The thing that made it click for me is to think about having multiple trials. Only one of the three doors has the car. So you have a 1/3 chance of correctly pi

The thing that made it click for me is to think about having multiple trials. Only one of the three doors has the car. So you have a 1/3 chance of correctly picking it and 2/3 of the time you'll pick a wrong door. Monty opens a door that he knows doesn't have the car. Since 2/3 of the time, you've picked a goat, knowing where the other goat is means switching will guarantee you get the car in those 2/3 of the trials in which you picked a goat initially. So if you always stay with your initial pick, you keep a 1/3 success rate over n trials. By always switching, you get a 2/3 success rate over n trials.