DM's who want you to Roleplay but can only say "No."

[Knaight]

Actually, you misunderstand it as well. It's never guaranteed.

The thing is - choosing the first door has a 33% chance of getting you the item. Choosing the second door gives you a 50% chance of getting the item. It's easier to visualize if you have 100 or more doors, and they open all but one other door.

I said "you are guaranteed to pick correctly within that set if the wanted object is in that set*". If it's within the door you picked the first time, then switching obviously doesn't produce it. Moreover, that 50% chance is incorrect, the chances are 1/3 and 2/3 between the first door and the second door (representing both of the other two doors). At no point did I, or anyone else, claim that there was any way that one was guaranteed to get the wanted object if it was anywhere in the initial problem space. Though I will say that the odds of getting it asymptotically approach 1 as the number of doors approach infinity.

*Another way to put this would be that if you switch you won't accidentally pick one of the doors that you already know to be wrong.