This post is of no interest to you unless you have trouble with the Monty hall problem.

I never believed the "correct" answer to the "Monty Hall problem." (In brief: you're on a game show and pick a door, hoping for a new car. The host opens one of the other doors and reveals a goat, and then gives you the option of switching to the unopened door you didn't pick. Should you do it? The problem presumes you prefer cars to goats, despite goats being cuter and more ecologically friendly and producers of feta.) It turns out that you always should, even though in my mind it shouldn't matter. No matter how many times I heard it explained I still couldn't get it. In part this is because if the host opened one of the other doors without knowing what lay behind it, and just happened to encounter a goat, the probabilities would in fact be equal. But I finally read an explanation which helps me to wrap my head around it:

It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens 999,998 of the other doors revealing 999,998 goats—imagine the host starting with the first door and going down a line of 1,000,000 doors, opening each one, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat. A rational player should switch.

Thanks Wikipedia!