Haha cool! I wasn't asking for people to read my mind, and wasn't thinking math specifically, just trying to open it up to all areas. But I will check this out now! :) Do you have a good 'glib' statement, like: 1) the problem, 2) the regular (but incorrect) intuition, 3) the counter-intuition, that's actually correct ? :)
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?
Regular intuition: switching doors doesn't matter, you have a 50/50 shot either way.
Counter-intuition: probably just check out the wikipedia article, there's a few different approaches.