A couple years ago, I heard about the “monty hall problem”, a question of probability that just was totally counterintuitive to me (and also a ton of mathematicians, so I don’t feel bad)… Here’s the situation:
You are offered a choice of three doors. Behind one is a car, behind the other two are goats. You pick Door #1 (for example). The host opens Door #2 and reveals a goat, then offers you the chance to switch your choice with #3.
Now, most people look at this and say “well now my chance is 50-50, I may as well stay”. But that isn’t the case. You actually have a much higher chance of winning if you switch doors. The reason is that the host knows what is behind the doors and deliberately opened a losing door, so while your original choice has a 1/3 chance of winning, the other door now has (odd as it may sound) a 2/3 chance to win.
You can try it yourself with this flash game over on the NY Times site:
Really, go give it a try.