In addition to the "100 door" formulation that helped me a lot, the way I rationalise it is that: * When you choose your first door, the chance the car is behi

In addition to the "100 door" formulation that helped me a lot, the way I rationalise it is that: * When you choose your first door, the chance the car is behind that door is 1/3, for obvious reasons. * When Monty opens the goat door, nothing actually changes that is relevant to your odds. He is always going to open a goat door, whether your first choice is a car or a goat, so it's basically irrelevant. He hasn't move the car, he hasn't given you any information you didn't already know when you made your first choice. So the odds of your first choice being correct can't have changed. They are still 1/3. * The only possible outcomes are that your first-chosen door has the car, or the other remaining door has the car. The probability if your first-chosen door having the car is (still) 1/3, and the probabilities of all possible outcomes must add up to 1, so the probability of the other door having the car are 1 - 1/3 = 2/3.