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Scholar

5,082 posts

You're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door and the host, who knows what's behind the doors, opens another door and reveals a goat - no matter what you have picked he will always reveal a goat. He then says to you "Do you want to switch?"

Should You? Why?

Should You? Why?

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

Ministry of Silly Cnuts

19,506 posts

What *** is the goat?

"I started out with nothin' and I still got most of it left" - Seasick Steve

Scholar

8,619 posts

I know what Aegis's Answer would be

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Worst. Title. Ever!

16,313 posts

Nobby wrote:

What *** is the goat?

They don't know, when the goat filled out his papers, for "***" he wrote "Yes".

Can't sleep, clown will eat me.

Scholar

2,122 posts

Yes, you have 2/3 chance of picking a goat first time around and when he reveals the other goat you win by changing

Belkira the Tulip wrote:

While I do tend to agree with Planks

This spot is no longer devoted to anyone in particular.

Repressed Memories

20,701 posts

You should switch. Doing so gains you a a two thirds probability of winning.

Scholar

5,082 posts

People round here are far too smart

Switch doors if you want a 2 in 3 chance of winning the car was the correct answer.

Switch doors if you want a 2 in 3 chance of winning the car was the correct answer.

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

2,189 posts

Allegory wrote:

You should switch. Doing so gains you a a two thirds probability of winning.

How does that work?

Viseziox wrote:

I think you're a forum ****

Fancy Shmancy Wiki

[ffxisig]186182[/ffxisig]

Worst. Title. Ever!

16,313 posts

Allegory wrote:

You should switch. Doing so gains you a a two thirds probability of winning.

Exactly how though?

I understand that you have a 67% chance of picking a goat the first time, and a 50% chance of picking a goat the second time if you repick. But in reality, him revealing one of the goats has no way of changing what is actually behind the first door you chose. (This isn't a cat in a box).

It's like if a teacher asked a question, which you had no clue what the answer was. Multiple choice, A, B, or C. You pick A at random, and the teacher tells you afterwards that C is not the correct answer. You don't gain anything really by changing your answer after that.

Can't sleep, clown will eat me.

Scholar

5,082 posts

TirithRR the Mundane wrote:

It's like if a teacher asked a question, which you had no clue what the answer was. Multiple choice, A, B, or C. You pick A at random, and the teacher tells you afterwards that C is not the correct answer. You don't gain anything really by changing your answer after that.

But you should change your answer...

You have a 1 in 3 chance of your first answer being correct, which means that the other 2 answers combined have a 2 in 3 chance of being correct.

If the teacher always tells you that one of the answers you didnt choose is incorrect and tells you which one it is then you have 2 choices i) stick with your original which has a 1 in 3 chance of being correct or ii) switch to the other remaining answer which now has a 2 in 3 chance of being correct.

Switch TirithRR, you know it makes sense

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

Unplanned

12,683 posts

Always switch doors unless you have "*faith*" in your door.

Just as Planned.

Repressed Memories

20,701 posts

To make the situation more apparent imagine that instead of 3 doors you have 100 doors.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.

Scholar

424 posts

If you want the car, you should switch.

The reason why it works is simple: There's 2 possibilities, on your first random pick you either pick the car 1/3 of the time, or a goat 2/3 of the time.

If you randomly pick the car, then the other goat is out of the picture and you lose by switching, meaning you lose 1/3 of the time.

If you randomly pick the goat, then the other goat is once again out of the picture, but by changing you pick the car, therefore winning 2/3 of the time.

The reason why it works is simple: There's 2 possibilities, on your first random pick you either pick the car 1/3 of the time, or a goat 2/3 of the time.

If you randomly pick the car, then the other goat is out of the picture and you lose by switching, meaning you lose 1/3 of the time.

If you randomly pick the goat, then the other goat is once again out of the picture, but by changing you pick the car, therefore winning 2/3 of the time.

2,189 posts

Allegory wrote:

To make the situation more apparent imagine that instead of 3 doors you have 100 doors.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.

You pick any door with a 99% chance of being wrong. The host then reveals every door remaining except one to have a goat. There are now two doors remaining, the one you picked with a 99% chance of being wrong and one unknown. This door has 1-.99 probability of being a goat, 1%. Therefore you should switch.

This makes no sense to me.. no matter HOW many doors are eliminated, there's 2 left, and each have an equal opportunity of being a goat... meaning that no matter what you do it's 50/50 when you're left with 2...

Or maybe i'm missing something.

Viseziox wrote:

I think you're a forum ****

Fancy Shmancy Wiki

[ffxisig]186182[/ffxisig]

Repressed Memories

20,701 posts

It's only 50% if you don't include the information about the previous doors.

Out of 100 doors any door you pick is almost certainly the wrong door. If you know you're wrong, and he takes away all other choices except one, then you know that must be the right choice.

Or you can try thinking of it this way. Instead of the doors you can actually see all the prizes. You can see which of the 99 are goats and which one is a car. Pick any prize at random (not caring what you win). Most of the time you will pick a goat, because there are 99 of them and only one car, after switching you would have ended up with a car. If you by chance pick the 1 car out of those 99 goats then after switching you would have picked a goat. So since you pick a goat most of the time, by switching you end up picking a car most of the time.

Out of 100 doors any door you pick is almost certainly the wrong door. If you know you're wrong, and he takes away all other choices except one, then you know that must be the right choice.

Or you can try thinking of it this way. Instead of the doors you can actually see all the prizes. You can see which of the 99 are goats and which one is a car. Pick any prize at random (not caring what you win). Most of the time you will pick a goat, because there are 99 of them and only one car, after switching you would have ended up with a car. If you by chance pick the 1 car out of those 99 goats then after switching you would have picked a goat. So since you pick a goat most of the time, by switching you end up picking a car most of the time.

Unplanned

12,683 posts

Because the door you picked has a higher probability of being a goat door than a car door. 1/3 probability to 2/3 probability, easy decision.

Perhaps a graphical interpretation will help.

O is car, X is goat. Always pick door #1 (for convenience sake). If you want to pick other doors, result is the same, it just requires 9 diagrams.

Edit: better formatting

*Edited, Mar 31st 2008 7:28pm by Timelordwho*

Perhaps a graphical interpretation will help.

O is car, X is goat. Always pick door #1 (for convenience sake). If you want to pick other doors, result is the same, it just requires 9 diagrams.

pick door #1, door 2 is revealed as goat. swap to door 3. sorry, screwed by probability this round. [o] [x] [x] pick door #1, door 3 is revealed as goat. swap to door 2, winnar! [x] [o] [x] pick door #1, door 2 is revealed as goat. swap to door 3, winnar! [x] [x] [o]

Edit: better formatting

Just as Planned.

Worst. Title. Ever!

16,313 posts

Ok. I get it now.

Can't sleep, clown will eat me.

Repressed Memories

20,701 posts

This video may help a few of those who are still confused; it makes a lot of sense.

Scholar

5,082 posts

Allegory wrote:

This video may help a few of those who are still confused; it makes a lot of sense.

Thanks, that certainly clears thing up

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

4,894 posts

Always switch.

Your initial pick is correct 1/3 of the time. (Random system)

After the host eliminates one of the doors, switching effectively gives you a 2/3 chance of winning. (Non-random system)

Your initial pick is correct 1/3 of the time. (Random system)

After the host eliminates one of the doors, switching effectively gives you a 2/3 chance of winning. (Non-random system)

PunkFloyd

Scholar

8,619 posts

Quote:

then you know that must be the right choice.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Wants you as a new recruit!

17,389 posts

SWM wrote:

Allegory wrote:

This video may help a few of those who are still confused; it makes a lot of sense.

Thanks, that certainly clears thing up

Nyan nyan

Nyan nyan

Nihao

Goujasu derishasu ekaruchaa

derailâ„¢ back.

Qui s'estime petit deviendra grand.

Bringing Qui s'estime petit deviendra grand.

Scholar

5,082 posts

Sogoro the Malevolent wrote:

SWM wrote:

Allegory wrote:

This video may help a few of those who are still confused; it makes a lot of sense.

Thanks, that certainly clears thing up

Nyan nyan

Nyan nyan

Nihao

Goujasu derishasu ekaruchaa

No this is awesomer

click

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

Unplanned

12,683 posts

Quote:

No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

Read my post and you'll see why this is incorrect.

When you pick a door, you have a 1/3 chance of being right, AND (now here is the important part) a 2/3 chance of being

Just as Planned.

Scholar

2,122 posts

Baron von tarv wrote:

Quote:

then you know that must be the right choice.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

Math says to **** off

Belkira the Tulip wrote:

While I do tend to agree with Planks

This spot is no longer devoted to anyone in particular.

Your Wet Nightmare

19,727 posts

SWM wrote:

That link contains perhaps my favorite viewer comment ever:

Quote:

this is *** like your dad cause i sucked your mom's tits

Totally ought to be a meme.

Unplanned

12,683 posts

Just as Planned.

Wants you as a new recruit!

17,389 posts

Timelordwho wrote:

The continuing saga of the Allakhazam office.

derailâ„¢ back.

Qui s'estime petit deviendra grand.

Bringing Qui s'estime petit deviendra grand.

2,189 posts

Viseziox wrote:

I think you're a forum ****

Fancy Shmancy Wiki

[ffxisig]186182[/ffxisig]

Scholar

8,619 posts

Quote:

Math says to @#%^ off

I am not arguing that you shouldn't pick the other one you think cnut, i am pointing out that when left with two boxes it is not automaticly a 100% result when switching.

2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated

Quote:

you know that must be the right choice.

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

4,894 posts

Baron von tarv wrote:

Quote:

Math says to @#%^ off

I am not arguing that you shouldn't pick the other one you think cnut, i am pointing out that when left with two boxes it is not automaticly a 100% result when switching.

2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated

Quote:

you know that must be the right choice.

With two doors to choose from, your odds are 50/50 only in a _random_ system.

But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.

PunkFloyd

Scholar

8,619 posts

Quote:

But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Your Wet Nightmare

19,727 posts

Baron von tarv wrote:

Quote:

But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.

You're such a f*cking moron. It's really funny.

Scholar

8,619 posts

Quote:

You're such a f*cking moron. It's really funny.

Go on try.

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Silent But Deadly

19,999 posts

Incidentally, this is *nothing* like how Deal or No Deal works.

SUPER BANNED FOR FAILING TO POST 20K IN A TIMELY MANNER

4,894 posts

Baron von tarv wrote:

Quote:

But when you are posed with your second choice (to switch or not), it is not a random system: one door will win 1/3 of the time and the other will win 2/3 of the time. This is, by definition, not random.

Exactly, I never said you had a 100% chance.

Baron von tarv wrote:

2 boxes left, only one has a car thus 50/50.

Your statement is 100% incorrect.

PunkFloyd

Imaginary Friend

16,045 posts

it's dead AND alive... or something?

Repressed Memories

20,701 posts

Baron von tarv wrote:

2 boxes left, only one has a car thus 50/50. the fact you have shortened the odds doesn't make it as was stated It's PROBABLY the right choice, but you CANNOT be certain.

Quote:

you know that must be the right choice.

I was trying to avoid tautology; it would be redundant to reiterate such a pleonasm.^^ Obviously the entire situation still involves probability.

Your statement about 50% is still incorrect.

Scholar

5,082 posts

Baron von tarv wrote:

Please explain how ANYTHING i have said is incorrect.

Go on try.

Go on try.

This bit is wrong

Quote:

2 boxes left, only one has a car thus 50/50.

The box you chose was chosen at random from 3 boxes thus a 1 in 3 chance of winning. The box that is left was not left unopened randomly, it was left unopened on the basis that the other box contained a goat and so the probability of it containing the car is the sum total of the boxes at the initial point of the game (1 in 3 plus 1 in 3 = 2 in 3).

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

Scholar

8,619 posts

Quote:

The box you chose was chosen at random from 3 boxes thus a 1 in 3 chance of winning. The box that is left was not left unopened randomly, it was left unopened on the basis that the other box contained a goat and so the probability of it containing the car is the sum total of the boxes at the initial point of the game (1 in 3 plus 1 in 3 = 2 in 3).

There is a 66% chance your CHOISE of box is correct, there is a 50% chance that the car is in a particular box.

the point i am making is no matter how much you swing the chance your CHOICE is correct because there is still two boxes left you can't be

Jarkeld Hammerhiem Lvl 36 Paladin/Lvl 30 Armourer

Lestril Hammerhiem Lvl 40 Monk/Lvl 28 Provisioner Blackburrow server

Iaedian Tailchaser lvl 60 Fury/36 Jeweler. Proud member of <Bane> Crushbone server

Your mind is like a Parachute, it only works if it's open.

Repressed Memories

20,701 posts

Tarv your original statement was:

It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.

I don't mean to be rude, but what your trying to arguing what you are saying is pointless. You're now arguing that you mean that out of the two boxes/doors there is a 50% chance one has a car and that one can't be certain which box/door has the car. While both of these statements are true they mean nothing useful. Out of any two objects you have a 50% chance of selecting one, and nearly every situation involving probability lacks perfect certainty. Right, but not relevant.

*Edited, Apr 1st 2008 4:58am by Allegory*

Quote:

No you don't, it's Equally as likely that you picked the right door the first time.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

a choise of 2 doors, one being right is still 50/50 reguardless of previous choices.

It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.

I don't mean to be rude, but what your trying to arguing what you are saying is pointless. You're now arguing that you mean that out of the two boxes/doors there is a 50% chance one has a car and that one can't be certain which box/door has the car. While both of these statements are true they mean nothing useful. Out of any two objects you have a 50% chance of selecting one, and nearly every situation involving probability lacks perfect certainty. Right, but not relevant.

Soulless Internet Tiger

35,198 posts

Allegory wrote:

It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.

Personally, I like to look at it the other way around. The doors I didn't pick, have a 2/3 chance of being wrong and after opening the third door, it increases the likelihood that the remaining door I didn't pick, is still wrong. In case none of you notice, I like to bend things so they work for me, because I'm never wrong.

Donate. One day it could be your family.

*An invasion of armies can be resisted, but not an idea whose time has come.* Victor Hugo

Vagina Dentata,

what a wonderful phrase

what a wonderful phrase

30,091 posts

When I was a kid (ha!), I had a pet goat named Florence. She slept on the end of my bed.

Turin wrote:

Seriously, what the f*ck nature?

Scholar

5,082 posts

Did you also have pets named Dylan, Dougal and Zebedee?

In Loving Memory of SatanWantsMe 2006-2008

SWM Wiki | Journal | What I am listening to right now

SWM Wiki | Journal | What I am listening to right now

Scholar

25 posts

Sogoro the Malevolent wrote:

Timelordwho wrote:

The continuing saga of the Allakhazam office.

This made my day.

Cervixhouse-Five

30,646 posts

I don't think this game sounds awesome.

But then, I'm not a big fan of "Deal or No Deal."

But then, I'm not a big fan of "Deal or No Deal."

Will swallow your soul

29,023 posts

From The Straight Dope:

Cecil wrote:

A friend of mine did suggest another way of thinking about the problem that may help clarify things. Suppose we have the three doors again, one concealing the prize. You pick door #1. Now you're offered this choice: open door #1, or open door #2 and door #3. In the latter case you keep the prize if it's behind either door. You'd rather have a two-in-three shot at the prize than one-in-three, wouldn't you? If you think about it, the original problem offers you basically the same choice. Monty is saying in effect: you can keep your one door or you can have the other two doors, one of which (a non-prize door) I'll open for you. Still don't get it? Then at least have the sense to keep quiet about it.

In a time of universal deceit, telling the truth is a revolutionary act.

4,894 posts

Uglysasquatch, Mercenary Major wrote:

Allegory wrote:

It's not equally as likely that you picked the right door the first time. It's not a 50% chance of one being right.

Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.

PunkFloyd

Bloodle-Oodle-Oodle

13,007 posts

I take it someone watched *21*.

I think the reasoning was ********* and you now have a 50/50 of winning with either door.

I think the reasoning was ********* and you now have a 50/50 of winning with either door.

Soulless Internet Tiger

35,198 posts

PunkFloyd the Flatulent wrote:

Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.

Ok, now you're being as dense as Tarv was. If you forget (should I bold that again or would you miss it again?) that there were 3 doors after one is opened, you only have 2 doors left. At this point, you do have a 50/50 shot. Taking the bigger picture, you never do. But, using the snapshot in time, where the 3rd no longer exists, you do have a 50/50 chance.

Donate. One day it could be your family.

*An invasion of armies can be resisted, but not an idea whose time has come.* Victor Hugo

4,894 posts

Uglysasquatch, Mercenary Major wrote:

PunkFloyd the Flatulent wrote:

Even if viewed as a snapshot in time, it's not a 50% chance. Nowhere in this particular example did you ever have a 50% chance of being right.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.

You can only make the claim that you've got a 50% chance if car is randomly behind one of two curtains. The point is that the car is not randomly behind the curtains. There is a 1/3 chance it's behind the curtain you originally picked and a 2/3 chance of being behind the other curtain. This is, by definition, not random so you do not have a 50% chance.

As an analogy, think of flipping a loaded coin.

Ok, now you're being as dense as Tarv was. If you forget (should I bold that again or would you miss it again?) that there were 3 doors after one is opened, you only have 2 doors left. At this point, you do have a 50/50 shot. Taking the bigger picture, you never do. But, using the snapshot in time, where the 3rd no longer exists, you do have a 50/50 chance.

I am not being dense, this is exactly my point. You do *not* have a 50/50 chance. You have a 33.3/66.6 chance.

You only have a 50/50 chance if the car is randomly behind one of the two curtains, but it is not randomly behind one of the curtains. It's twice as likely to be behind the curtain not initially picked.

PunkFloyd

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