I think there is an easy and intuitive explanation: Two thirds of the time, you pick the wrong door on your first choice. So far, so obvious. Now, you picked a

I think there is an easy and intuitive explanation: Two thirds of the time, you pick the wrong door on your first choice. So far, so obvious. Now, you picked a wrong door, Monty opens the other wrong door, and there are only three doors. Obviously the remaining door has the prize. Every time you pick the wrong door, and then switch, you win. That means two thirds of time, if you switch, you win. That makes switching the right strategy.