The real trick is in the wording. You choose a door. Monty chooses a door that is NOT be the car, leaving one that may or may not be the car, depending on if th

The real trick is in the wording. You choose a door. Monty chooses a door that is NOT be the car, leaving one that may or may not be the car, depending on if the contestant was wrong. In words Monty pretends to be removing ONE door from the pool of choices, but he's not doing that - he is removing ALL possible doors except for the one that is a car if you were wrong, or a goat if you were right, and then saying (truthfully) that every single other one is a goat. When there are 3 doors, that is one that gets discarded. But that's the tricky word play. Now, if you did it with 100 doors, Monty isn't simply removing 1 option to give you the appearance of a 50/50 chance. He is removing ALL of them except for 2 - one that he shows is not a car, and the other that you have to decide whether your first choice was right or not. Following the same exact sequence, he removes 97 of them from the pool because they are all goats, leaving the one you chose, the one he says is NOT a car, and one that is the car if your original choice was wrong, or a goat if your original choice was correct. Suddenly it is super obvious that this is no 50/50 choice. That's how the Monty problem actually scales. Looking at it from a game with 100 doors makes it extremely obvious that the person's first bet is more likely to be wrong than right, and that changing is the obvious choice to make since the odds are 1/100 that your first choice was right, and 99/100 that the one Monty left behind is the car. Hence in the normal way of playing the game, it is a 2/3 chance the contestant is initially wrong, and should always choose to change their choice.