Can anybody explain the Monty Hall effect?

[Jeff In Milwaukee]

I've been Googling and there's nothing very helpful out there. Theory is supposed to be that you have three choices (a la Monty's three curtains) and pick one; If Monty shows you that the big prize isn't behind one of the curtains you didn't pick, you're supposed to be mathematically better off by changing your pick to the other unopened curtain. This doesn't seem to make sense -- I don't see how it would improve your odds of winning. But supposedly it does.

Any statisticians or hardcore gamblers out there?

[aden_nak]

1. I've actually see that before.

And while it doesn't make sense, from a common sense perspective, independant testing suggests that it IS the case. The site I read about it on even had a little java applet that simulated the tests so you could try them yourself.

[Ready4Change]

2. I didn't believe it, then tested it. It is a fact.

I wrote a computer program myself, and was very surprised that the results verified the effect.

[billyskank]

3. So, there's three possible options:

(1) You pick the curtain which hides booby prize no 1. Monty shows you booby prize no 2. By switching, you will win.

(2) You pick the curtain which hides booby prize no 2. Monty shows you booby prize no 1. By switching, you will win.

(3) You pick the curtain which hides the big prize. Monty shows you one of the booby prizes at random. By switching, you will lose.

So you can see that by not switching, you have a 1 in 3 chance of winning. However, if you do switch, then you can see that in 2 out of the 3 possible outcomes, you win the big prize.

Therefore, switch.

[TlalocW]

4. We went over this in a couple of

Math and engineering courses I took in college, but while I have a degree in math, I never cared much for statistics. I can dig out my notes for you if you like? :)

TlalocW

[billyskank]

5. The thing with statistics is

you have to forget about logic. If you try to work something out by logic, you'll probably get the wrong answer. For example:

The probability of getting a head when flipping a coin is 0.5. If you flip the coin twice, that doubles the probability, right? Wrong, of course, because if you flip a coin twice you are still not guaranteed to get a head.

The only way to approach probability is to calculate how many possible outcomes there are, how many of those outcomes satisfy what you want, and divide the one by the other. No matter how fancy the maths may be (and probability involves some reasonably fancy looking maths), that's what it boils down to in the end.

[Hav]

6. it's explained quite well here

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

[billyskank]

7. That's where I got my explanation (post 3) from.

[Jeff In Milwaukee]

8. Great site!

I wonder why Google didn't provide this as a result.