I love situations that challenge our “Common” Sense.”
Imagine you are dressed as a giant chicken and a crowd of strangers, each dressed more strangely than you, are all shouting their opinions, but the decision is up to you. Monty Hall himself has said that a car is behind one of the three curtains before you. Goats are behind the other two. After much crowd urging, you select curtain number 2. Instead of showing you what is behind your curtain, Monty shows you the goat behind curtain number 3 and then says, “Do you want to stay with curtain number 2 or do you want to switch to what is behind curtain number 1?”
Given that Monty knows where the car is and that he is bound by his contract to always reveal a goat behind one of the other curtains, the question is: Should you stay with curtain number 2, switch to curtain number 1, or does it not matter?
A veridical paradox is not a logical paradox as much as an intuitive one and the answer to the Monty Hall paradox qualifies as highly counter-intuitive. Most people assume that there would be no difference in odds if you make the final switch, but that is wrong. Neither should you stay with your first choice. The fact is, given the conditions mentioned in Monty’s contract and his natural honesty, you will get the car 1/3 of the time if you stay pat and you will get a car 2/3 of the time if you switch.
As a group, we really aren’t that good at evaluating the odds…