More intuitive explanation. Let's play a similar game with three doors, two goats and a car. But you get to pick one of two rules to play by: A) You get to p

More intuitive explanation. Let's play a similar game with three doors, two goats and a car. But you get to pick one of two rules to play by: A) You get to pick one door you want and get what's behind that door. B) You get to pick one door you don't want and get the better prize behind the other two doors. Pretty much everyone is going to pick rule B. So after picking the door you don't want I will open the other doors. If the car is behind one of those doors I will always open that door last. Does the last sentence make you wish you picked rule A to play by? Heck no. We already know that one of those two will be a goat. The order I open the doors won't change anything. Even if I let you retroactively switch to rule A after opening the first door? This is what trips people up. They think they're getting new information and that their original door choice may be incorrect. But in this version of the game it's easy to see that we're not changing our choice of door, we're changing from the better game rule B to the worse rule A. So the correct choice is to always stick with rule B. Now we map the rules onto the real Monty Hall game. Rule A is pick the door you want and stick with it. Rule B is pick the door you don't want and switch. So the correct choice is to always switch.