Current Events > Do you understand the Monty Hall problem?

(+) Yeah! (+)

I think the best explanation I got of why switching is better is from my Algebra 2 teacher.

Door 1: Car
Door 2: Goat
Door 3: Goat

Pick Door 1, Monty opens 2, switch to 3, LOSE
Pick Door 2, Monty opens 3, switch to 1, WIN
Pick Door 3, Monty opens 2, switch 1, WIN

Although it looks like a 50/50 after Monty opens a door, your odds are 2/3 when switching. Stuff like this is always interesting because it seems wrong at first glance and its a mindfuck when you try to understand it.

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yes

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I get why it's 2/3 but I still hate it.

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Yeah I think I covered it twice in my schooling for stats classes.

And it's brought up in Zero Time Dilemma.

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The best way to make people understand the problem is to increase the number of doors. If there are 100 doors, and he opens 98 doors with goats, are you going to feel more comfortable with your original guess, or switching to the one other door he didn't open?
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Yes, there were more doors before the reveal, so its more likely you were wrong the first time.

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It's not really hard once you understand that Monty knowing which door is the right one is what changes the probability and makes it counter-intuitive.

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UnholyMudcrab posted...

The best way to make people understand the problem is to increase the number of doors. If there are 100 doors, and he opens 98 doors with goats, are you going to feel more comfortable with your original guess, or switching to the one other door he didn't open?

That, and that Monty will never open the door with the car inside.

I understand it, but my brain still gets angry when it tries to solve it.

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Too many numbers, I'm checking out

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OffTempo posted...

Pick Door 1, Monty opens 2, switch to 3, LOSE
Pick Door 2, Monty opens 3, switch to 1, WIN
Pick Door 3, Monty opens 2, switch 1, WIN

I've tried to understand this problem a million times, but this just made me get it.

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yeah

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what i have to remember is that monty knows where it is
it's the key factor

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It makes sense. I think the most confusing part for someone who hasn't looked into the problem before is understanding that someone with more information than you is intentionally opening a door with nothing behind it. If they just picked a door at random and had a chance to reveal the prize with their pick as well, it would still be a 50/50 chance on your second pick and it wouldn't matter if you switched or not.

theAteam posted...

I get why it's 2/3 but I still hate it.

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All it takes is to expand the problem to 100 doors and 99 goats to demonstrate to anyone why switching is always advantageous.

As an information problem, the only way the odds could be 50/50 is if a different person is brought in after all but one of the goat doors were opened and does not know which door was initially picked and is told to pick one of the two remaining doors at random.

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It's not at all complicated, especially if you consider 100 doors instead of three doors. If you pick a random door, and the host opens 98 empty ones, you would be an idiot if you stayed with the door you chose.

That said, there is a fundamental flaw in the problem. That flaw is the assumption that the game show host knows which door contains the prize. If he doesn't, and just gets lucky and opens all the empty doors, the odds are indeed 50/50.

Edit: looks like the guy right above me said exactly the same thing right before I did

People try to apply the Monty Hall problem to that one episode of Deal or No Deal where the lady stayed with her case and won $1M, but in reality that's actually a situation in which she correctly eliminated, by chance, all of the lower value cases without actually knowing it. In her situation, the odds of winning was indeed 50/50.

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I bet you simpletons also actually believe that 0.999~ = 1

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DarkRoast posted...

That flaw is the assumption that the game show host knows which door contains the prize. If he doesn't, and just gets lucky and opens all the empty doors, the odds are indeed 50/50.

I think that's seminal to the exercise. There has to be a reveal that is known to be a wrong choice.

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