Ah, my favorite way of figuring things out...

Just push the numbers up to ridiculous heights, and generally the reasoning becomes obvious. (I'm sure there's a name for this, but whatever)

Anyway, this is definitely a popular problem, run across it a few times (including the movie Cheebee mentioned, 21). I don't find the answer much of a surprise, but I guess I am quite good at math

LuisPacheco said: Hi, first let me start by reintroducing myself. I'm the poster formerly known as LuStaysTru. Lost my password.....I came back just for this lol Well anyways, I believe this to be what is called the "Gambler's Fallcy". The odds in fact do not change. From wiki: Now suppose that we have just tossed four heads in a row, so that if the next coin toss were also to come up heads, it would complete a run of five successive heads. Since the probability of a run of five successive heads is only 1⁄32 (one in thirty-two), a believer in the gambler's fallacy might believe that this next flip is less likely to be heads than to be tails. However, this is not correct, and is a manifestation of the gambler's fallacy; the event of 5 heads in a row and the event of "first 4 heads, then a tails" are equally likely, each having probability 1⁄32. Given the first four rolls turn up heads, the probability that the next toss is a head is in fact, . While a run of five heads is only 1⁄32 = 0.03125, it is only that before the coin is first tossed. After the first four tosses the results are no longer unknown, so their probabilities are 1. Reasoning that it is more likely that the next toss will be a tail than a head due to the past tosses, that a run of luck in the past somehow influences the odds in the future, is the fallacy.

It's not really the same thing.

When Monty opens a door, he knows what he's doing. Say you aways keep the door you first chose. It would be the same thing as just choosing a door and seeing if it has the car. What are the odss of choosing the right one between the trhee doors? 1/3. So if you decide to always keep your door, your chances of winning are 1/3. Now since always changing your door is complementary to that, it gives you 2/3 of getting the car.

EDIT: Take a look at this: http://www.andafter.org/images/album/design-grafico/infograficos/Monty_Hall_a.GIF

oh my god this is old as shit.

People still don't know this ? I thought this is getting teached in every school by now...

Just look what richardhutnik posted and it's veeeery easy to understand.

Let there be a million doors and one of them has the prize in it. Pick one, your chances to win are 1/1000000 at the moment. The host closes every other door except for 2, naturally there is only the one you picked at the very beginning left and a second one.

Your door STILL has the probability of 0,000001%, thus the other door IS in 999999 cases the right one.

If your odds start at 1/3 they stay at 1/3.

Of course Monty knows what he's doing. He knows which door has the car. If you choose the goat he'll show you a door with a goat. If you choose the car, he'll show you a door with a goat. See how nothing changes there either. The odds at the start are 1/3 and they don't change. It doesn't even become 1/2 it stays at 1/3.

A simulation (only works on IE ¬¬) : http://www.grand-illusions.com/simulator/montysim.htm

I got 31-69 keeping and 66-34 changing over a thousand tries each.

Read about it last week. The simplest way I can break it down is that if you stay with your choice, you only open one door on the three. If you switch, it's as if you opened two doors. Another way to see it is that you have 2/3 chance that you picked the wrong door, 1/3 you chosed the right one. If you picked the wrong door, switching will win.

Well when I first heard about it I also thought it was 50:50 (that was in tenth class or so), but if you already knew the correct answer you're probably much smarter than many many high educated people. (Read it up what I mean in the wiki article)

Maybe it's just me being dense but you already knew 999,999 doors did not contain the car. 999,998 are revealed to be goats. So where's the new information? You weren't given any. You have the same information you always had, that 1 box out of a million had a car. Now it could either be door #1 or door #2. The chances remain the same for each and that's 1 in a million.

thats an amazing book btw

The example I gave I believe I got out of a book, and it made it clear to me.  I originally thought it was 50-50 before I happened to get ahold of that example from the book.  I don't recall which book I read it in though.