2008-02-06

The Monty Hall Problem

I pride myself on understanding stuff. But I don't understand this:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
For whatever reason, this is known as The Monty Hall Problem. It is a counter-intuitive problem because, for some reason, it IS to your advantage to switch your choice. In other words, there isn't a 50-50 chance of getting it right if the game show host offers to change your decision.

Apparently the important variable to consider is the Game Show host - he knows what is behind each door. The fact that he knows means that it is to your advantage to change your choice. For some reason there is a 2 in 3 chance of getting the right answer. But if he didn't know - and just opened some random door - then the chance of getting it right remains 50-50.

So if you find yourself in a game show and this happens, you can thank me for helping you. Just give me a share of the prizes.

3 comments:

Reuben Kincaid said...

I don't know about you but I'd rather the carbon-neutral, left leaning, chaddonnay sipping, latte drinking, eco-friendly, US recession advocating, U2 loving goat. Instead of the gas gazzling, right wing, environment polluting, fossil fuel burning, GW Bush loving car.

Then again, if the car is a lifted 100 series Landcruiser, with bullbar, winch, spotties, UHF, HF, rear wheel carrier, secondary fuel tank, dual batteries and a draw system - then I'd think again. Mmmmm, nice!

Ron Lankshear said...

Off the Wiki site was a link to Lets Deal show with a link to a Java game

http://people.hofstra.edu/steven_r_costenoble/MontyHall/MontyHallSim.html

I did 20 of each and on stay 5 and on switch 14. SO the maths is right or is this proctor hoc

Ron Lankshear said...

I like this
Explanation # 2. When you start out there are three doors. Your chance of guessing right on the first pass is 1 in 3. We all probably agree on this. The probability that you were wrong is 2 in 3. Most likely the money was behind one of the 2 doors that you didn't choose, as a matter of fact twice as likely. Before Monty shows you the empty door, would you be willing to switch your one door for the other two? I assume you would (that's actually what you get to do if you switch: you get both of the other doors; at least one just happens to be empty.) You know that at least one of the two remaining doors must be empty. They both can't be hiding the money. So when Monty shows you that one of those two doors is empty, it shouldn't be a surprise. He is just telling you something you already know - that one of the two remaining doors is empty. The odds have not changed. Most likely you still picked the wrong door initially; most likely the money is behind one of the two other doors; Monty does give you clue about which one NOT to switch to (since it is empty), and therefore you should switch to the other closed door.

from http://www.dcity.org/braingames/3doors/explain.htm