." Also, great videos on mathematics, too.

[@MinecraftLetstime]

This is how programming tutorials should be!! Exactly in that voice

[@peterclaassen5865]

The Best Ever Tutorials, entertaining ,CLASSY, always waiting for her deadpan "The city of Monte Carlo... you'll never find a more wretched hive of scum and villany." or the like. And I actually learn a lot. Thanks!

[@rashayahya]

This channel became my one of my favorite KZbin channels

[@cyndicorinne]

I think the reason that random walks with even numbers of steps lies in the trivial cases wherein 0 steps lands you right at home, 1 step definitely won’t end up back home, 2 steps may or may not, and so forth.

[@ThePowerchimp]

The "high-tech virtual girl" delivery in these videos SHOULD be cringe-inducing, but somehow you guys manage to make it fun and engaging!

[@syd6358]

Why it should be cringe

[@CarlosOrtiz-ht6rn]

Thank you for this explanation of Monte Carlo simulations.

[@ashketchum7768]

Her way of speaking and her voice remind me of Diana from the game Hitman

[@chrislam1341]

i found it like metal gear..

[@the_emmo]

I was expecting a "Good luck 47" right at the end of the tutorial lmao

[@TheRealWindlePoons]

She reminds me of Pree from Red Dwarf

[@sandeepn94]

Not at all!

[@bisratgetachew8373]

Now that you brought that up, I am reminded of Hit man2

[@rogrp1241]

These are the videos I like most about python, do not stop uploading that content please, thank you very much!

[@antiquarian1773]

This channel is so underrated.

[@rs-tarxvfz]

Most Intelligent KZbinr!

[@ahmadzorjis6263]

I fall in love with this channel.

[@sharpEAGLES]

"...Our release schedule will be less random!" 😂 Atlast! a programmer with good sense of humor. This is really amazing BTW.

[@District876]

You are the only one who keeps the ability to make me understand all the difficult problems of the world .You are great ,awesome ..I dont know how to express my respect ,gratitude towards you . Thank you mam ...pls keep uploading more videos on python

[@Socratica]

Your kind message brought a smile to our faces today! 💜🦉

[@District876]

@@Socratica Mam please keep making videos on such topics ,Its a humble request mam .

[@shadowskillz1975]

isnt she the best?? hands up for that explanation

[@okunolakehinde5357]

I love ..socratica...You guyz are the best online tutors...I want you to give a teaching on PHP programming as well. thanks

[@OlumideOni]

Guys lets support this channel financially as much as possible. They are doing a great job here

[@michaelwood2292]

From what I have seen on the Socratica Channel, you have a "WINNER"... Hope you get funding to do great and wonderful things. Thank you for that "gamble" .

[@davecain5406]

Laurel and hardy

[@bryanchambers1964]

"You will never find a more wretched hive of scum and villainy". Ha ha. That is the greatest sentence in the English language ever.

[@pungavaD]

if someone had taught me random walk in this way earlier, I would have been a prodigy by now. thanks for this awesome video. I have already subscribed and believe this video to be more useful for me than previous ones.

[@kristoffersonfox9665]

The difference in probability between an even/odd number of moves may be related to the fact that the origin is special: Every move from there increases the distance to the origin with 100% probability. The first move (odd) increases the distance, and if you happen to get back to the origin, this will happen again. You need an even number of moves to get back to the origin, therefore every move from the origin is an odd move. So, odd moves are slightly move "evil". The further you get away from the origin, the less relevant this becomes, therefore the probability difference is reduced with the number of moves.

[@guiray2000]

She is the best teacher ever!

[@mdrafiqul2898]

Wow! That's the best monte Carlo simulation tutorial I've ever seen.

[@rileynobles7146]

No better way to prove you are a tech geek than to throw in a "Star Wars" Quote. Excellent!

[@Socratica]

We're halfway there. We still need your help! Support Socratica Python Kickstarter: bit.ly/PythonKickstarter

[@rickall]

That description of Monte Carlo. She seems pretty cool AI. The 100.

[@pinkmolly5660]

so finally I've found you. this is probably the best tutorial i've ever seen on yt.

[@PewPew_McPewster]

I wish I watched this video like 5 years ago, the Monte Carlo method is a cornerstone of many important fields of research, but I had felt locked out of it for the longest time because classrooms simply dismissed it as an abstract idea from which we derive a single average value. Whelp, time to jump back into polymer science!

[@rahulraj233]

No Errors No Surprises. Thanks.

[@mahimsd7645]

I walked randomly and found Socratica ...just 0 block from my house

[@semabkhan]

I dont understand half of the content but I have seen almost all of this series.. Interesting.. I know

[@Glademist]

Oh wow i enjoyed this video so much. Very educative and well though out. The female voice is catchy and the background noise actually is not disturbing but sort of stimulating. Awesome.

[@dylankirk6166]

Gamble amble preamble... you have officially made my day.

[@TehFingergunz]

fantastic production value!

[@reinforcer9000]

To see if I have an accurate understanding: To get an accurate estimate of the ratio of paths fewer than 4 blocks from home to paths more than 4 blocks from home for a given walk size, you perform Monte Carlo simulation. That ratio is basically a Bernoulli distribution which is the true underlying distribution that we're trying to estimate, unknown to us, for each walk size. What we could do is simply exhaustively generate every permutation of paths for each walk size, and divide by the total to get that distribution. But in higher dimension, the number of permutation blows up, and is intractable to solve. So we do Monte Carlo simulation which is just drawing a large number of samples to approximate the underlying distribution. The more trials we do, the more our estimation converges toward the true value according to the law of large numbers. The problem of longest walk size over 50% is irrelevant. The heart of Monte Carlo simulation is accurate estimation of a probability distribution via efficient random sampling to overcome intractability, right?

[@reysombi]

i really feel into video Game Mass effect when i see Socratica. Great job!!

[@toothlessinnovations8578]

this channel is the best among others. we need more videos on python.

[@MrBlpvivek]

oh man.. I love the narration and the background music. Great !!

[@shanepython]

The stunning beautiful woman initially caught my eye. The straight forward, easy to understand tutorials caused me to subscribe. The humor is a nice added bonus. Oh why we're YOU not my Pascal teacher in the 80's?

[@jursamaj]

Here's a way to save time for larger simulations: Make a list running of size (maximum number of steps you will take+1), setting all elements to 0 at the start. At each step, determine if you are in or out of taxi range. If in, increment your_list[step_number]. At the end of the run, you will now have data for every walk length, without running each walk length separately.

About the even/odd probability, I believe that the even number of steps has a higher chance of getting closer to the origin because even numbers can perfectly cancel the total displacement; It's easy to see if you reduce the dimension of the problem and put it on a line where you can go a positive or negative direction; Let's begin analyzing the 1,2 scenarios with one step you will in the best scenario be at at least one step away of the origin, with 2 steps you can be at 2 or zero steps away; Again with the 3,5,7... you cannot get zero displacements.

[@bahabwa]

This channel makes learning so easy

[@peristhiongo9712]

Socratica, you're amazing. Just believe in that. You've been a great source of knowledge to many I included.

[@isuryashashank]

I can relate. It gives a normal programmer the environment of a "programmer in movies". By the way, I learnt a lot. Thanks

[@deepakbharti2800]

Superb video .......I really love scifi movies and watching this video is almost same. Great Job

[@Ptr-NG]

What a delivery! Blessed be...!!

[@sebastiandonickler.6715]

I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.

[@itzhakrasooly9081]

It's perhaps worth pointing out that the question is ambiguous. As stated, the question is: "What is the longest random walk you can take so that, on average, you will end up 4 blocks or fewer from home?" When I read this, I thought it concerned the expected (i.e. "average") net distance travelled given random walks of a particular length. That is, I interpreted the question as "What is the longest random walk you can take such that you end up 4 blocks or fewer from home in expectation?" On this interpretation, the answer does not seem to be 22 -- it is (I think!) only 12! Here are my full results: Number of steps = 1 / Expected blocks to home = 1.0 Number of steps = 2 / Expected blocks to home = 1.504775 Number of steps = 3 / Expected blocks to home = 1.87875 Number of steps = 4 / Expected blocks to home = 2.18895 Number of steps = 5 / Expected blocks to home = 2.460925 Number of steps = 6 / Expected blocks to home = 2.7177 Number of steps = 7 / Expected blocks to home = 2.93355 Number of steps = 8 / Expected blocks to home = 3.142575 Number of steps = 9 / Expected blocks to home = 3.341525 Number of steps = 10 / Expected blocks to home = 3.519475 Number of steps = 11 / Expected blocks to home = 3.70665 Number of steps = 12 / Expected blocks to home = 3.87785 Number of steps = 13 / Expected blocks to home = 4.02005 Number of steps = 14 / Expected blocks to home = 4.17785

[@DavidAnderson-dm5kf]

the monte carlo comment make me laugh so loud! didnt see it coming. like your style

[@revlwalter9952]

I found the best YT Channel lol

[@sathjayaperera848]

She's the one!

[@lutpulla7183]

You mean singleton?

[@prabhashprakash]

Arislan Makhmudov NEO

[@Richard_is_cool]

I read that in David Mitchell's voice and I'm hope I'm not the only one.

[@yb801]

Neo , Matrix

[@sergiocortesgodoy]

I get 31 steps for prob>50% with 5 steps but skipping some even steps. This is pretty cool, thanks!

[@roborebel6031]

Great video!! I love this series it is both entertaining with the great sense of humor and explains everything in a way that I can understand. Did anybody else get 31 as the answer to the problem at the end of the video?

[@samelias2947]

Hi Socratica, very impressive and that makes it all the more difficult to have a different understanding. 22 seems to be the highest number that you may be able to come back with no transportation. In other words, above that number you will have to pay for transportation. That is not the same as what the problem is asking - which is the highest number that with which you'll end up 4 blocks or less from home. This number seems to be 14. In between those two numbers the probability seems to oscillate up and down, in both runs, but that's a separate observation. I'd appreciate a reply for a sanity check. Thanks

[@AjeetKumar-oc8sb]

This is so fascinating, she is my programmer teacher now

[@hv1461]

I appreciate all the efforts you put into these videos. And I'm impressed with how supportive the community was for your kickstarter campaign. I wonder if that suggests a new model for how educational content will be developed. I'm also thinking about the aesthetic you've established here and the pedagogical efficacy. I wonder if you've studied whether any increased learning efficiency emerges and it generates a return on your production costs. If so, you might have a scalable business model.

[@330iBook]

This is addicting...the humor is great

[@sayanpaul728]

Can you make a full course on Machine Learning and AI from scratch, to advanced with few project, so that a lot of other people will benefited from it. There are also some other video on the said above, but your video is stand alone. I really appreciate you for doing hard work for us. Thank You.

[@adilsher]

These are not just coding tutorials but programming mindset tutorials!

[@aldnav]

"Solemn programmer's duty"

[@MrRahul15937]

😂

[@coldarif]

Nice, you guys make it look simple and easy to understand

[@mariogalindoq]

I will try to explain why even walks are closer to home than odd walks. It is very difficult to present here the full mathematical explanation, so I will give you only an intuition. Note that the possible distance to home with only 1 walk is only 1. It cannot be 0. Therefore the set of possible distances is {1}. Note that the possible distances to home with 2 walks are 0 or 2. The distace cannot be 1. Therefore the set of possible distances is {0, 2}. With 3 walks the set of possible distances to home is {1, 3}, the distance cannot be neither 0 nor 2 Continuing with this, you can note that the distances to home, depending of the number of walks are: Walks 1: {1} Walks 2: {0, 2} Walks 3: {1, 3} Walks 4: {0, 2, 4} Walks 5: {1, 3, 5} Walks 6: {0, 2, 4, 6} Walks 7: {1, 3, 5, 7} Walks 8: {0, 2, 4, 6, 8} ... Walks 10: {0, 2, 4, 6, 8, 10} Walks 11: {1, 3, 5, 7, 9, 11} Walks 12: {0, 2, 4, 6, 8, 10, 12} Now look that, in general, the alternatives of distances that are less or equal to four are only 2 for odd walks {1, 3}, while they are 3 for even walks {0, 2, 4}. Therefore, even walks have a greater probability of ending at a distance 4 or less to the home than odd walks. The deduction of the formula for those probabilities are beyond this simple explanation. However, you can explore further reading Random_walk in wikipedia. Anyway, the limit of the Monte Carlo algorithm while the number of tests increment are those probabilities that can be deduced analytically.

[@spiderjerusalem]

Great instructions. Thanks SHODAN.

[@a2dxp168]

All examples are very well selected for the topics.

[@pankaj_pundir]

Socratica give you chills, an AI teaching you to code.

[@cbartthompson1]

This actress rocks. Hilarious script, great job keeping a straight face.

[@cbartthompson1]

"This concludes my gamble amble preamble."

[@LabGecko]

Her dry delivery completely sells it - Ulka Simone Mohanty

[@conanfortuna4665]

Simple and a very crisp code example! Thank you!

[@febryer1824]

Good Demonstration of the technique, but I have a small restraint on the code! There should be no for loop for the number of blocks n in the second part of the program, and for n=30, the % of the no_transport is ~ 41 for 10,000 experiments.

[@user-lq7lg5jt4k]

i love the ambiental electronic bird chirp stuff

[@thebuggser2752]

What a great presentation!

[@лекарстванет]

Really nice and useful.You are my favourite robot now .

[@nakulv2761]

5:06 was really funny :D

[@pradeep422]

thts sound of racing

[@kino.kylo.kin1]

Mois eisley space station :p

[@bigfootpegrande]

They should rename it to Canto Bight Method

[@SomeOtherPooma]

More accurately: "you will seldom find a /less/ wretched hive of scum and villany..." It's the land of the super rich, also they have sun, and very large boats.

[@MyLinuxToyBox]

I love the way she speaks.

[@havarchitecture4251]

I LOVE YOU! excellent presentation!

[@NewyJimmy]

Haven't seen your channel before but I quite enjoyed this video

[@sashwotkoirala3934]

So for east its (1,0) because of x increase by one but for the west, its (-1,0). Is it because east and west are lined up in the x-axis.

[@mainak_das]

wow!! it blew my mind!!!