Thursday, September 08, 2005

To switch or not to switch



The Monty Hall dilemma

You are probably familiar with the problem from the TV show ‘Lets make a deal’. Here is the problem. There are three doors and there is a car behind one of the doors and goats behind the other two doors. You don’t know which door the car is behind, but the game show host knows where it is. You get to pick a door and once you pick a door, the host will open a door with a goat behind from the remaining two doors (i.e. the doors you didn’t pick). Then you have two choices, either you stick with the door you originally picked or switch to the other door.

What would you do?

According to Marilyn Vos Savant, if you switch you have a higher probability to win. The reasoning being that 2 /3 times you will pick the wrong door and when the host opens a door with the goat, he has no choice but to pick the only other door with the goat behind. So 2/3 of the times if you switch you will get the car.

Not convinced yet? There is a computer simulation for this problem, which is fun to try out. Go to http://www.cut-the-knot.org/hall.shtml

So would you switch or stick?

4 comments:

buckwaasur said...

nice one...had me completely foxed when u posed it to me...

here's an interesting link to the monty hall problem on wikipedia:

http://en.wikipedia.org/wiki/Monty_Hall_problem

josh said...

More than the gift, the thrill is in our ignorance, which is stimulating and frightening at once. Like life.

Animesh said...

[Answer inspired by the Rishyashringa story]

Depends on whether you "really" want the car, or the goat :-)

Nice blog.. great to see you find so much time from grad school.

Animesh

Atrakasya said...

I've read that the "correct" answer according to Marilyn Vos Savant is to switch.
However her logic calculates the chances after the first door has already been opened as if the first door is still closed.
Very clearly, once the first door has been opened - it does not figure into any calculations. Hence the chances do not remain 1/3rd any longer - they just become 50:50
Based on this flaw in Marilyn Vos Savant's logic, I am inclined to believe that her highly tom-tommed superior IQ was not that superior.
What is amazing is that people still get taken in by her skewed logic, and that she was so in love with her apparently non-intuitive solution that she pushed it right till the end.