The Monty Hall Problem is a fascinating piece of mathematics and probability. The above video by Numberphile gives a great, in-depth, mathematical explanation of how it works, and they also have a few other videos on the problem. For a bit of history on it, as well as how and when everyone “corrected” the world’s smartest woman, Marilyn vos Savant, head over to Priceonomics. It’s an engrossing read, clearly explaining the Monty Hall Problem, and showing how much controversy it provoked. I love the fact that, despite knowing the correct answer, probability problems still appear odd to us.
If you ever come across this, remember: always switch doors. Onwards!