Here’s an example of a counterintuitive result I came to accept.
Imagine you are a contestant on a game show whereon the host (the canonical example being Monty Hall) stands before three doors.
Behind one of the doors is a brand new car, of a brand and model which maketh you swoon. Let’s say a Tesla Roadster, just to give focus. Behind the other two doors are goats, and not very attractive goats at that; at minimum, they are goats not to be compared to a Tesla Roadster.
Monty has you pick a door out of the three. After you have picked, he gestures extravagantly toward the remaining two doors, but somewhat more extravagantly toward one than toward the other. That door flies open to reveal a goat. Monty then provides you a choice:
Do you want to stick with your original pick, or switch to the one of Monty’s doors which he hasn’t yet opened?
The question you have to ask yourself is, are your chances of winning improved by switching, by staying the same, or does it not make a gnat’s ass of difference which you choose?
I shall reveal the answer some indeterminate time after I have gotten at least one guess in the comments.