fuckin probability

for what it's worth, i was actually pretty good at discrete math, calculus, and the little bit of probability i took in college.
came across the monty hall problem this morning. this is one of those weird things in math that gets a lot of smart people arguing and calling each other idiots. the setup for this is simple, and based off the show 'let's make a deal': you pick one of three doors, one has a car behind it, the other two doors have goats. the host, monty, opens a door, which has a goat behind it, and offers to let you switch which door you've picked. does switching doors help your chances of winning the car?


the fuck you solution is that, yeah, it does. by a lot. but only under certain circumstances that almost everyone already assumes.
eg: if monty opens a door at random that still always has a goat behind it, it changes the percentage of how often you win if you choose to switch doors. the solution above only works when monty will always open a door with a goat behind it, after you've chosen your door, and knows which doors have goats behind them, and always offers you the opportunity to switch doors.

now that i've got a handle on this, i'm going to take a crack at the two envelopes problem.