I think the reason that people can't shake off their intuition is that the intuition is based on the idea that the host (Monty Hall) has agency. The specific p

I think the reason that people can't shake off their intuition is that the intuition is based on the idea that the host (Monty Hall) has agency. The specific posing of the problem is that the game is you are presented with three doors, you choose one, and the host opens a door showing a goat, and you have to decide if you want to switch. The problem is that people imagine a game where you choose a door and the host decides whether to open a second door to convince you to switch OR they open the door you chose to show the goat. So given that they CHOSE to open a goat-door, is it the right move to switch? That problem is a game theory problem and requires that you understand the strategy that the host is employing; the intuition is that the host WANTS you to lose, so will only open the goat-door if you chose right (or has a significantly higher probability of doing so) so switching is "falling for" the trick. Re-imagining the problem as a different scenario, where you can ask to see which of two doors contains a goat, and then deciding which door to take avoids this trap. Then the solution is not obvious, but not counter-intuitive (maybe; depends on your intuition).