The Monty Hall problem is a probability puzzle made famous by the supposedly “smartest person in the world” Marilyn vos Savant:

*Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?*

Vos Savant said that the contestant should switch doors because when the contest started, the odds against them were 1:3 but after one of the other doors was opened the odds were better at 1:2 on the remaining door. When a regular smart person is asked whether they want to switch, about 90% stick with their original choice because it’s self evident the odds are the same, but because the most intelligent person in the world disagrees with them and presents a slight-of-hand perpetuating the hoax, they are convinced they must be wrong,

Well, can't fool me...

Suppose the show was taped, and a week later you walked in and started watching during the second choice between the two remaining doors; what’s your odds of guessing the car? 50/50. But what if you were also the contestant from the week before? Let me repeat: everything is the same except separated by a week. Odds don’t care what time it is; you started out with 1:3 odds which changed to 1:2 odds, and they are totally independent of the door. Smartest person in the world my ass.

p.s. What’s the odds if you want the goat?