Monty Hall is the Devil

There was an article in the New York Times last week about how people rationalize their decisions and how the concept of 'cognitive dissonance' comes into play in human decision making.

The example that they used, 'The Monty Hall Phenomenom' was fascinating. Here's the scenario: You are on a game show and the host (Monty) shows you three closed doors. Behind one of the doors is a car. Behind the other two are goats. You are asked to pick a door.

After you pick a door, Monty will open one of the two doors that you did not pick, and reveal a goat. Now you have a decision to make: Do you stay with the door that you picked, or do you switch your pick to the other remaining door?

Most people will stick with their original selection. (This is where the cognitive dissonance comes in.) People that are math oriented will think that there are only two doors left, there is one car and one goat, so it is even odds.

They are wrong. You should switch doors.

WHA?!?

At this point, you are likely to think that I, the New York Times, and the scientists involved in the tests are all crazy. Just like my wife did. (does) But it is true, you are twice as likely to win the car if you switch your pick to the other door that remains.

Think about it for a while. Still not make any sense? Of course not! It is insanely hard to get past the 50/50 odds point. So do what I did... draw out the possibilities:

Cases Door1 Door2 Door 3
Case1 Car Goat Goat
Case2 Goat Car Goat
Case3 Goat Goat Car

The car can only be behind door 1, 2 or 3, so there are only three possibilities. Now lets assume that you pick door number 1. Put a rectangle around what is behind door number 1 for all three cases. Now act like Monty Hall. Circle one of the remaining goats behind either of the remaining doors. So far so good.

So the rectangles are your pick and the circles represent the door that Monty opened. You can see that you win in only one out of three cases, which makes sense.

Now look at the choices that don't have a circle or rectangle around them. Um, in two out of the three cases, if you switch, you win the car. In one case, you would give up the car for a goat. So the odds are better if you switch.

Let that sink in.

Still frustrating, isn't it?

Monty Hall is the Devil.