This video took so long to make it makes me feel sad. I'm actually so proud of this and it is an idea that which I think is so elegant. I really hope you enjoy the video and if enjoy, be sure to like and subscribe. :D

This is my submission for the Summer of Math Exposition, hosted by @3blue1brown

Gigantic Credits Go To The Following:
Franek1334 - Helped me hugely with the animations in 3D. An incredible teacher and coder who helped a lot.
Abulafia - Helped me smooth out the animations and improve the quality of the video. (and save a couple hours)
Uwezi - Also helped me with the animations in 3D.
Aiyush Gupta - Helped produced the model for the binomial distribution and trinomial distribution and by helped, I mean saved me from torture. Actual Legend. Helped a lot with some major design choices too. Seriously big credit.

If you want to get in touch - [email protected]

Animation of the Pentacharon - JasonHise at English Wikipedia, Public domain, via Wikimedia Commons under a CC0 License which I definitely don't know how to code.

Timestamps:
0:00 The Game
1:23 Introduction
2:21 Binomial Expansion
6:08 Trinomial Expansion
11:46 Probability Distributions
13:07 Quadnomial Expansion?
16:47 Conclusion