This reminds me of the classic “Monty Hall” problem and its amazing and revealing effect on people. I have had intelligent friends get red faced and yell at me as they reject the outcome of the “problem”. It reveals something about human intelligence. It also demonstrates why the greatest tool science has is the “Scientific Method”

Boiled down to essentials the problem is this. You are presented with three inverted cups. Two are empty. Under the third is a pea. Monty moves the shells around, mixing them up (yes, the classic shell game). Monty knows where the pea is but you do not. You choose one of the shells, your guess for where the pea is hiding. Monty randomly eliminates one of the cups you didn’t choose, one he knows is empty. Now there are two inverted cups. Under one is the pea. Monty smiles and offers to let you change your choice of cups. Should you? Will simply switching your choice improve your odds ?Reality says yes, switch your choice. When you do that you increase your odds of having located the pea.

Most people will say, “my chance is one in three no matter what so I might as well keep my first choice” However computer simulation shows that always switching improves your chance of locating the pea.

Simple explanation is…. if you do not always switch your choice you have frozen a 1/3 chance and passed up a 1/2 chance. Monty, by removing an empty cup, has in effect started a new game, one in which your odds are fifty fifty. By not switching you choose the less friendly odds offered by the first game.

I said that the response to this problem and its solution reveals something about the human mental process — but I’m not sure just what. Thank God we have computers, they give us a “sanity” check.