Mythbusters Discussion, Episode last night confused me ... a lot Options

[Gharphield]

So last night I was watching Mythbusters (as the title suggests).

Anyway, the did this myth where you have 3 doors. The 'prize' is behind 1 of those doors. You pick a door. Then they open up one of the other ones that DOESN'T have the prize behind it. Then they ask the person if they want to switch doors or stick with their current one. Now, they tried this on a bunch of random people and they all stuck with their initial choice.

Anyway, that wasn't good enough and didn't give them a result they wanted, so they just did a test where Jamie would always stick with his initial choice and Adam would always switch.

So they did that about 50 times and the result was that Adam got the prize the VAST majority of the time whilst Jamie got only a handful right. They then went on to say that 'switching' greatly improves your chances.

But I don't full understand this. In the end doesn't this all come down to a 50/50 chance no matter HOW you look at it? Initially it's a 1/3 chance. But then they reveal a door and ask for a switch. So in other words you can pick whatever of the 2 doors you want. I fail to see how switching on a random chance in 1/2 makes it 'better' or makes your chances better.

But there's also a 99.9% chance I'm completely missing something here as my brain doesn't function well on small amounts of sleep. can anyone of you smart peeps shed some light here?

[Blackorchad]

i found this explained it well enough for me

http://www.youtube.com/watch?v=cXqDIFUB7YU

Yes it's from a movie, but the idea of what was said, is simple and made sense.

This post has been edited by Blackorchad: May 8 2012, 11:51 AM

[SquallStrife]

But I don't full understand this. In the end doesn't this all come down to a 50/50 chance no matter HOW you look at it? Initially it's a 1/3 chance. But then they reveal a door and ask for a switch. So in other words you can pick whatever of the 2 doors you want. I fail to see how switching on a random chance in 1/2 makes it 'better' or makes your chances better.

But there's also a 99.9% chance I'm completely missing something here as my brain doesn't function well on small amounts of sleep. can anyone of you smart peeps shed some light here?

The answer to the problem appears very counter intuitive at first.

Draw a tree of all possible results, and it all becomes clear.

http://en.wikipedia.org/wiki/Monty_Hall_problem

This post has been edited by SquallStrife: May 8 2012, 11:55 AM

[elvenwhore]

I could have sworn I read something about this on Cracked, but for the life of me, do you think I can find it?
I can hear you thinking, "no, she can't" - would you like to stick with this answer? Do you want to try your luck in thinking, "yes, I think she has found it?"

<muzak>

[TinBane]

It's the Monty Hall problem:

http://en.wikipedia.org/wiki/Monty_Hall_problem

The wiki link explains it well enough.

But the basic premise is the following:

Switching is ONLY worse, if you have correctly picked the original prize door.
As you only pick the original prize door 1/3 of the time, 2/3 of the time the other door has the prize.

Your brain works by not doing things from first principles. In this case, it says two doors is too easy, 50% chance. What it doesn't think about in general, is that the reveal will always show a "fail" door, but that's not relevent because you aren't choosing between two equal doors. You are choosing a binary "was I correct", where the initial probability of your correct assessment comes into play.


Does that make sense?

It's probabilistic sleight of hand.

When you think about it in terms of betting on whether you picked a 1/3 probability event in the first step, you should see straight away why it's not 50/50.

This post has been edited by TinBane: May 8 2012, 11:55 AM

[Gharphield]

Awesome man, thanks :)

Also found this one which explains it well too: http://www.youtube.com/watch?v=mhlc7peGlGg...feature=related

In a nutshell, you're more likely to pick a Goat door at the start 2/3 chance. So swapping AFTER that based on probability makes it statistically logical!

... /feels enlightened

It's the Monty Hall problem:

http://en.wikipedia.org/wiki/Monty_Hall_problem

The wiki link explains it well enough.

But the basic premise is the following:

Switching is ONLY worse, if you have correctly picked the original prize door.
As you only pick the original prize door 1/3 of the time, 2/3 of the time the other door has the prize.

Your brain works by not doing things from first principles. In this case, it says two doors is too easy, 50% chance. What it doesn't think about in general, is that the reveal will always show a "fail" door, but that's not relevent because you aren't choosing between two equal doors. You are choosing a binary "was I correct", where the initial probability of your correct assessment comes into play.


Does that make sense?

It's probabilistic sleight of hand.

When you think about it in terms of betting on whether you picked a 1/3 probability event in the first step, you should see straight away why it's not 50/50.

I need to refresh before making posts ... but yeah +1 to TB :)

[@~thehung]

this is one of those things that endlessly fascinates and frustrates me.

why? because even though ive well understood the solution for a long time and will never forget it, it remains STUPIDLY easy for me to knowingly start with the wrong premise and then all but convince myself the 50/50 answer is correct. (just like the logic puzzle about the missing $1 dollar of change)

anyway, i explain it like this:

anytime you make a one in three choice, you are probably wrong — that is, there is a 67% chance either of the OTHER two options were correct.
when one of those other options is taken away, all of that 67% naturally falls onto the remaining OTHER option.

[g__day]

First time someone asked me this (without revealing the answer) - I had to think hard awhile; it took me about 30 minutes to find a simple way of realising the result.

Imagine there are 1,000,000,000 planets - and life exists on only one of them. Now pick a single planet and a host eliminates all the others bar one then allows you to swap choice. Consider - are your chances of having chosen the correct planet 50 - 50 or 1 in 1,000,000,000? If you change your choice is it immaterial or have the odds suddenly shifted completely in your favour? The host introduces ouside information; they are not randomly shifting the odds they are eliminating false results, which doesn't change the odds of your initial choice but do improve the odds by selecting from the choices remaining.

With most challenging problems - the inspiration is seeing the issue in a way so the solution drops out and you can believe the answer. I was stunned when my friend told me I was correct - but it took serious mathematicans alot longer than hours to figure that one out. In fact when the author of the Monty Hall solution posted about it in the papers (as it refered to a rather famous tv show of the times) - she was generally widely derired as being a quack! Serious egg on faces when folk thought longer and a lot harder on her answer (which then killed the tv show) and realised she was absolutely correct!

This post has been edited by g__day: May 8 2012, 10:19 PM

[xnatex]

brain = blown

what just happend lol

I love mythbusters

[nesquick]

brain = blown

what just happend lol

I love mythbusters

its all about maximising chances of wining

you will only pick the car 33% of the time to begin with and pick a goat 66% of the time by removing 1 goat you now have 2 choices a car or a goat since you have with 66% chance picked a goat the inverse of this would now be you have 66% chance of getting a car if you switch but retain 33% chance if you stay with your choice.

This post has been edited by nesquick: May 8 2012, 11:41 PM

[xnatex]

I wonder how many of these sorta things exist in day to day life that we over look.
Sounds like a good idea for a book “statistically increase your chance to win at life”

[robzy]

Imagine there are 1,000,000,000 planets - and life exists on only one of them. Now pick a single planet and a host eliminates all the others bar one then allows you to swap choice. Consider - are your chances of having chosen the correct planet 50 - 50 or 1 in 1,000,000,000? If you change your choice is it immaterial or have the odds suddenly shifted completely in your favour? The host introduces ouside information; they are not randomly shifting the odds they are eliminating false results, which doesn't change the odds of your initial choice but do improve the odds by selecting from the choices remaining.

The million doors (albeit with cars and donkeys) is how I choose to think of it too.

A tree diagram would also help.

Rob.

[mykl_c]

The other side of this particular coin is the idea of investment - we tend to believe in our own choices and so, regardless of how important the choice, we stick with it.

[Foods]

Imagine there are 1,000,000,000 planets - and life exists on only one of them. Now pick a single planet and a host eliminates all the others bar one then allows you to swap choice. Consider - are your chances of having chosen the correct planet 50 - 50 or 1 in 1,000,000,000? If you change your choice is it immaterial or have the odds suddenly shifted completely in your favour? The host introduces ouside information; they are not randomly shifting the odds they are eliminating false results, which doesn't change the odds of your initial choice but do improve the odds by selecting from the choices remaining.

The million doors (albeit with cars and donkeys) is how I choose to think of it too.

A tree diagram would also help.

Rob.

How the fuck does that help?


'

[Nich...]

A tree diagram would also help.

How the fuck does that help?

Whether it helps or not, why are you showing wood to Rob?

He's only 14 you know, that's highly inappropriate. Especially for a girl like yourself.

[SquallStrife]

I like how that tree has a "truck" in the middle.

VROOM!

[Foods]

I like how that tree has a "truck" in the middle.

VROOM!

Its even LESS helpful. Nice one Rob, idiot.


'

[@~thehung]

The host introduces outside information

yep. thats at the crux of the Jedi mind trick.

we dont properly consider the implications of the host's choice. there is never a chance that they might choose 'wrongly'.

if we imagine instead, the host randomly removing one of the options by painting a big "X" on the door. it would clearly be a 50/50 choice (between two perfectly preserved 1 in 3 chances).

then when you add the host's deliberate meddling, it becomes amply clear the odds must be skewed.

[metallitragic]

Shoot the host. open all the doors. Problem solvered

[kamerong]

Same thing happened to me once, except my neighbour fucked my dog.