Monty Hall Bsuinss

[Bicephalous Bob]

if monty chooses the door randomly, it doesn't matter whether you switch

switching only makes sense because you're able to use the information monty has about the game

this aspect is typically not emphasized in the problem nor in the solutions, which is why many people consider the problem to be misleading

[Bicephalous Bob]

Monty knows where the car is, I mean, and he uses the information in deciding what door to open. I guess the problem isn't exactly misleading, but many popular explanations are.