Sheep or a Car

[Cerpin Taxt]

It really seems to me that if it is given from the outset that the host will inevitably open a door that shows a goat, then it is no different than if that door is already open before the contestant's choice is made.

So you have a contestant presented with 3 doors, 1 of which is already open and shows a goat. NOW he makes a choice between the 2 remaining doors. What are his odds?

But then again, that isn't really what the question is asking. The question asks how often it will pay to switch after a certain choice has already been made among 3 CLOSED doors. I think that is the distinction that escapes the naysayers.

 

[Malak]

Originally posted by: Garth
But then again, that isn't really what the question is asking. The question asks how often it will pay to switch after a certain choice has already been made among 3 CLOSED doors. I think that is the distinction that escapes the naysayers.

For that I will say 58% of the time.

 

[sieistganzfett]

this is a logic problem.. i would switch since the original chance of me picking the car is only 33%. once that other door opens the 33% that now opened door had now transfers to the door the host left closed, i stayed with my 33% since that doesnt change, we are still in the same game and nothing behind my door changed, except maybe the sheep taking a pee or a dump.. so i will switch to the door the host left closed instead of my original choice since there is now a 66% chance that the car is behind the door i did not originally chose. if i just to happened to pick the car the first time, well i lost then and get to have fun with a sheep, at least it's not with monty hall. but the chance of me picking the sheep is less, thats why i switch to the other door.

if there is anyone who still thinks its 50/50 once the 3rd door opens. lets put it this way. the host says there are 3 doors and you can open two. you have a 66% chance of getting the sweet ride (not the sheep).

 

[mugs]

Are people really debating this? You can find in-depth explanations all over the Internet. You can find simulators all over the Internet. I even wrote a quick simulator last time this topic came up. You can SIMULATE IT ON YOUR OWN WITHOUT EVEN USING A COMPUTER OR MATH. There is no way in hell this should be debated. Ever.

 

[Malak]

Originally posted by: mugs
Are people really debating this? You can find in-depth explanations all over the Internet. You can find simulators all over the Internet. I even wrote a quick simulator last time this topic came up. You can SIMULATE IT ON YOUR OWN WITHOUT EVEN USING A COMPUTER OR MATH. There is no way in hell this should be debated. Ever.

And yet it was so hotly debated by people far smarter than you or I when the topic first came up. You really think we are above that?

 

[Mo0o]

Anyone still determined that the probabilities are not 1/3 and 2/3 should play with this program: http://www.grand-illusions.com/simulator/montysim.htm

 

[chrisms]

Change choice: 1600 times Wins: 1010 cars (63%)
Losses: 590 goats (37%)

Keep choice: 1501 times Wins: 499 cars (33%)
Losses: 1002 goats (67%)

 

[Garet Jax]

Originally posted by: chrisms
Let's say you're on a game show, and you're given the choice of 3 doors: Behind one door is a car, and behind the others, sheep. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a sheep. He then says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice?

always switch.

 

[JujuFish]

Awwww man. I can't believe I missed this thread when it started.

One thing that makes the problem much better than the airplane problem is this one is easy to prove. Those who think the odds are 50/50 after a goat is revealed can try the problem in real life with a friend.

 

[mugs]

Originally posted by: Malak

Originally posted by: mugs
Are people really debating this? You can find in-depth explanations all over the Internet. You can find simulators all over the Internet. I even wrote a quick simulator last time this topic came up. You can SIMULATE IT ON YOUR OWN WITHOUT EVEN USING A COMPUTER OR MATH. There is no way in hell this should be debated. Ever.

And yet it was so hotly debated by people far smarter than you or I when the topic first came up. You really think we are above that?

Well, I don't debate the Pythagorean Theorem even though it seems just a little too convenient and I haven't see it derived, because I can see through demonstrations that it is true.

 

[chrisms]

Originally posted by: Mo0o
Anyone still determined that the probabilities are not 1/3 and 2/3 should play with this program: http://www.grand-illusions.com/simulator/montysim.htm

Great site! http://www.grand-illusions.com/opticalillusions/amazing_dots/

http://www.grand-illusions.com/opticalillusions/dragon_illusion/

 

[Garet Jax]

Originally posted by: iamaelephant
I'm done trying to explain this to you. You're ignorant, arrogant, stupid and the worst thing is you think you're smart. You are too stupid to understand something that has been explained in plain English. I have come across paper weights with more brain power than you. Good day sir.

Edit - as a matter of interest, what do you think of the 0.999...=1 discussion, and do you think the plane takes off?

Although, I agree with your stance on the problem, I do not understand why you get so mad (and personally offended) because someone disagrees with you.

 

[SlitheryDee]

Yep switching is the logical course of action.

 

[JujuFish]

Originally posted by: Mo0o
Anyone still determined that the probabilities are not 1/3 and 2/3 should play with this program: http://www.grand-illusions.com/simulator/montysim.htm

Nice. After running it 10,000 times with keep, 10,000 with change, here are the results:

Keep choice: 10000 times
Wins: 3319 cars (33%)
Losses: 6681 goats (67%)

Change choice: 10000 times
Wins: 6708 cars (67%)
Losses: 3292 goats (33%)

 

[Malak]

Originally posted by: chrisms
Change choice: 1600 times Wins: 1010 cars (63%)
Losses: 590 goats (37%)

Keep choice: 1501 times Wins: 499 cars (33%)
Losses: 1002 goats (67%)

Do you notice the variance? This is part of my issue. It's a little hard to explain, but for now I'm saying if you switch it's approximately a 58% chance of winning, not 66%. If you don't switch, you have a 33% chance of winning, and thus a 66% chance of losing. I'm not good at explaining things so I won't even bother explaining my confusing thought pattern that let me to 58%, but the tests I've seen show a variance between switching and not switching.

 

[mobobuff]

Originally posted by: Malak

Originally posted by: chrisms
Change choice: 1600 times Wins: 1010 cars (63%)
Losses: 590 goats (37%)

Keep choice: 1501 times Wins: 499 cars (33%)
Losses: 1002 goats (67%)

Do you notice the variance? This is part of my issue. It's a little hard to explain, but for now I'm saying if you switch it's approximately a 58% chance of winning, not 66%. If you don't switch, you have a 33% chance of winning, and thus a 66% chance of losing. I'm not good at explaining things so I won't even bother explaining my confusing thought pattern that let me to 58%, but the tests I've seen show a variance between switching and not switching.

58+33 < 100. Your poor math basically sums up your poor reasoning.

Naah I'm just messing with you. I didn't believe it at first either. But it's very, very correct. There's a reason they call it counter-intuitive.

 

[dxkj]

edit nm i give up

 

[Mo0o]

Originally posted by: Malak

Originally posted by: chrisms
Change choice: 1600 times Wins: 1010 cars (63%)
Losses: 590 goats (37%)

Keep choice: 1501 times Wins: 499 cars (33%)
Losses: 1002 goats (67%)

Do you notice the variance? This is part of my issue. It's a little hard to explain, but for now I'm saying if you switch it's approximately a 58% chance of winning, not 66%. If you don't switch, you have a 33% chance of winning, and thus a 66% chance of losing. I'm not good at explaining things so I won't even bother explaining my confusing thought pattern that let me to 58%, but the tests I've seen show a variance between switching and not switching.

The percentages have to add to 100%. Otherwise what happens the other 9% of the time?

After running it 10,000 times with keep, 10,000 with change, here are the results:

Keep choice: 10000 times
Wins: 3319 cars (33%)
Losses: 6681 goats (67%)

Change choice: 10000 times
Wins: 6708 cars (67%)
Losses: 3292 goats (33%)

That was Jujufish's results, here are mine:
Keep choice: 10000 times
Wins: 3339 cars (33%)
Losses: 6661 goats (67%)

Change choice: 10000 times
Wins: 6736 cars (67%)
Losses: 3264 goats (33%)


It's amazing you're still fighting this despite theoritical, computer simulated as well as real life simulated evidence to the contrary

 

[sieistganzfett]

The percentages have to add to 100%. Otherwise what happens the other 9% of the time?

maybe the other 9% of the time the goat stole the car? or maybe aliens abducted the goat since they thought the goat was the king of the world, and wanted to negotiate earth's surrender with that goat? i'm obviously not serious about either possibility since they approach 0%, so neither could happen in my view.

It's amazing you're still fighting this despite theoritical, computer simulated as well as real life simulated evidence to the contrary

haha, i agree with that. it's hard to accept the #s. logic is a complex, yet beautiful thing.

You goto an island where everybody living there is a liar. You see a native standing there when you approach a fork in the road, and you need to get to your destination. However, the one path leads to a death swamp where no one makes it out alive if they go that way, and the other path is safe to travel, leading right to your destination. You can only ask the native 2 questions, what are the 2 questions you should ask the native when you stand at a fork in the road and have to go down one of the paths in order to arrive at your destination alive?

 

[soulcougher73]

Well after much reading and explanations. I am man enough to admit i was wrong in disputing it. I can tottaly grasp that swtiching is the right thing to do when there are more then 4 doors involved in the game. But for some reason when its just 3 doors im still seeing a 50/50 chance to win. Oh well someday it will click i guess lol.

 

[Rayden]

If you know anything about probability and you think about this for a little bit you can't dispute that its advantageous to switch. Before you choose each door has 1/3 chance of having the card. You choose one door which has 1/3 chance of being right. The other two doors combined have 2/3 chance of being right. Once you know one of those doors does not have a car, it doesn't change that the probability of that and the other unopened door has 2/3 chance of having the car. The door you chose still has 1/3 chance.

Think about it this way. You get to pick one door, and you win whatever is in the other two doors. That is effectively what happens when you switch doors.

 

[iversonyin]

Holy goat, this thread is still running!

 

[Whoozyerdaddy]

Originally posted by: soulcougher73
Well after much reading and explanations. I am man enough to admit i was wrong in disputing it. I can tottaly grasp that swtiching is the right thing to do when there are more then 4 doors involved in the game. But for some reason when its just 3 doors im still seeing a 50/50 chance to win. Oh well someday it will click i guess lol.

Don't think of it like the host opened one door leaving you with two doors to choose from. Think of it in terms of the host opening all the doors that... 1) are not the door you chose and... 2) do not have a car behind them.

Obviously with three doors the host can only open one door. And under those circumstances your odds would not be as strong as if there were 6 doors or 100 doors but the advantage is still better than 50/50 to change doors once the other goat is exposed.

Remember, when you picked the first door, the odds were that you picked a goat. By opening all the doors that you didn't choose and didn't have a car behind them and realizing that your first choice, as far as the odds are concerned, was probably wrong, you should change to the other door.

 

[Schfifty Five]

Originally posted by: soulcougher73
Well after much reading and explanations. I am man enough to admit i was wrong in disputing it. I can tottaly grasp that swtiching is the right thing to do when there are more then 4 doors involved in the game. But for some reason when its just 3 doors im still seeing a 50/50 chance to win. Oh well someday it will click i guess lol.

it doesn't matter how many doors there are...the host will open as many wrong doors necessary until there are only two doors left: yours and his.

so if you do'nt understand it with 3 doors, you don't understand the problem at all.

Like i said before...don't think of it as your door vs his door, but rather: your door vs ALL his doors (opened and closed). You always want to trade for his doors.

 

[Malak]

Originally posted by: Mo0o
The percentages have to add to 100%. Otherwise what happens the other 9% of the time?

No they don't have to add up, they are probabilities for two different situations, they do not coincide.