# Python: Monty Hall modeling

You’ve all heard this classic statistics problem, based on an old game show:

A contestant is shown 3 doors. Only one of those three doors hides something of value to the contestant (perhaps a new car), while the other two contain nothing. The contestant chooses one door, but that door remains closed. The host then opens up a 2nd door, and this door is always a losing door. At this point, the contestant may choose to now open the originally-chosen door, or switch to and open the last remaining door.

So why is this interesting? It turns out that the way to maximize your chances of winning is to always switch, and this maximized chance is 67%. It also turns out that this is totally non-intuitive, and that most people think that, if the contestant always switches, the chances of winning are at best 50%. If you haven’t heard the solution to this problem before, you should think through it and see what you expect the chances of winning are under the two conditions: After the contestant chooses a door, and is subsequently shown that one of the other two is a losing door, [1] the contestant always switches to the remaining door, or [2] the contestant never switches. After the jump, I’ll explain this intuitively and then show a Python script to simulate this problem.

# More Puzzling

In a previous post, I discussed my attempt to write a program to solve a puzzle. I never updated that post because, well, I ran the program all night and it didn’t find the solution!

I had made up a fake puzzle that I knew had a solution for testing, and the program could solve it in 15 minutes. But it couldn’t solve the one I had recorded for the real puzzle. I figured (and hoped) that I had simply recorded it wrong and to check, I re-recorded the pieces and tried again. And it worked! Here’s how: