the monty hall problem
17 April 2006 - 12:48pm
It's hard to believe, isn't it? After all,
when the host opens one door there's a straight choice between two doors
- one hiding a goat, the other the car. The argument that there's a fifty-fifty
chance of winning is a very seductive one - but it's wrong.
The problem is based on a real-life scenario from the American TV gameshow Let's Make a Deal and gets its name from the show's host. The problem gained notoriety when it became the subject of the syndicated American newspaper column Ask Marilyn. Responding to a correspondent who posed the problem, Marilyn vos Savant provided a detailed explanation of the correct answer, explaining that there is a two in three chance of winning the car by switching doors.
The outcome is so different from our intuition that it is very hard to accept. Indeed, after her first explanation Marilyn received a vociferous postbag from a disbelieving public. Many letters came from indignant mathematicians who failed to agree with vos Savant.
The true result, however, is quite easy to verify. I've written a simulation of the Monty Hall Problem in Flash to try out for yourself.
run the simulation
Have a go! Choose a door, and decide whether to stick or switch when prompted. At the end of each trial you will be given a summary of the effectiveness of your strategy. Perform a large number of trials to get a more accurate result.
Not convinced? Here's my attempt at an explanation:
For further reading, chapter three of "The Magical Maze" by Ian Stewart (Weidenfeld & Nicolson, ISBN 0-297-81992-5) explains the mathematics behind the Monty Hall problem and gives further examples of questions of probability that give counter-intuitive answers.
Google search: 'Monty Hall Problem'
Official "Let's Make A Deal" website
The problem is based on a real-life scenario from the American TV gameshow Let's Make a Deal and gets its name from the show's host. The problem gained notoriety when it became the subject of the syndicated American newspaper column Ask Marilyn. Responding to a correspondent who posed the problem, Marilyn vos Savant provided a detailed explanation of the correct answer, explaining that there is a two in three chance of winning the car by switching doors.
The outcome is so different from our intuition that it is very hard to accept. Indeed, after her first explanation Marilyn received a vociferous postbag from a disbelieving public. Many letters came from indignant mathematicians who failed to agree with vos Savant.
The true result, however, is quite easy to verify. I've written a simulation of the Monty Hall Problem in Flash to try out for yourself.
run the simulation
Have a go! Choose a door, and decide whether to stick or switch when prompted. At the end of each trial you will be given a summary of the effectiveness of your strategy. Perform a large number of trials to get a more accurate result.
Not convinced? Here's my attempt at an explanation:
- There is a one in three chance that the car is behind the door you originally picked.
- There is a zero in three chance that the car is behind the door Monty picks (because he always picks a goat).
- There must therefore be a two in three chance that the car is behind the remaining door.
For further reading, chapter three of "The Magical Maze" by Ian Stewart (Weidenfeld & Nicolson, ISBN 0-297-81992-5) explains the mathematics behind the Monty Hall problem and gives further examples of questions of probability that give counter-intuitive answers.
links
List of sites dealing with the Monty Hall ProblemGoogle search: 'Monty Hall Problem'
Official "Let's Make A Deal" website