From the Archives: Monty Hall

My “Day I Left Pennsylvania” led me to some archived website posts (before blogs were invented) I had written many years ago. I’m re-posting them now. Bear in mind that most of the content in this series is over 5 years old. I have left the content more or less intact. I have removed some links and added some others — but that’s it. Enjoy!


UPDATE

After John W’s skepticism, I decided to put my code where my mouth is — please see:

http://amhill.net/projects/montyhall/

It has a simulator, demonstrating the superiority of switching, based on a sample size of 10,000 or less. Source code included.  Check it out!

For those of you who remember Let’s Make a Deal the idea of the three-door choice is very familiar. For those who aren’t familiar with Monty Hall and his extravaganza of game-showness, here’s the low-down:

Door 1
Door 2
Door 3
Goat
Goat
New Car

The contestant is presented with a choice of three doors. Two of them have a goat, and one of them has a fabulous prize, like a new car, or a boat, or an evening with Brad Pitt, or whatever. (the contestants were mostly women, since at the time less women were in the workforce, therefore they were the target demographic). Anyways, here’s how it works. They pick one of the doors, then Monty reveals one of the two doors they did not choose; but the door revealed will always contain a goat. The contestant is then allowed to stick with their choice, or change it. The puzzle here is: Is it better odds, statistically speaking, to stick with your choice, or change it, after the goat is revealed? Most mathematicians have said yes in the past, but Marilyn Vos Savant disagreed. Here is a paraphrasing of her proof: Continue reading