20 February 2012

When common sense is senseless: the Monty Hall Problem

How often have you heard this: "It's just common sense"? Probably far more often than you care to remember. Common sense is often seen as a sort of innate intuition that leads us to the correct conclusions only a moron would deny.

However, as I will show in this and the following article, common sense can also lead us to the wrong conclusions, indicating that common sense is not to be trusted.

Consider the following problem. In this problem, a player is offered the chance of winning a car. The player is presented with three closed doors. One door is hiding a car, the two other doors are hiding a goat. The trick is to select the door hiding the car.

How the game is played can be seen in the following video clip on YouTube:

Now, let's look at each step separately as far as we can. First, the player is confronted with the three closed doors. He or she has no idea where the car is, every door has an equal chance of hiding it.

The player, who has no idea where the car is, selects a door. Unless the player has a preference or is superstitious, this is a completely random choice:

The host of the game, who knows where the car is, must now open one of the two other doors and reveal the goat behind that door. He/she will not reveal the car. This means that the car is either behind the closed door previously chosen by the player or behind the other closed door. The host graciously offers the player a chance to change her/his mind and switch to the other door.

The player has now two options: switch to the other closed door or stay with her/his original choice. What should he/she do to maximise her/his chances of winning? There are three possible answers:
  1. Switching increases the chances of winning
  2. Staying with the original choice increases the chances of winning
  3. It makes no difference at all
Did you figure it out? Write it down, so you remember what you chose. Don't cheat! I'll wait. Answer in the next article...

Fine print:
 I have written this article on my personal "authority" as a computer programmer and skeptic. Any errors, inaccuracies, omissions or other flaws are therefore mine, and mine alone. While I have done my best to be as accurate as possible, this article is nevertheless open to correction, modification or refutation. Please do not hesitate to comment or send me an e-mail if you think something is wrong. I will do my utmost to reply to every comment or message within a reasonable amount of time. Please consult a properly qualified professional before using any information in this and any other of my articles.

This page was last updated on 21 February 2012

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