Sheep or a Car

[Schfifty Five]

Originally posted by: 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.

malak, think of it this way...intead of it being your door vs host's door...think of it as the host offering ALL his doors for yoru door.

Would you trade switch in that case? Obviously right? I mean, having two doors is better than one. That is relaly what he is doing.....even if he opens one known wrong door, he's pretty much saying "keep your door, or trade it for all my doors (opened and unopened)"

you should be able to see that you are getting 66% wins from switching to his doors.

 

[Scarpozzi]

I agree with the point that the "host knows what's behind the doors". Because if he didn't and picked door 3, the car could be behind it. Since the car didn't move though, I have to say it could still be behind either. So while, this does make sense to say that there is a higher chance because on of the doors has been eliminated, no matter what the percentages are when you crunch the numbers, it's still either behind 1 or 2.

 

[Schfifty Five]

Originally posted by: Scarpozzi
I agree with the point that the "host knows what's behind the doors". Because if he didn't and picked door 3, the car could be behind it. Since the car didn't move though, I have to say it could still be behind either. So while, this does make sense to say that there is a higher chance because on of the doors has been eliminated, no matter what the percentages are when you crunch the numbers, it's still either behind 1 or 2.

so are you part of the "50/50" crowd or "33/66" crowd?

Yes it's either behind YOUR door or HOST remaining door, but it's not a 50/50 shot, 66% of the time, the HOST'S door will have the car.

 

[dxkj]

A B C

you pick A, host shows C has a sheep... The host didn't show your door, because he cant... the host didn't show door B for one of 2 reasons... either it had a car and he cant show that, or it had a sheep but he chose the other door instead...

So the information you gained about A is ... nothing
The information you gained about B is, that there is a 50% chance that it has a car behind it

Based on that information, you have to choose B, because it wasn't shown by the dealer, there is a higher chance that it has a car behind it.

 

[jjones]

The easiest way to look at it is to just reverse the roles. There are three doors, only one car, and two sheep. You get to choose 2 doors, knowing for sure one of those will have a sheep behind it. Now what would you rather have, the selection of two doors, or just the selection of one door? I'll take the two doors Monty!

Or you could look at it this way. What would you rather have? One door as your choice, or one door to eliminate from the three keeping the other two as your choice? In essense, that what this is about. The door you initially choose, is the door that you are eliminating. This changes your odds from 1 in 3 to 2 in 3.

 

[JujuFish]

Here's another thing to think about, and I believe it's been mentioned in the thread already:
Because Monty always shows a goat, since he knows what's behind everything, it becomes a situation that if you had sheep and switch, you will win, and if you had car and switch, you will lose. Right?

Well, when you chose your door to begin with, there was a 2/3 chance that it was a sheep. So, since you win automatically if you had originally chosen a sheep, your chance if winning, should you switch, is also 2/3.

 

[Mo0o]

Malak still hasn't addressed Jujufish and I's experimental evidence

 

[BeauJangles]

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?

Above what? Incredibly intelligent people believed the world was flat, thought the sun orbited the earth, and that natural selection didn't exist. Eventually, however, through evidence, they were proven incorrect. That doesn't make them any less intelligent, but that doesn't mean anybody today can't go back, examine the evidence, and realize that they were wrong.

Honestly, Malak, it sounds like you are riding some sort of high horse. I would encourage you to get off of it and join a reasonable discussion. Instead of expounding on how intelligent you are, why don't you consider the evidence in front of you? Raise objections, that's what every intelligent person does, but then listen to those who are reasonable enough to reply to you in a courteous way. Try to have some patience with people who get frustrated with you, and, hopefully, people will have patience with you too.

That being said, if after an honest examination of the evidence, you realize you are incorrect, it would be great to hear you say that.

Beyond theoretical explanations, I would recommend visiting a link posted earlier in this thread - http://www.grand-illusions.com/simulator/montysim.htm You can run simulations there to your heart's content.

 

[hellokeith]

Car--------Goat--------Goat
initial-------shown------switched-------LOSE

Car--------Goat--------Goat
switched---shown------initial-----------WIN

Car--------Goat--------Goat
switched---initial-------shown----------WIN

Switching won 2/3 of the time


Car----------Goat--------Goat
initial--------shown-------no switch-------WIN

Car----------Goat--------Goat
no switch----shown------initial------------LOSE

Car----------Goat--------Goat
no switch----initial-------shown-----------LOSE

not switching won 1/3 of the time


The reason why switching improves your odds is because you know you will be initially wrong 2/3 of the time. Since you know you will be initially wrong more often than you are right, and you are shown one of the wrong choices after your initial choice, you improve your odds by switching. It is not necessarily intuitive, but it is mathematically correct.

Now, if you are only given this scenario one time, there is of course no guarantee you will win even if you do switch, because you still have a 1/3 chance of losing.

 

[Schfifty Five]

lol at so many ppl in this thread.

 

[Malak]

Originally posted by: BlinderBomber
Honestly, Malak, it sounds like you are riding some sort of high horse.

High horse? Have you read anything I've posted? I already admitted the 1/3rd, 2/3rd makes sense. I already addressed the data. I already even posted that I post stupid things. What more do you want? I am attempting to evaluate a probability problem that was so difficult to understand that the greatest minds argued over it and people made simulators for it. I see no problem looking deeper into it rather than dismissing it like you.

 

[BeauJangles]

Originally posted by: Malak

Originally posted by: BlinderBomber
Honestly, Malak, it sounds like you are riding some sort of high horse.

High horse? Have you read anything I've posted? I already admitted the 1/3rd, 2/3rd makes sense. I already addressed the data. I already even posted that I post stupid things. What more do you want? I am attempting to evaluate a probability problem that was so difficult to understand that the greatest minds argued over it and people made simulators for it. I see no problem looking deeper into it rather than dismissing it like you.

Apologies if I missed that. No need to get hostile, I just was responding to what I perceived as your tone at the beginning of this conversation. Statement retracted.

Oh, I'm not dismissing the problem. I worked it out for myself and it makes sense.

Good luck.

 

[Malak]

Originally posted by: BlinderBomber

Originally posted by: Malak

Originally posted by: BlinderBomber
Honestly, Malak, it sounds like you are riding some sort of high horse.

High horse? Have you read anything I've posted? I already admitted the 1/3rd, 2/3rd makes sense. I already addressed the data. I already even posted that I post stupid things. What more do you want? I am attempting to evaluate a probability problem that was so difficult to understand that the greatest minds argued over it and people made simulators for it. I see no problem looking deeper into it rather than dismissing it like you.

Apologies if I missed that. No need to get hostile, I just was responding to what I perceived as your tone at the beginning of this conversation. Statement retracted.

Oh, I'm not dismissing the problem. I worked it out for myself and it makes sense.

Good luck.

Well my problem with the thing isn't going to get resolved here anyway so I'm not even going to bother with this anymore. I don't think anyone here is qualified, least of which me.

 

[WHAMPOM]

This was much simpler to me. Your chance of picking the door with the car is 33%(one door out of three). One door is opened to show a sheep, now the other door has a 50% of being a car but your choice still counts as 33%, so you trade. 50% beats 33%.

 

[Malak]

Originally posted by: WHAMPOM
This was much simpler to me. Your chance of picking the door with the car is 33%(one door out of three). One door is opened to show a sheep, now the other door has a 50% of being a car but your choice still counts as 33%, so you trade. 50% beats 33%.

It's more complicated than that and real world results show otherwise.

 

[Schfifty Five]

Originally posted by: Malak

Originally posted by: WHAMPOM
This was much simpler to me. Your chance of picking the door with the car is 33%(one door out of three). One door is opened to show a sheep, now the other door has a 50% of being a car but your choice still counts as 33%, so you trade. 50% beats 33%.

It's more complicated than that and real world results show otherwise.

actually, it's not complicated at all.

Malak, try thinking of the question like this. What if the host doesn't open any of the doors. Basically it's, you choose a door, and host gets remaining doors.

Now instead of opening any doors, he just asks you: "would you like to trade your 1 door for my 2 doors?"

Obviously you would say yes b/c you will ahve a 66% of winning vs your original 33%. Do you agree with me here?

Well if you do, then that is exactly the same as the original scenario where the host opens one door. By opening one door and revealing the trash item behind it does nothing to the %'s.

Essentially, you are just being asked if you want to trade your one door for his two doors. And the answer is yes you trade all the time b/c 2 is better than 1 in this case. don't even worry about him opening anything...it[s just there to throw you off.


Does that make sense?

 

[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.

 

[BlancoNino]

So I guess I'm confused too.

There are 2 doors to pick from basically. One has a car behind it, one doesn't. How is that not 50/50?


Am I not understanding the rules or something?

Whoa, I think I get it now.

 

[Schfifty Five]

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.

ok i'll take that as a no.

so wait, let me clarify...do you not agree with the actual % numbers? or do you not agree that by switching, you increase your odds?

 

[Mo0o]

Originally posted by: BlancoNino
So I guess I'm confused too.

There are 2 doors to pick from basically. One has a car behind it, one doesn't. How is that not 50/50?


Am I not understanding the rules or something?

read teh explanations. the solution is described to be counterintuitive for a reason.

 

[BlancoNino]

I guess it's because you have a 66% chance to pick a sheep the first time. Since you are more likely to pick a sheep the first time, and the host is going to pick the other sheep, then the car is likely behind the door that you need to switch.

Makes sense.

 

[Malak]

Originally posted by: Schfifty Five

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.

ok i'll take that as a no.

so wait, let me clarify...do you not agree with the actual % numbers? or do you not agree that by switching, you increase your odds?

I have already stated, twice, that I agree you are at a disadvantage when not switching. I am amazed at how you all have such a tendency to ignore half of my posts....

 

[Mo0o]

Originally posted by: Malak

Originally posted by: Schfifty Five

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.

ok i'll take that as a no.

so wait, let me clarify...do you not agree with the actual % numbers? or do you not agree that by switching, you increase your odds?

I have already stated, twice, that I agree you are at a disadvantage when not switching. I am amazed at how you all have such a tendency to ignore half of my posts....

But you still claim switching gives 58% chance of winning when in fact its 66%. That was shown with simluated data posted a bit ago. At the second turn there are only two choices you can possibily make so the probability of those two choices added together MUST be 100%.

 

[Schfifty Five]

Originally posted by: Malak

Originally posted by: Schfifty Five

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.

ok i'll take that as a no.

so wait, let me clarify...do you not agree with the actual % numbers? or do you not agree that by switching, you increase your odds?

I have already stated, twice, that I agree you are at a disadvantage when not switching. I am amazed at how you all have such a tendency to ignore half of my posts....

Well, i went back and read your one post about variance and you came to a conclusion of 58% through your own tests....but I must ask, how many times/repetitions did you do for a test? You should run whatever tests you did 10,000 times and see if you still get 58%.

 

[sieistganzfett]

58% is still better than 50% and if he says switching is advantageous, thats all that matters to me, i give up on the rest of the % that vanished if i were you guys.

so what would happen if the 1 goat chewed a big hole in the wall, then got into the car, and you pick the door with the car and the goat in it? would you have a 66% chance or a 58% or a 50% chance after monty opens the one door that had the goat too lazy to chew a hole in the wall and start screwing the other goat in one of his doors, or to get in the car?