Monday, 1 November 2010

KataMontyHall

I was at the local Ruby User Group last night, and I coded up KataMontyHall (see below) as a prepared Kata in front of the group. I got some great comments and feedback while I was coding, and I think the solution I ended up with was better than any I had created by myself during my practice sessions. I also got some new ideas about different approaches which I plan to try out and see if they improve the code even more.

Dave Hoover was visiting from the US, on his way to a speaking engagement at Öredev. He and I were both surprised to discover a common interest in the Monty Hall Dilemma. Dave has previously worked on it, and he showed us some code that he wrote 5 or 6 years ago when he was still learning Ruby. He even wrote an online version of the game when he was first learning ajax, that you can play yourself!

The Monty Hall Dilemma
There is a gameshow hosted by Monty Hall where contestants try to win a big prize, which is behind one of three doors. The contestant begins by choosing a door, but not opening it. Then Monty steps forward and opens one of the other doors. He reveals a goat (!). Then the contestant has the choice of either sticking with the door they have already chosen, or switching to the other unopened door. Whichever door the contestant decides on will be opened, and if they find the prize, they get to keep it. (I'm not sure what happens if they get the second goat!) So what's the best strategy? Stick or switch?

People are biased towards sticking with what they've chosen, and the vast majority of people stick with the door they choose originally. Intuitively there should be an equal chance of the prize being behind any of the three doors, so it shouldn't matter if you stick or switch. However, in this case, your intuition is wrong. You are twice as likely to win the prize if you switch to the other unopened door.

I am not the only one to think this result is incorrect, apparently famous mathematicians have also refused to accept it. What finally convinced them, was a computer simulation. Hmm I thought, that sounds like an interesting piece of code :-)

Pigeons are smarter than Humans
I heard about the Monty Hall Dilemma listening to the quirks and quarks podcast. Apparently humans are strange, because they don't learn to switch doors. Some researchers set up the same problem for pigeons, with birdseed behind one of the doors, and found the birds quickly learnt to switch doors. You can read the research for yourself!

So if you, like me, are keen to prove yourself more intelligent than a pigeon, why don't you spend some time writing a little program that simulates the game? If you get it right, your version of KataMontyHall should clearly show that switching doors is the best strategy :-)

2 comments:

Jörgen said...

A nice explanation of why you should switch door.

http://www.youtube.com/watch?v=koPBkK_Ra-k

Emily Bache said...

The reason people want to keep the first door they choose could be because of the psychological effect known as the "Illusion of control" http://en.wikipedia.org/wiki/Illusion_of_control - mentioned to me by Henrik Berglund