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[pikachu17]

Sorry, Chairman Poo.

[Pancakes]

wait are we trying to get goats or cars

[ChairmanPoo]

wait are we trying to get goats or cars

You canīt ****  a car. Just saying.

[pikachu17]

Wait, you can't?

[Pancakes]

Not with that attitude!

[TD1]

wait are we trying to get goats or cars

You canīt ****  a car. Just saying.

The inversion of that is more true.

[McTraveller]

Oh goodness folks!

If you switch, the probability of getting the car is equal to the probability your initial guess was not the car.  The probability your first guess was the car is only 1 in 3.  So the probability switching gives you the car is 2 in 3.

[Felissan]

Instead of going in circles and saying the exact same thing, I'll reformulate this reasoning - the mistake pikachu makes is assuming that there are only 2 possibilities - being a goat or the car.

In reality, the initially picked door has 3 possible contents: goat #1, goat #2 and the car, which are all just as likely as each other. The rest follows immediately from that.

[Kagus]

I originally had a lot of trouble with this one, as a delving into the forum's sordid past will show. Much of my issue had to do with how it had been explained to me previously, with people trying to state that staying with your choice was a 50% success chance, while swapping would be 66%. The problem with that explanation should be obvious.

The esteemed Chairman has already broken down the salient points better than I could (notably: the doors aren't important; the host is).

An important note to remember is that the car never moves. Before the start of the game, the car is placed behind one of the available doors, with equal probability for each. The car's position does not change when you initially pick a door, nor does it change when one of the doors it is not behind gets opened by Monty.

Also remember that this is specifically made to screw with how our brains think... it's supposed to not make sense. There's a reason it's called the Monty Hall Problem and not the Monty Hall Reasonable Thing.


Additionally, I like goats. Not the way our honorable Chairman likes goats; I like them in a purely platonic sense.

[ChairmanPoo]

I like goats for their eating habits.

Also, I think its not infrequent to struggle to understand it at first.  I didnt understand it when I was a teen, and found the whole thing asinine. Then I revisited it years later and suddenly everything clicked together and I had this feeling of... enlightement? It feels really funny because once you realize the logic behind monty hall you kind of wonder how you could see it otherwise. The whole perspective flips. Pikachu, I promise that sooner or later you'll see it and you'll feel amazed as well.

[Kagus]

I was first exposed to it in some pop sci rag back in the day, alongside another zinger about how 0.999... is == 1.

I've never had that explained to me, and I'm not sure I want it to be.

Also,

I like goats for their eating habits.

...filth...

[Trekkin]

I was first exposed to it in some pop sci rag back in the day, alongside another zinger about how 0.999... is == 1.

I've never had that explained to me, and I'm not sure I want it to be.

Here's a try at a quick explanation:

The difference between 0.999... and 1 gets smaller the farther out you go with the series of 9s. Go infinitely far, and the difference is infinitely small, or 0.

[ChairmanPoo]

I was first exposed to it in some pop sci rag back in the day, alongside another zinger about how 0.999... is == 1.

I've never had that explained to me, and I'm not sure I want it to be.

Here's a try at a quick explanation:

The difference between 0.999... and 1 gets smaller the farther out you go with the series of 9s. Go infinitely far, and the difference is infinitely small, or 0.

Here's another one
1/3=0.333.....
0.333...x3=0.999...
1/3x3=3/3=1
0.999..=3/3=1

[hector13]

Jesus Christ guys let's not go from one maths problem to another one.

..

Let's stick with teh fist wan!

The esteemed Chairman has already broken down the salient points better than I could (notably: the doors aren't important; the host is).

The doors are important, the host just gives you information on them. Specifically, they know where the car is, and they're not going to show you where it is.

The odds remain the same throughout the problem; that's where I think people get tripped up.

[Kagus]

But that's just it, it becomes infinitely small, not "no difference at all". I can easily accept that it's "close enough" or "effectively the same", but that does not mean it is exactly equal. This is mathematics, not engineering.

An infinitely large fraction is as much the whole number as an infinite number of zeros can equal anything other than zero. It doesn't matter that it's infinite, the fact that it can continue shortening the gap between 0.999... and 1 (I.e., being infinite) proves that it isn't exactly 1. If it were exactly 1, it wouldn't be able to be any more 1 than it already was.

So, 0.999... = 1? Sure. 0.999... == 1? No.