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[alway]

Or to put it another way: Imagine instead there were 100 doors. There were 99 goats and 1 car. Choose a random door. The chance of it being the car is 1%. The chance of it being behind one of the other doors is 99%.

Now imagine opening 98 doors with goats behind them, knowing beforehand where the goats were and thus which doors could be opened without revealing a car. If the car was behind one of the 99 doors you didn't choose, it is now the one door left unopened. Thus your original door still has a 1% chance of being the car, while there is now a 99% chance that the unselected door has a car.

[KingofstarrySkies]

...

MY BRAIN HUUURTS

[Rolan7]

But what if I ignore the fact that there were originally 3 doors and focused on the fact that I can now choose between two doors?

I don't understand how knowing something will cause reality to rearrange itself.

I was having the same problem, the answer is that the doors aren't equivalent.
One is the door you pointed at first, which means the host couldn't open it.  So it's not weird that they have different probabilities.

The actual math has been repeated a lot already, but that's just how I got over the weirdness factor.

[Darvi]

If you ignore the fact that there were 3 doors at first, you're not doing the Monty Hall problem.

[Orange Wizard]

I rationalise it as for the first choice, you have a one in three chance of picking the door with the car. Then a goat door is opened, and there's now a one in two chance of the final door having a car behind it.

...

It's a weird problem, in any case.

[RedWarrior0]

The host opening incorrect doors is just a distraction.

By choosing a door (let's just say Door 1 for convenience), you split the three options into two sets: Set A, which is just Door 1, and Set B, which is every single door you didn't choose (normally Doors 2 and 3)

Set A has a 1/3 chance of being correct, and Set B has a 2/3 chance of being correct.

If the host told you at this point you could switch from all the doors in Set A to all the doors in Set B, I think most people would agree to switch. That's basically what you get to do, except the host distracts you from this fact by opening doors he knows to be incorrect.

[KingofstarrySkies]

Nearly every one of these posts has made me go WTF today.

[UXLZ]

Oh, so that's why. That's totally understandable. I thought it was that you could to choose one other door and I never understood how that thing worked.

[RedWarrior0]

You do choose 1 other door, it's just that it functions the same as if you choose all the other doors and the host nicely pre-opened them for you.

[Descan]

... Assuming you're correct in your logic: Holy crap. That is actually completely understandable.

Red, you should be proud! :O!

go be a teacher you doofus pokemon

[SirQuiamus]

Obligatory.
I don't want any stinkin', pollutin', gas-guzzlin' car -- I want a goat!

[MagmaMcFry]

Fun fact: By opening the door, the moderator gives you exactly 2/3 Shannons of information.

[McDonald]

I had a brief moment of realization, but it went away. I'm still as clueless as ever.

[Helgoland]

Greek philosophers.

According to legend, a bunch of Greek philosophers were once debating on how many teeth a horse has in its mouth. A farmer happened by and suggested they get a horse and count its teeth. The philosophers got angry and chased the farmer off.

I fully sympathize - I hate it when people use data to take all the fun out of arguing. You're not arguing to get a solution, after all, but to have fun with your mates.
Not that I'm suggesting that those philosophers were debating with children.

[hops]

I thought Greek philosophers have other form of fun with children.