One of my favorite critical thinking games is the "Monty Hall Problem" as it is yet another demonstration of how our intuition fails us where reason succeeds. The problem is as follows:
Imagine you are on a game show where there are 3 doors and behind two of the doors are goats (one behind each door) and behind one of the doors is a new car. Assuming you like new cars and don't have some weird goat fetish, you want to pick the door behind which is the new car. You make your choice.
Now the host of the game show opens one of the two doors that you did NOT pick to reveal one of the two goats. The host asks you if you want to stick with your choice, or switch doors. What do you do? Think about it for a moment then read on when you have your answer.
Most people would stick to their original guess figuring that the odds are 50/50, and they would kick themselves if they switched and lost, but you are not like most people. You know that your chances of picking the right door at the start of the game were 1 in 3, now, based on the elimination of one of the doors that definitely does not have the new car behind it, IF YOU SWITCH you have a 2 in 3 chance of winning the car. If you don't, your chances remain 1 in 3. Based on this information, you switch doors.