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[ChairmanPoo]

Please explain to me where there is a different number of doors I could get in the Monty Haul problem.

This isnt the monty haul problem. This is the "pick one door or two doors" problem. Pick

[pikachu17]

One door.

[pikachu17]

OK then, here's an easier problem to contextualize. You're given 2 coins: one of them is normal, the other is fake and has 2 heads. You flip a coin and it lands on heads. What are the odds that it's the fake one?

1 in two.

[Felissan]

Before you look at the results of the flip, there are 4 equally probable possibilities:
1: you pick the real coin and it lands on tails
2: you pick the real coin and it lands on heads
3: you pick the fake coin and it lands on its first side
4: you pick the fake coin and it lands on its other side

When you look at the result and see heads, the 1st option is removed from existence, but the other 3 are still equally probable, since they were from the beginning. Of those 3 options, 3 and 4 have the fake coin, and 2 has the real one.

[ChairmanPoo]

One door.

Why?

[pikachu17]

Easier to defend from goblins. Just pop up a single bridge.
NOTE:Not being snarky. Actual reason.

-snipped-

Biowrath, but staying with your original choice would also have a 999,999/1,000,000 chance of paying off.
And that would suggest the other doors have a chance of having the car, which they don't.

Again, the door(in the original Monty Haul Problem) that is shown with a goat has no chance of having the car, so only one of the two remaining doors could have it. One of them must have a car, and precisely one, so one in two chances of getting a car either way.

[ChairmanPoo]

Easier to defend from goblins. Just pop up a single bridge.
NOTE:Not being snarky. Actual reason.

Cute. Now answer for real: Three doors, one car. Would you rather open ONE door or TWO doors?

[pikachu17]

Sorry. You didn't ask that question before. I was confused a bit.
Two, in that case. Which happens in the Monty Haul problem, either way.

[milo christiansen]

Every damn time this subject comes up, there is at least one person who doesn't "get" it. This is similar to "The Goddamn Airplane on the Goddamn Treadmill"

Read this, and be enlightened

[Pancakes]

Well think of it this way with the 1,000,000 door scenario:

Initially, there is a 1/1,000,000 chance that you get the first choice right, and a 999,999/1,000,000 chance that you got it wrong.

Since you are overwhelmingly more likely to pick wrong initially, when the host narrows it down to two doors, it is a better idea to switch, because your first choice had such a low chance of being correct, while now it is reversed; after eliminating all 999,998 doors, your odds of getting the car from a switch are 999,999/1,000,000.

Another way to think of it:

Let's imagine there are a near infinite number of goat doors, and still only a single car door. When you initially pick, you're all but certainly wrong. When the host reveals a near infinite number of goats (truly a sight to behold!), and one other door, you can safely assume it's the car because your first choice simply wasn't likely to be it.

This scales all the way down to three doors, but the chance of the switch helping decreases to 2/3, which is still better than 50/50 or 1/3.

[ChairmanPoo]

Ok. Now, we´re talking about chances. But consider the following. You´re Monty Hall. You have three doors, two empty and one with a car. You have a contestant who is supposed to choose a door and get a prize based on that. He picks a door that has no car behind it.  What are the odds that when he opens that door, the car will be behind it?

[Rolan7]

The key to understanding the Monty Hall problem is knowing that humans are intrinsically awful at conditional probability. That's really all there is to it.

Yeah.  I "hate" the problem because it makes me feel dumb, especially after stepping through the proofs.  It feels like proving an impossibility, like I must have missed a step.

That makes it very educational, of course.  I bristle at it anyway

Edit:  In other words, there was never an "Aha!  Now it makes sense!" moment for me like with normal puzzles.  The explanations that sound like carnival-speak are somehow accurate.

[Teneb]

Human no like prize doors. Make Human head hurt.

[NJW2000]

Milo's site was really good. I hadn't looked at it from the "consider only the initial choice" angle before.

[TamerVirus]

The real solution is to throw Monty Hall into a volcano and take the car and the two goats when there's nobody to stop you