There is a linguistic illusion at work here. In the Monty Hall problem, you think you are choosing between one door and one other door. But in fact, you are ch

There is a linguistic illusion at work here. In the Monty Hall problem, you think you are choosing between one door and one other door. But in fact, you are choosing between one door and two doors. The choice is between "this door" (1/3 probability for winning) and "all other doors" (2/3 probability for winning).