do you switch your door?

[ElFenix]

monty has 3 doors
behind 1 door is a car
behind 2 doors are goats
you select a door.
monty then shows you a door with a goat behind it
he then allows you to switch
do you?

the answer is yes

i know this has come up before, but here is a really simple proof

there are only 3 ways this can be set up:

1 2 3
CGG
GCG
GGC

you always pick door 1
if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win
if you pick door 1 in the third case, monty has to show you door 2. if you switch, you win

i hope that is easy enough to grasp.

 

[hjo3]

I've heard this before, but I fail to see how him showing you a goat-door changes the odds that there's a car behind your door... it's still 50/50 as far as I can tell.

 

[shamrock1313]

Right...

 

[Pathogen03]

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

 

[imported_Pablo]

is this one of those jedi mind tricks?

 

[stan394]

Originally posted by: Pathogen03

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

in the first case, it doesn't matter if monty shows you door 2 or 3, you switch, you lose
in the second case, monty is forced to show you door 3 because door 2 has the car

 

[ElFenix]

Originally posted by: Pathogen03

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

monty will never show you the door with the car behind it. if you pick a door with a goat (which is more likely than picking the door with the car, everyone should agree with that), monty has to show you the ONLY other door with a goat.

if you pick the door with the car, monty can show you any other door, this is true. but you only pick the door with the car one out of every three chances.

essentially, by allowing you to switch monty is allowing you to pick BOTH of the other two doors, the open and the closed one.

 

[ahurtt]

Originally posted by: ElFenix
monty has 3 doors
behind 1 door is a car
behind 2 doors are goats
you select a door.
monty then shows you a door with a goat behind it
he then allows you to switch
do you?

the answer is yes

i know this has come up before, but here is a really simple proof

there are only 3 ways this can be set up:

1 2 3
CGG
GCG
GGC

you always pick door 1
if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win
if you pick door 1 in the third case, monty has to show you door 2. if you switch, you win

i hope that is easy enough to grasp.

I understand you are saying that in 2 cases you switch and win and only 1 case do you lose if you switch . . .so your odds are better of winning if you switch. But why, in the first case, does monty have to show you door 3? Why couldn't he just show you door 2?

 

[SaturnX]

Originally posted by: Pathogen03

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

Yeah the logic doesn't make sense for this whole thing.

--Mark

 

[ElFenix]

Originally posted by: hjo3
I've heard this before, but I fail to see how him showing you a goat-door changes the odds that there's a car behind your door... it's still 50/50 as far as I can tell.

don't worry, every mathematician in america said the odds were 50/50.

but you're right about one thing... the fact that monty shows you a door with a goat behind it doesn't change the odds that a car is behind your door. those odds are still 1/3. but by showing you a goat, monty has made the odds of a car behind that door be 0. those odds have to be somewhere, and they're behind the other door.

 

[ggnl]

Originally posted by: ElFenix

Originally posted by: Pathogen03

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

monty will never show you the door with the car behind it. if you pick a door with a goat (which is more likely than picking the door with the car, everyone should agree with that), monty has to show you the ONLY other door with a goat.

if you pick the door with the car, monty can show you any other door, this is true. but you only pick the door with the car one out of every three chances.

essentially, by allowing you to switch monty is allowing you to pick BOTH of the other two doors, the open and the closed one.

If you pick a goat on the first pick and switch then you win. You have a 66% chance to pick a goat on the first pick. So by always switching you effectively have a 66% chance to win.

Edit: Not arguing, just clarifying.

 

[ElFenix]

Originally posted by: ahurtt

I understand you are saying that in 2 cases you switch and win and only 1 case do you lose if you switch . . .so your odds are better of winning if you switch. But why, in the first case, does monty have to show you door 3? Why couldn't he just show you door 2?

he could show you door 2. then if you switch to door 3, you'd lose. but it isn't a different case. he could show you either other door if you pick the door with the car behind it. it still isn't a different case, there are only 3 cases.

 

[KillyKillall]

Originally posted by: ElFenix
monty has 3 doors
behind 1 door is a car
behind 2 doors are goats
you select a door.
monty then shows you a door with a goat behind it
he then allows you to switch
do you?

the answer is yes

i know this has come up before, but here is a really simple proof

there are only 3 ways this can be set up:

1 2 3
CGG
GCG
GGC

you always pick door 1
if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win
if you pick door 1 in the third case, monty has to show you door 2. if you switch, you win

i hope that is easy enough to grasp.

Watching "Numbers" again or reading the sites?

 

[ElFenix]

Originally posted by: KillyKillall

Watching "Numbers" again or reading the sites?

just had this explanation given to my m&a class. it's only the first class day so he's explaining odds to law students.

 

[EMPshockwave82]

Originally posted by: SaturnX

Originally posted by: Pathogen03

Originally posted by: ElFenix

if you pick door 1 in the first case, monty shows you door 3. if you switch, you lose
if you pick door 1 in the second case, monty has to show you door 3. if you switch, you win

.... this is stupid.

How do you know monty HAS to show you door three. You say if he shows you door 3, and you switch you lose. Then you say if he shows you door 3, and you switch you win...

But how do you know he is FORCED to show you 3? You could be on the door with the car, and he just chose door 3 to show you.

If he lets you know he is forced, then it means you are on the other goat, meaning the whole thing is just stupid..

Yeah the logic doesn't make sense for this whole thing.

--Mark

try this yourself with a deck of cards... take an ace and 2 kings and have someone shuffle them and try this. You will come out with a higher # of positive outcomes if you switch after being shown


The theory behind it (i may be mistaken) is that you have a 1/3 chance of guessing correctly and then you are shown 1 negative outcome and you then have a 1/2 chance. Your chance of winning improves.

 

[dullard]

I like to show it in a slightly different way.

Monty gives you a choice between 3 doors. Suppose behind one door is a car and behind the other two doors are nothing.

You choose one car, Monty gives you the choice of taking the door you select or BOTH the other doors. Do you switch? Most people would say "yes, switch".

The fact that a goat is behind a door (or multiple doors) doesn't change the answer that you should switch. The fact that Monty shows you a door with nothing behind it doesn't change the answer that you should switch. Combine the two unimportant details (goat and opened door), and you get ElFenix's problem.

 

[Toasthead]

think of it this way...I lay out a deck of 52 cards and tell you to pick the ace of spades. You pick a card. I eliminate 50 of the cards so all that is left is the card you picked and another card, ONE of which is the ace of spades? do you switch to the only card I didnt eliminate that wasnt the one you picked?

 

[Demon-Xanth]

Hell no I wouldn't switch. I'd love a GTO!

 

[GeekDrew]

I still don't get it.

 

[dullard]

Originally posted by: GeekDrew
I still don't get it.

Do you want both doors (car and nothing or two doors with nothing), or do you want the door you originally picked (car or nothing)?

 

[GeekDrew]

Originally posted by: dullard

Originally posted by: GeekDrew
I still don't get it.

Do you want both doors (car and nothing or two doors with nothing), or do you want the door you originally picked (car or nothing)?

If I picked one door, then I would have picked either nothing or a car. Not a multiple of a car and nothing, or two nothings.

 

[dullard]

Originally posted by: GeekDrew
If I picked one door, then I would have picked either nothing or a car. Not a multiple of a car and nothing, or two nothings.

Lets try it.

Pick a door: (A), (B), or (C).

 

[GeekDrew]

Originally posted by: dullard
Pick a door: (A), (B), or (C).

C.

 

[dullard]

Originally posted by: GeekDrew
C.

Do you want to keep door C? Or do you want both doors A and B?

 

[GeekDrew]

Originally posted by: dullard

Originally posted by: GeekDrew
C.

Do you want to keep door C? Or do you want both doors A and B?

How is that a choice? How does A+B=C?