Sheep or a Car

[So]

Originally posted by: jman19

Originally posted by: Malak

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.

I don't know why you have to continue to insult me, it doesn't help your arguement any. Furthermore I should like to refer to the part in the article where people much smarter than you or I disputed this as well.

You might be a genius, but you aren't educated. See the Wiki article for several clear explainations.

True. I was originally of Malak's opinion, but after reading the Wiki article I am convinced.

 

[Mo0o]

Originally posted by: slayer202

Originally posted by: mercanucaribe
As soon as I read that the game show host knows which door has one, I realized that that is the key.. Either you picked the car and the host picked the door to open randomly, or you picked a sheep and he had to pick the sheep instead of the car. I don't know the math, but it feels to me like your odds are better if you switch.

This helps, but I am still skeptical.

Let's say the situation is the same. However, you do not pick a door until the host takes away one of the sheep. You now have a 50% shot at it. What makes this choice any difference than if you had picked in the beginning?

No, the host hsa to know which door you pick initially so he can show you one of hte other doors

 

[Mo0o]

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%

Malak will accuse you of cheating to skew the results because he's a genius

 

[chrisms]

The chances that you pick the right door in the beginning is 1/3. Thus sticking with the door gives you a 1/3 chance of winning overall. The host opening the door has no effect on the probability. Think of it as the host opening all three doors and never giving you a chance to switch. Just because he walks over to #1 first and shows a sheep does not mean your odds just went to 50/50. The probability of success here remains 1/3.

Now, if the chances that you picked the wrong door are 2/3, then it is most likely you picked the wrong door. Thus switching would give you a better chance of winning. Remember the host opening the door has no effect on the probability.

I don't know why I explain this I think just about everyone gets it.. now it seems much clearer to me though.

 

[Kyteland]

Originally posted by: Malak

Originally posted by: QED
If the odds of your door having the car is 1/3, that means the odds the remaining door has the car must be 2/3.

The problem changes considerably if the host has no idea which door has the car behind it, and opens one of the two remaing doors at random.

I am going to ponder on this and get back with you.

An equivalent problem would be this: I roll a dice and you roll a dice in an attempt to match the number. After we've rolled I will tell you 4 numbers that my dice didn't roll (and they *have* to be 4 that aren't your number and aren't my number) and you have to decide to switch your number of not. The key work here is I tell you *after* I roll the dice. The odds that I rolled your number are still 1 in 6 (you can assume the dice are fair ) and the odds that I didn't roll your number are still 5 in 6. The numbers I reveal to you can't affect the odds of the dice in any way. What I'm doing by telling you the 4 numbers is I'm allowing you to simultaneously pick all 5 numbers at once.

The odds will always be 1 in 6 that you rolled the same number originally and 5 in 6 that you didn't.

You may have to quote my post to see this table properly, but here's an exhaustive cycle of all dice rolling possibilities.

You Me Best Action Prob Host can remove
1 1 Stay 1/36 2,3,4,5 or 2,3,4,6 or 2,3,5,6 or 2,4,5,6, or 3,4,5,6
1 2 Switch 1/36 3,4,5,6
1 3 Switch 1/36 2,4,5,6
1 4 Switch 1/36 2,3,5,6
1 5 Switch 1/36 2,3,4,6
1 6 Switch 1/36 2,3,4,5
2 1 Switch 1/36 3,4,5,6
2 2 Stay 1/36 1,3,4,5 or 1,3,4,6 or 1,3,5,6 or 1,4,5,6, or 3,4,5,6
2 3 Switch 1/36 1,4,5,6
2 4 Switch 1/36 1,3,5,6,
2 5 Switch 1/36 1,3,4,6
2 6 Switch 1/36 1,3,4,5
3 1 Switch 1/36 2,4,5,6
3 2 Switch 1/36 1,4,5,6
3 3 Stay 1/36 1,2,4,5 or 1,2,4,6 or 1,2,5,6 or 1,4,5,6, or 2,4,5,6
3 4 Switch 1/36 1,2,5,6
3 5 Switch 1/36 1,2,4,6
3 6 Switch 1/36 1,2,4,5
4 1 Switch 1/36 2,3,5,6
4 2 Switch 1/36 1,3,5,6
4 3 Switch 1/36 1,2,5,6
4 4 Stay 1/36 1,2,3,5 or 1,2,3,6 or 1,2,5,6 or 1,3,5,6, or 2,3,5,6
4 5 Switch 1/36 1,2,3,6
4 6 Switch 1/36 1,2,3,5
5 1 Switch 1/36 1,2,3,4
5 2 Switch 1/36 1,3,4,6
5 3 Switch 1/36 1,2,4,6
5 4 Switch 1/36 1,2,3,6
5 5 Stay 1/36 1,2,3,4 or 1,2,3,6 or 1,2,4,6 or 1,3,4,6, or 2,3,4,6
5 6 Switch 1/36 1,2,3,4
6 1 Switch 1/36 2,3,4,5
6 2 Switch 1/36 1,3,4,5
6 3 Switch 1/36 1,2,4,5
6 4 Switch 1/36 1,2,3,5
6 5 Switch 1/36 1,2,3,4
6 6 Stay 1/36 1,2,3,4 or 1,2,3,5 or 1,2,4,5 or 1,3,4,5, or 2,3,4,5

so 6/36 of the outcomes you will win by staying and 30/36 you will win by switching.

Originally posted by: Malak
If this so-called genius cares to argue it with me, he/she can try. I will bury her/him.

How do you ever expect to learn anything if you don't have an open mind?

 

[jman19]

Originally posted by: Mo0o

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%

Malak will accuse you of cheating to skew the results because he's a genius

Mo0o, don't you know, TheChort didn't perform enough experiments to "prove" this - there is still a chance that these numbers are an anomaly

 

[imported_Baloo]

Oh not this again. There is no advantage to changing the door, the odds are the same. I have a perpetual motion machine, you want to buy it?

 

[jman19]

Originally posted by: Baloo
Oh not this again. There is no advantage to changing the door, the odds are the same. I have a perpetual motion machine, you want to buy it?

:roll:

 

[hoyaguru]

Originally posted by: iamaelephant

Initially when you chose a door, you essentially divided the complete set of 3 doors into two parts, the one door you chose and the 2 remaining doors. So you know that there is a 2/3 chance that the car is behind one of the two doors, and a 1/3 chance that the car is behind the door you chose. Are you following? We now have two sets of doors. One with a 2/3 chance of finding a car, and one with a 1/3 chance of finding a car.

For your second choice, of course you will want to choose the side that has a 2/3 chance of finding a car. Well one of those doors is already open, so you now have one door with a 2/3 chance of a car and one door with a 1/3 chance.

I think this is what throws everybody. When you are saying that a choice between two doors gives something different than a 50/50 chance, it doesn't seem to make sense. I wonder if this type of thinking would help the contestants on that Howie Mandell game show where they pick suitcases (can't remember the name of it).

This problem reminds me of the old one about three guys checking into a hotel and paying $10 each for the room. The manager realizes that it is only $25 for the room, so he sends the bellboy up with five one dollar bills. Each man takes a dollar back, and give the remaining two dollars to the bellboy as a tip. Now each man has paid $9 each for the room. $9 times 3 equals $27, the bellboy kept $2, where did the other dollar go?

 

[iamaelephant]

Originally posted by: DaShen

Originally posted by: PhattyB
There is no advantage. All it does is gaurentee you have a 50% chance of winning some sheep love.

Nope, wrong.

It goes from 1/3 to 1/2 chance if you switch.

One of the reasons so many people don't get it is because people like you are spreading misinformation about the problem. Am I to assume that you made a typo, or are you really that stupid? Please read the Wiki article and the posts by all of the rational people in this thread. Avoid Malak.

 

[iamaelephant]

Originally posted by: hoyaguru
This problem reminds me of the old one about three guys checking into a hotel and paying $10 each for the room. The manager realizes that it is only $25 for the room, so he sends the bellboy up with five one dollar bills. Each man takes a dollar back, and give the remaining two dollars to the bellboy as a tip. Now each man has paid $9 each for the room. $9 times 3 equals $27, the bellboy kept $2, where did the other dollar go?

Arg damn you! Now you've got that problem in my head and I can't remember the solution!

 

[soulcougher73]

ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

 

[iamaelephant]

Originally posted by: soulcougher73
ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

You are wrong. I'm not going to go to the trouble of explaining it again. You're just wrong, mmkay?

 

[Kyteland]

Originally posted by: iamaelephant

Originally posted by: hoyaguru
This problem reminds me of the old one about three guys checking into a hotel and paying $10 each for the room. The manager realizes that it is only $25 for the room, so he sends the bellboy up with five one dollar bills. Each man takes a dollar back, and give the remaining two dollars to the bellboy as a tip. Now each man has paid $9 each for the room. $9 times 3 equals $27, the bellboy kept $2, where did the other dollar go?

Arg damn you! Now you've got that problem in my head and I can't remember the solution!

$25 room charge + $2 room tip = $27 paid by the tree men + $3 taken back by the men = original $30

 

[hoyaguru]

Originally posted by: iamaelephant

Originally posted by: hoyaguru
This problem reminds me of the old one about three guys checking into a hotel and paying $10 each for the room. The manager realizes that it is only $25 for the room, so he sends the bellboy up with five one dollar bills. Each man takes a dollar back, and give the remaining two dollars to the bellboy as a tip. Now each man has paid $9 each for the room. $9 times 3 equals $27, the bellboy kept $2, where did the other dollar go?

Arg damn you! Now you've got that problem in my head and I can't remember the solution!

lol, sorry...

 

[iamaelephant]

Originally posted by: Kyteland

Originally posted by: iamaelephant

Originally posted by: hoyaguru
This problem reminds me of the old one about three guys checking into a hotel and paying $10 each for the room. The manager realizes that it is only $25 for the room, so he sends the bellboy up with five one dollar bills. Each man takes a dollar back, and give the remaining two dollars to the bellboy as a tip. Now each man has paid $9 each for the room. $9 times 3 equals $27, the bellboy kept $2, where did the other dollar go?

Arg damn you! Now you've got that problem in my head and I can't remember the solution!

$25 room charge + $2 room tip = $27 paid by the tree men + $3 taken back by the men = original $30

Grr it's so obvious.... Yet it gets me every time.

 

[iversonyin]

Originally posted by: soulcougher73
ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

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.

Does this help?

 

[soulcougher73]

"A mind is like a parachute, it only works when open"

You are helplessly blinded by what you have read. Once you realize 1 of the 3 doors in the given scenaro is just a distraction, you will see you have always had a 50% chance from the get go to win the car regardless if you switch or not.

As i said if the host had no idea what was behind any of the doors and i picked door #3 we will say, and he opened THAT door only. Then i only had a 1 in 3 chance from the beginning.

But when the host plays the i know what is behind each door game then your chances have always been 50% because he will ALWAYS reviel one of the doors you did not chose as a sheep.

I dont see how that is so hard to grasp.

And its not that i dont grasp where you are coming from, i do. It is just flawed logic is all.

 

[Mo0o]

Originally posted by: soulcougher73
"A mind is like a parachute, it only works when open"

You are helplessly blinded by what you have read. Once you realize 1 of the 3 doors in the given scenaro is just a distraction, you will see you have always had a 50% chance from the get go to win the car regardless if you switch or not.

As i said if the host had no idea what was behind any of the doors and i picked door #3 we will say, and he opened THAT door only. Then i only had a 1 in 3 chance from the beginning.

But when the host plays the i know what is behind each door game then your chances have always been 50% because he will ALWAYS reviel one of the doors you did not chose as a sheep.

I dont see how that is so hard to grasp.

And its not that i dont grasp where you are coming from, i do. It is just flawed logic is all.

if i randomly choose a door, then close my eyes and refuse to see what happens. i h ave a 50/50 shot of winning?

Does that work for n number of doors? Given 10000 doors, i randomly choose one. Then the host starts revealing all the wrong doors. You're saying from the get go i had a 50/50 shot of winning?

 

[iversonyin]

Originally posted by: soulcougher73
"A mind is like a parachute, it only works when open"

You are helplessly blinded by what you have read. Once you realize 1 of the 3 doors in the given scenaro is just a distraction, you will see you have always had a 50% chance from the get go to win the car regardless if you switch or not.

As i said if the host had no idea what was behind any of the doors and i picked door #3 we will say, and he opened THAT door only. Then i only had a 1 in 3 chance from the beginning.

But when the host plays the i know what is behind each door game then your chances have always been 50% because he will ALWAYS reviel one of the doors you did not chose as a sheep.

I dont see how that is so hard to grasp.

And its not that i dont grasp where you are coming from, i do. It is just flawed logic is all.

Run through the scenarios and you will see why it PAYS to switch. Re-read the scenario and you will understand. Don't fight it.

 

[iamaelephant]

Originally posted by: soulcougher73
"A mind is like a parachute, it only works when open"

You are helplessly blinded by what you have read. Once you realize 1 of the 3 doors in the given scenaro is just a distraction, you will see you have always had a 50% chance from the get go to win the car regardless if you switch or not.

As i said if the host had no idea what was behind any of the doors and i picked door #3 we will say, and he opened THAT door only. Then i only had a 1 in 3 chance from the beginning.

But when the host plays the i know what is behind each door game then your chances have always been 50% because he will ALWAYS reviel one of the doors you did not chose as a sheep.

I dont see how that is so hard to grasp.

And its not that i dont grasp where you are coming from, i do. It is just flawed logic is all.

Read iversonyin's scenarios above. Tell me where the "flawed logic" is there. Explain to me why he got the answer he did, then explain to me how it is wrong.

 

[soulcougher73]

Originally posted by: iversonyin

Originally posted by: soulcougher73
ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

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.

Does this help?

It really depends on how you look at it i guess. Mathmatically you are correct. But logically you are not. The best way i can think to explain it is with the old math thing about if you only go half way each time you will never actually get there thing. Mathmatically in numbers that is correct, but in the real world that is not true.

Maybe that will help to explain it or not. Who knows. Doesnt really matter

 

[Mo0o]

Originally posted by: soulcougher73

Originally posted by: iversonyin

Originally posted by: soulcougher73
ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

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.

Does this help?

It really depends on how you look at it i guess. Mathmatically you are correct. But logically you are not. The best way i can think to explain it is with the old math thing about if you only go half way each time you will never actually get there thing. Mathmatically in numbers that is correct, but in the real world that is not true.

Maybe that will help to explain it or not. Who knows. Doesnt really matter

looks like someone is backpeddaling

 

[iamaelephant]

Originally posted by: soulcougher73
It really depends on how you look at it i guess. Mathmatically you are correct. But logically you are not. The best way i can think to explain it is with the old math thing about if you only go half way each time you will never actually get there thing. Mathmatically in numbers that is correct, but in the real world that is not true.

Maybe that will help to explain it or not. Who knows. Doesnt really matter

This moronic assertion is proved wrong by the myriad experiements that have been performed, including a couple in this thread itself. You're wrong. I think even you know it. Just admit it, dipsh!t.

 

[Venix]

Originally posted by: soulcougher73

Originally posted by: iversonyin

Originally posted by: soulcougher73
ive only read up to the 3rd page, but Malek is correct. No matter what door you choise the host will always reviel a sheep in one of the 2 doors you did not select as a distraction technique and for drama sake.

We will say for arguement sake your first pic was the door with the car. The host knows this but you do not. Instead of saying OMG you picked the right door, he shows you a door with a sheep behind it. Which no matter what door you pick he WILL do this as a distraction. So the 3rd door is a moot door. It does not matter at all.

You are left with a 50% chance to win regardless if you switch doors or not. Because only 2 doors really matter, the 3rd door is always revieled as a sheep regardless if you picked the right door the first time or not.

Again all this will change if the host has no idea what is behind what door, and you just pick a door and he opens that door only. Then it is 1/3 chances to win.

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.

Does this help?

It really depends on how you look at it i guess. Mathmatically you are correct. But logically you are not. The best way i can think to explain it is with the old math thing about if you only go half way each time you will never actually get there thing. Mathmatically in numbers that is correct, but in the real world that is not true.

Maybe that will help to explain it or not. Who knows. Doesnt really matter

Uh, earlier in the thread TheChort actually did a real world experiment and got the same results. ~33% chance of winning if you don't switch, ~66% if you do.