Here's the explanation I like to use every year when this makes it to HN: You pick door 1. Out of three doors you have a 1/3 chance of having a car behind your

Here's the explanation I like to use every year when this makes it to HN: You pick door 1. Out of three doors you have a 1/3 chance of having a car behind your door. The chance that the car is behind one of either of the other two doors is 2/3. Let's pretend that instead of opening a door and revealing a goat, Monty instead says to you "You can switch to both of the remaining doors. If the car is behind either one of them you get to keep it." Your likelyhood of getting the car by switching is now 2/3. Instead, Monty does the statistical equivalent: He allows you to know for sure which of the other doors definitely has a goat.