Sheep or a Car

[chrisms]

There is no need to insult people, it can be a difficult concept to grasp. I do believe if one actually reads the Wikipedia article they will believe that switching is advantageous. However I get the feeling that those who disagree aren't reading the article fully, because two ways they use to explain it should work to get it through your head. One way is by listing every possibility and showing switching gives a 2/3 chance of success, and the other is increasing the number of doors to 100. The dice example given here was also very good.

I encourage anyone who still believes the chances are 50/50 to reread the article over and over until it clicks. These things are the most fun when you get proven wrong, so get to it

 

[dafatha00]

Originally posted by: chrisms
There is no need to insult people, it can be a difficult concept to grasp. I do believe if one actually reads the Wikipedia article they will believe that switching is advantageous. However I get the feeling that those who disagree aren't reading the article fully, because two ways they use to explain it should work to get it through your head. One way is by listing every possibility and showing switching gives a 2/3 chance of success, and the other is increasing the number of doors to 100. The dice example given here was also very good.

I encourage anyone who still believes the chances are 50/50 to reread the article over and over until it clicks. These things are the most fun when you get proven wrong, so get to it

Er, were you addressing me? I don't see how I insulted anyone in my post.

 

[chrisms]

No not anyone in particular but if you read the responses people get quite upset when they don't hear the right answer.

 

[lokiju]

Originally posted by: Malak
The reasoning behind the explanation is stupid and I will continue to dispute it. You are left with only 2 choices, the third choice is now moot and cannot be even considered in your decision. It is a 50/50 chance and there is no reason to switch nor to not switch. It comes down to chance. You have zero advantage.

QFMFT!

 

[RayH]

Another link:

Bayes's Theorem

 

[chrisms]

There is no reason to argue with Malak. If someone is going to be closed minded and say things like "I will continue to dispute it," then they are guilty of the fault of pseudoauthority and cannot be argued with in a productive manner. If someone says from the beginning that they will refute any direct evidence and never be proven wrong, well then obviously argument isn't going to solve anything because no matter how much evidence you present them with they will not give it priority over their own authority.

 

[yowolabi]

Originally posted by: chrisms
There is no reason to argue with Malak. If someone is going to be closed minded and say things like "I will continue to dispute it," then they are guilty of the fault of pseudoauthority and cannot be argued with in a productive manner. If someone says from the beginning that they will refute any direct evidence and never be proven wrong, well then obviously argument isn't going to solve anything because no matter how much evidence you present them with they will not give it priority over their own authority.

Malak actually hasn't posted in quite a while. He stopped prior to some of the best examples being posted. I don't think it's a coincidence. In the plane thread, many more people stopped arguing when they realized their mistake rather than admit that they were wrong.

But you're right that it's useless to argue with someone who states that they will ignore all arguments.

 

[Kelemvor]

For anyone that doesn't believe you shoudl always switch, you can do it yourself with a random number generator and a friend.

Have your friend generate a number from 1-3.
You guess a number from 1-3.
Your friend tells you one of the other two numbers that is NOT correct.
You either switch or don't.

To make it easy, just do it 20 times and don't switch at all. Then do it 20 times and witch every time. You'll see that it averages out to you win 66% of the time when you switch and 33% when you don't because your initial choice was based out of a 1 in 3 chance.

And if you still don't think you should always switch, you probably think the plane won't take off either... And there's just no hope for you.

 

[TheChort]

Originally posted by: lokiju

Originally posted by: Malak
The reasoning behind the explanation is stupid and I will continue to dispute it. You are left with only 2 choices, the third choice is now moot and cannot be even considered in your decision. It is a 50/50 chance and there is no reason to switch nor to not switch. It comes down to chance. You have zero advantage.

QFMFT!

how can you say that so resolutely?
i can safely say that more than a handful of people have rationaly and thoroughly explained this problem without reverting to name calling or flaming of any manner.

Have you read the thread thoroughly?
Before being so sure that it's wrong, try the experiment yourself. Here's my pass at it. Use it as a model to make one for yourself. (I posted this about 50 posts into the thread)

Originally posted by: TheChort
Since this is easy to do IRL (unlike some other threads we have had ), I did this one with my sister just now.
Granted, this is fairly crude, but it is some kind of result.

Here's what I did:
I had 3 DVD boxes opened up, standing. While she was watching TV and not paying attention to me, I put an orange behind one of them. We did 37 attempts where she didn't switch her answer, and 35 attempts where she switched her answer.

Whether or not she picked the right answer on her first guess, I always deliberately showed an empty box.

That means, if she picked the right box, but switched her answer, she would automatically be wrong. If she picked the wrong box, but switched her answer, she would automatically be right, because I would already reveal the other wrong answer.

RESULTS

Switching
Win: 21/35 = 60%
Loss: 14/35 = 40%

Not Switching
Win: 10/37 = 27%
Loss: 27/37 = 73%

 

[dxkj]

Read this, if it doesnt make sense, tell me why.

Set up the scenario the same, and run it 3 times.

Door A
Door B
Door C

Car is behind door B, run it once for each choice

Pick A, they show C has a sheep, you switch, you win
Pick B, they show A or C has a sheep, you switch, you lose
Pick C, they show A has a sheep, you switch, you win

vs

Pick A, they show C has a sheep, you stay, you lose
Pick B, they show A or C has a sheep, you stay, you win
Pick C, they show A has a sheep, you stay, you lose

Im not sure how it gets any clearer than that.

 

[hanoverphist]

Originally posted by: BrownTown
This thread is gonna end up just like the airplane on a treadmill thread.

im new here... whats the "plane on a treadmill" thread about?


and it pays to switch, learned this in college when they covered odds/ probability

 

[Schfifty Five]

Here's another easy way of looking at tihs problem.

You've got a 1/3 chance of picking the right car. That means you've got a 66% chance of being wrong.

Host has 2/3 chance of having the car in his doors.

Essentially it's YOUR DOOR vs HIS REMAINING DOORS.

By SWITCHING, you are essentially receiving ALL OF HIS DOORS.

The only reason it looks like it's a one door vs one door (50/50) scenario is b/c he opens one door, but really he's asking "Do you want to trade your ONE door for my TWO doors?"

Obviously YES YOU SWITHC B/C 2 DOORS IS BETTER CHANCES OF WINNING!!!!

 

[dxkj]

The key is that you didn't know which door had a sheep in it before they revealed one, meaning you could have picked that door instead, and they would have opened another one.


Lets change the game.... the host doesnt reveal any doors, but you can pick any two doors.... would you have better odds if you could pick two doors, or one door?

Sure if you pick two doors, you will always get one sheep in the bargain, but you have a better chance of netting the car.

The host opens one of the two doors you picked and it is a sheep.... does that mean you now have a 50% chance of winning? Nope, because observation doesn't change the original results.

 

[chrisms]

I think you guys are arguing against nobody now

 

[Schfifty Five]

Originally posted by: dxkj
Read this, if it doesnt make sense, tell me why.

Set up the scenario the same, and run it 3 times.

Door A
Door B
Door C

Car is behind door B, run it once for each choice

Pick A, they show C has a sheep, you switch, you win
Pick B, they show A or C has a sheep, you switch, you lose
Pick C, they show A has a sheep, you switch, you win

vs

Pick A, they show C has a sheep, you stay, you lose
Pick B, they show A or C has a sheep, you stay, you win
Pick C, they show A has a sheep, you stay, you lose

Im not sure how it gets any clearer than that.

exactly.

 

[Mo0o]

all this goat talk makes me hungry

 

[Malak]

Originally posted by: iversonyin
If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...if you switch, you win.

If you picked a goat (G2) , and the host shows you a goat (G1) (he has to)...if you switch, you win.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you switch, you lose.

These are the 3 scenarios and why the math came out to be 2/3 switching vs 1/3 not switching. Is there another scenario? let see what happen if you always stay:

If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...If you stay, you lose.

If you picked a goat (G2), and the host shows you a goat (G1) (he has to)...If you stay, you lose.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you stay, you win.

That makes perfect sense and shows the 1/3rd, 2/3rd theory. However, after careful consideration of the problem I have come to a different conclusion altogether. I see the confusion between the two camps and I conclude they are both correct given the situation.

 

[Schfifty Five]

Originally posted by: Malak

Originally posted by: iversonyin
If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...if you switch, you win.

If you picked a goat (G2) , and the host shows you a goat (G1) (he has to)...if you switch, you win.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you switch, you lose.

These are the 3 scenarios and why the math came out to be 2/3 switching vs 1/3 not switching. Is there another scenario? let see what happen if you always stay:

If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...If you stay, you lose.

If you picked a goat (G2), and the host shows you a goat (G1) (he has to)...If you stay, you lose.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you stay, you win.

That makes perfect sense and shows the 1/3rd, 2/3rd theory. However, after careful consideration of the problem I have come to a different conclusion altogether. I see the confusion between the two camps and I conclude they are both correct given the situation.

both correct? There is only one correct answer. Those who think 50/50 do not understand the problem.

 

[Malak]

Originally posted by: Schfifty Five

Originally posted by: Malak

Originally posted by: iversonyin
If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...if you switch, you win.

If you picked a goat (G2) , and the host shows you a goat (G1) (he has to)...if you switch, you win.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you switch, you lose.

These are the 3 scenarios and why the math came out to be 2/3 switching vs 1/3 not switching. Is there another scenario? let see what happen if you always stay:

If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...If you stay, you lose.

If you picked a goat (G2), and the host shows you a goat (G1) (he has to)...If you stay, you lose.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you stay, you win.

That makes perfect sense and shows the 1/3rd, 2/3rd theory. However, after careful consideration of the problem I have come to a different conclusion altogether. I see the confusion between the two camps and I conclude they are both correct given the situation.

both correct? There is only one correct answer. Those who think 50/50 do not understand the problem.

You have a 33% chance of being right on your first choice, but if you switch in phase 2 you only have a 58% chance of being right.

 

[RaistlinZ]

There is no spoon. /Neo

 

[TheChort]

Originally posted by: chrisms
I think you guys are arguing against nobody now

:laugh:

 

[chrisms]

Originally posted by: Malak

Originally posted by: iversonyin
If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...if you switch, you win.

If you picked a goat (G2) , and the host shows you a goat (G1) (he has to)...if you switch, you win.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you switch, you lose.

These are the 3 scenarios and why the math came out to be 2/3 switching vs 1/3 not switching. Is there another scenario? let see what happen if you always stay:

If you picked a goat (G1), and the host shows you a goat (G2) (he has to)...If you stay, you lose.

If you picked a goat (G2), and the host shows you a goat (G1) (he has to)...If you stay, you lose.

If you picked a car (C), and the host shows you a goat (G1 or G2 because he knows you have the car, so he can show either goat). If you stay, you win.

That makes perfect sense and shows the 1/3rd, 2/3rd theory. However, after careful consideration of the problem I have come to a different conclusion altogether. I see the confusion between the two camps and I conclude they are both correct given the situation.

You can't have a 1/2 chance and a 2/3 chance at the same time. I figure this is as close as you come to admitting being wrong so I will accept it and move on.

 

[imported_Baloo]

When a person arrives at conclusion irrationally, it is not possible to convince the person using rational arguments of the error in their judgement, that is why you can't explain to these guys why odds are the same for either option.

 

[chrisms]

Originally posted by: Baloo
When a person arrives at conclusion irrationally, it is not possible to convince the person using rational arguments of the error in their judgement, that is why you can't explain to these guys why odds are the same for either option.

Obviously you have not bothered to read the article. Turn that criticism back on yourself.

 

[imported_Baloo]

Originally posted by: chrisms

Originally posted by: Baloo
When a person arrives at conclusion irrationally, it is not possible to convince the person using rational arguments of the error in their judgement, that is why you can't explain to these guys why odds are the same for either option.

Obviously you have not bothered to read the article. Turn that criticism back on yourself.

Actially, I did, you will note I did not change the article - there's no point, as i said. Do you want to buy a perpetual motion machine?