There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts.
Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely wrong now that any statistician can so easily just code up a computer to run it a zillion times and get an empirical answer. But despite that, your intuition might still say otherwise.
I'm fascinated by the gap between intuition and logic particularly because it can be closed as soon as you find the right lens to take to a problem. I like the example in the article about 100 doors, or even a million doors, where it really helps drive it home in your gut.
That moment when you find the right intuition for a thing is a magical one that makes me love math.
Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely wrong now that any statistician can so easily just code up a computer to run it a zillion times and get an empirical answer. But despite that, your intuition might still say otherwise.
I'm fascinated by the gap between intuition and logic particularly because it can be closed as soon as you find the right lens to take to a problem. I like the example in the article about 100 doors, or even a million doors, where it really helps drive it home in your gut.
That moment when you find the right intuition for a thing is a magical one that makes me love math.