Unbelievable, every second of this 19-minute, 13-second video was characterized by a very clear sequence of sentences that meshed together, without any mistake, to form a very crafted, well-understood explanation of all the ideas together. For instance, what makes the difference between most who explain and those like you is found here at 15:38: "Because when I'm in this loop, this is going to run for a long time when p is large, because it's barely ever gonna see two loses in a row." I was following along but it didn't completely click in a concrete sense until you grounded the logic with saying "because it's barely ever gonna see two loses in a row." You founded all explanations with some set of "extra words" that made everything you say click with minimal rewinding and mental pounding to understand them, and I find that two types of teachers/explainers/communicators exist in this world, those who consistently don't employ those extra words and those who consistently do incorporate them. I might nickname that feature the "connecting back to concrete-land" or "those extra few click words" whose presence or absence in speech make the difference between it clicking to an audience and it not. And the absence of such extra words, when multiplied over the many chunks of speech to hundreds of someone's utterances over a video or lecture, can culminate to a superficial understanding where you are left in abstract land but have an itchy, uneven feeling of why the circle around the explanation didn't make a complete closure of concreteness or a filling understanding. Those extra words, the attention to detail, and ensuring your learners really following along all the way to the end and closure of the circle of the explanation you intend to communicate really makes the difference in reaching a wider audience and making critical concepts well-understood. Thank you for the video!!

Another cool thing about your approach is that your "toy example" follows closely from Baye's original paper in which discussed tossing balls onto a flat surface and then locating an unknown point more and more closely. Thank again for these great videos!

Superb! What is so remarkable in your presentation is the balance that you bring to the challenge. Each approach has strengths and weaknesses and it is essential to keep those in mind at the start. We are currently weathering a huge storm in which someone advocates for "their" method and says explicitly (or strongly hints)  that every other approach is garbage or "not science". That makes your channel a big breath of fresh air! Thank you!

I am not an expert, but I enjoyed the dart and circle/square explanation.  You should start something like khan academy.

You make some valid points in the end of your videos and you even give the difference of perspective between someone who does engineering and pure science

This channel is the BESTESTESTESTEST data science channel I've ever watched. AMAZINGLY wonderful. THANKS dude

I use MC for some fabrication process variation simulations in my research, and I must say this is one of the better explanations for the simulation. Good job.

Couple of things:
1) The rules, emerge from understanding the problem. In my case the behavior of the material, possible probability distribution of faults (from case studies of real fabrication imperfections). You use MC when you know what the real world solution would look like but you need a more approachable, repeatable, or approximate approach to the solution (Eg: I  cannot just fab the chip every time I want to see the impact of fabrication imperfections).

2) not everything has an analytical solution, or more correctly saying, the solution is very complex, having to consider various factors to reach the "true" solution. It's in scenarios like this where the application of MC truly shines.

Thanks for taking the time to put this together 🤝

Your videos are so clear and simple and I believe you will be the top youtube in data science concepts in the near future. One good suggestion will be to provide a snapshot of the things you wrote on board.

Your second example immediately reminded me of the negative binomial distribution.  =)

I am really happy with you and eric grimson  who taught  me lots of maths

love all the videos I've watched so far! very easy for beginners to follow and learn!

As always, amazing explanations. Thank you!

again, thanks for the splendid easy to understand  explanation.  
coming up with  a recursive  formulae seems very challenging.

I have understood it perfectly. Thanks for the video.

Wonderful presentation. Ticks all the boxes. Look forward to watching your other videos.

Thank you so much! :) , you offer nice, easy to follow explanations and different perspectives for important data science concepts.

Thank you bro, your contribution benefits many people from developing countries, God bless you

@ritvikmath, great video! You sub-consciously made me find the analytical solution for the 'harder problem' using algebra! Being a bit rusty, it took sometime. However, I did manage to eventually solve it. Its a shame that YouTube doesn't allow pictures to be shared in comments, otherwise, I'd have shared my method!

Surely you could look at the run times of various experiments too and infer what kind of graph it’s going to be.  You could use a curve fit to interpolate the expected graph.