Sheep or a Car

[kranky]

When this topic comes up from time to time, it's cool to see how people come around to understanding why you should switch - that "light bulb goes on" moment.

It could have been the same this time too, except iamaelephant doesn't know how to help people understand without being an insulting clown at the same time.

 

[jjones]

The only thing I know at this point is that behind every door is a dead horse that keeps getting flogged for no apparent reason.

 

[6000SUX]

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

 

[PlatinumGold]

Originally posted by: TheChort

Originally posted by: Malak

Originally posted by: Schfifty Five
Does that make sense?

I hate to repeat this again and again and again...

If it were that simple, it wouldn't have been so hotly debated. I've said enough on this subject.

Personally, I don't care how you come to your conclusion on this one, or if you ever do for that matter, mostly because I will probably never meet you.

But for that very same reason, my advice to will hopefully seem more sincere:
Stop thinking so highly of yourself and your mental processes. You are not a genius. You are probably above average, but that's about it.Your attempts to seem like some overly intelligent person doesn't fool anybody except yourself.
Look at some of the comments you've made

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

you sound like some 60 year old playing a game of chess over snail mail. Take it easy on yourself. There will be plenty of time for boring people by talking like this when you get older.

he's just trying to save face, leave it at that.

saying it is more complicated than the explanation given is more evidence of that.

frankly it's not that complicated. it is pretty simple if you are willing to factor in that the host already knows what's behind each door.

 

[DivideBYZero]

Originally posted by: ElFenix
the plane doesn't take off and .999... does not equal 1, goddamnit!

What if I pop my car into neutral to coast while shopping for bulk beef, onlilne?

 

[PlatinumGold]

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

your point while almost correct is moot. as what would be the point of choosing between the remaining doors if the host were to open the door with the car behind it?

obviously the question is posed such as to inform the reader that the host is choosing a door without the car, otherwise the question itself is meaningless.

 

[6000SUX]

Originally posted by: PlatinumGold

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

your point while almost correct is moot. as what would be the point of choosing between the remaining doors if the host were to open the door with the car behind it?

obviously the question is posed such as to inform the reader that the host is choosing a door without the car, otherwise the question itself is meaningless.

The point is that the question, as posed, was wrong. The question is not posed so as to inform the reader of something it neither says nor implies.

 

[Born2bwire]

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

Reading it literally it says, "You pick a door and the host, knowing what's behind each door, opens another door which has a sheep" because that is what the OP typed. Where do you get the idea that it just "happens" to contain a sheep? This isn't splitting hairs, this is basic reading comprehension.

 

[6000SUX]

Originally posted by: Born2bwire

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

Reading it literally it says, "You pick a door and the host, knowing what's behind each door, opens another door which has a sheep" because that is what the OP typed. Where do you get the idea that it just "happens" to contain a sheep? This isn't splitting hairs, this is basic reading comprehension.

Nope. So soddy. From the Wikipedia article mentioned earlier in the thread:

A widely known statement of the Monty Hall problem appeared in a letter to Marilyn vos Savant's Ask Marilyn column in Parade Magazine (vos Savant 1990):

Suppose 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, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

While this is a common presentation of the problem, it leaves crtitical aspects of the host's behavior unstated making the problem mathematically ambiguous. In a more precise statement of the problem (Mueser and Granberg 1999) the host is constrained to always open a door revealing a goat and to always make the offer to switch:

A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door."

You begin by pointing to door number 1. The host shows you that door number 3 has a goat. Do the player's chances of getting the car increase by switching to Door 2?

The problem as generally intended also assumes that the particular door the host opens conveys no special information about whether the player's initial choice is correct. The simplest way to make this explicit is to add a constraint that the host will open one of the remaining two doors randomly if the player initially picked the car.

You are pwned, but only by yourself. Come with something a little stronger next time you attack someone a little more... with it than you.

 

[JujuFish]

Originally posted by: 6000SUX
Don't try to school your betters.

I don't have to do so. You're doing a good job making an idiot of yourself for me. :thumbsup:

 

[6000SUX]

Originally posted by: JujuFish

Originally posted by: 6000SUX
Don't try to school your betters.

I don't have to do so. You're doing a good job making an idiot of yourself for me. :thumbsup:

ROFLMAO You are probably feeling pretty poorly about yourself right now. You did it to yourself. Read the Wikipedia article and weep, dumbass.

 

[Schfifty Five]

Originally posted by: 6000SUX

Originally posted by: PlatinumGold

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

your point while almost correct is moot. as what would be the point of choosing between the remaining doors if the host were to open the door with the car behind it?

obviously the question is posed such as to inform the reader that the host is choosing a door without the car, otherwise the question itself is meaningless.

The point is that the question, as posed, was wrong. The question is not posed so as to inform the reader of something it neither says nor implies.

So if the question was worded correctly, where you choose a door, host opens one of the remaining doors that he knows is wrong, do you switch?

Do you believe the % of winning goes from 33% (not switching) to 66% (switching)?

 

[6000SUX]

Originally posted by: Schfifty Five
So if the question was worded correctly, where you choose a door, host opens one of the remaining doors that he knows is wrong, do you switch?

Do you believe the % of winning goes from 33% (not switching) to 66% (switching)?

Yes. Thank you. I even posted what I think may be the easiest-to-understand explanation of the concept yet in this thread (although I haven't read the whole thing), one that anyone can grasp:

A very simple way to explain this is that the car will only be behind the contestant's originally picked door 1/3 of the time. When it is not (the other 2/3 of the time), it will be behind the [other] door not opened by the host.

 

[Seekermeister]

The odds are equal, only looking at the mathematics of it. But, it is also necessary to look at the general attitude of the show and the host. They may be wanting to induce either a right or wrong choice, to either increase or decrease their costs. Since the show's popularity is based on the idea of winning, it may be to their advantage to want a person to win, but too many winners costs too much.

 

[cvstrat]

I think it might be easy to understand if you look at it this way.

You know there are 2 sheep and one car, so when you pick your first door you are most likely (66% chance) to pick a sheep. I think we can all agree on this.

Now the host is always going to remove the other sheep, per the game guidlines for this example.

So I you most likely picked one sheep, and he revealed the other sheep, the car is most likely behind the other door, aka the one you should switch to.

I wouldn't look at it as improving your odds (even tho you technically are) but I'd look at it as trying to eliminate the sheep, then choosing the car. (which is most likely the 3rd door)

Sure if you picked the car first and switch you lose, but remember you're more likely to NOT pick the car right the first time, which makes switching the right choice.

 

[Schfifty Five]

Originally posted by: Seekermeister
The odds are equal, only looking at the mathematics of it. But, it is also necessary to look at the general attitude of the show and the host. They may be wanting to induce either a right or wrong choice, to either increase or decrease their costs. Since the show's popularity is based on the idea of winning, it may be to their advantage to want a person to win, but too many winners costs too much.

you're wrong.

it's not even. You stand to increase your chances of winning to 66% if you switch doors.

 

[A Casual Fitz]

I don't think I agree with it, but I follow the logic. I just don't think that the past is something to think about once that 3rd door opens.

 

[CountZero]

Ok so I was bored and wrote a simulation in matlab. I ran two scenarios.

In the first it is assumed that Monty will always pick a door that 1) you did not pick and 2) does not have the car behind it. This is the actual gameshow version of the question. In this case with 1000000 cases run you have a 66.6% chance of winning by switching (and therefore a 33.3% chance of winning by not).

In the second Monty will always pick a door that you did not pick but it could be the door with the car. In this case you have a 33.3% chance of winning whether you switch or not.

If it was painfully obvious that you should switch such scenarios would not arise on game shows like Let's Make a Deal so if it isn't clear try writing up a simulation or do a run with someone, even if you still get why it does work out.

 

[PlatinumGold]

Originally posted by: 6000SUX

Originally posted by: PlatinumGold

Originally posted by: 6000SUX

Originally posted by: Born2bwire
The OP doesn't say, "he opens a door which happens to contain a sheep", he says, "he opens another door which has a sheep." Big difference between happens to have and has. The only beef that one could say with the statement is that the OP does not specify whether or not the host has to open a door everytime. That does change the outcome and was one of the main points of debate in the original statement of the problem in print.

Yes, he opens a door which has a sheep. It just so happens to contain a sheep; you're splitting a nonexistent hair. Nothing in the language indicates that he chose on the basis of it being a sheep. Reading it literally, there is a 50% chance. Of course, that's not the problem.

your point while almost correct is moot. as what would be the point of choosing between the remaining doors if the host were to open the door with the car behind it?

obviously the question is posed such as to inform the reader that the host is choosing a door without the car, otherwise the question itself is meaningless.

The point is that the question, as posed, was wrong. The question is not posed so as to inform the reader of something it neither says nor implies.

wrong,

the purpose is communication, if the idea was communicated whether or not the grammar is correct is really irrelevant.

your reasoning was, the op's question was poorly stated hence i initially got the wrong answer is incorrect, because the average person upon reading the question would understand the intent of the OP.

again, let's examine your logic.


because the OP didn't specify whether or not the host CHOOSE the door with the goat behind it vs accidently choosing the door with the goat behind it is moot.

we know that in the end the door opened had a goat behind it, and we also know that the odds of switching once that goat had been revealed are better than not switching,

so in this instance the actual intent of the host is not relevant.

now this is different from the logic that says, the host doesn't know whether or not the player had chosen the door with a car behind it and is randomly choosing.

instead we are assuming that the host (whether or not he knew which door had the car behind it) ended up opening a door with a goat behind it.

once this fact is established, than the odds of finding the door with the car behind it are much higher by switching than not switching.

hence your b1tching about how the question is worded is moot.

 

[6000SUX]

Originally posted by: PlatinumGold
blather blather blather

... hence your b1tching about how the question is worded is moot.

Maybe I could take you seriously if your reasoning and English abilities were a little closer to average. Go read the Wikipedia article, which also points out the vagueness. I made no mistake, but solved the problem exactly as worded. You, on the other hand, cannot even perceive that the vagueness exists, or the folly of reading meaning into text when it doesn't exist. You wouldn't do well as a programmer or a lawyer, I can definitely say that much.

 

[sieistganzfett]

6000sux, why you got to get over logical on the logic problem? you're acting like a lawyer!

 

[Fayd]

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.

not really. if you switch, it's a 66% chance of success. the chance of the item being behind your current door is 33%.

reason being, with switching, you're getting doors 2 and 3 with 1 shot.



example to make it clearer. there is 1000 doors.

you choose door 1. the game show host, opens all doors except door 1, and door 687. do you switch to door 687?

of course. reason being? it's a 999/1000 chance that it's behind 687.

 

[TheChort]

Originally posted by: Fayd

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.

not really. if you switch, it's a 66% chance of success. the chance of the item being behind your current door is 33%.
reason being, with switching, you're getting doors 2 and 3 with 1 shot.
example to make it clearer. there is 1000 doors.
you choose door 1. the game show host, opens all doors except door 1, and door 687. do you switch to door 687?
of course. reason being? it's a 999/1000 chance that it's behind 687.

Do you realize that this explanation has been posted exactly the same way at least 3 times already.
And why are you quoting someone that hasn't posted in 2 days

to all:
PLEASE READ ALL THE POSTS BEFORE POSTING -- SOMEONE ELSE HAS PROBABLY SAID WHAT YOU ARE THINKING OF

 

[Special K]

I am taking a probability class this semester and just happened to stumble upon this thread after discussing this very problem in class last week. I can't believe something so simple has generated so much debate. I'm guessing the people arguing against always switching fall into one or more of the following categories:

1. People who have never taken a formal probability class, and are instead trying to argue based purely on common sense (many results in probability, even to common and everyday occurences, can have very counterintuitive results)

2. People who know what the right answer is, but just like to argue to keep the flames going (which admittedly can be entertaining at times )

3. People who once believed the wrong answer but are now too proud to admit they were wrong

 

[6000SUX]

Originally posted by: sieistganzfett
6000sux, why you got to get over logical on the logic problem? you're acting like a lawyer!

Sorry. I don't like people telling me I'm wrong when I'm right. I'll stop now.