Solve the riddle

[Cen]

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?

Tell yes/no and reason.

If you know the problem already, shut your mouth, if you don't, no google, be fair.

[-KaMiKaZa-]

did u saw the movie with that guy counting cadrs in blackjack? xDDD

[Mladenus]

It's mathematics... I know, so I shut my mouth. I'll observe the others. :)

[-KaMiKaZa-]

i know the answer u noob,im sure its from that movie xDDD

[eXtasY]

Well.. Considering you already missed one goat possibility that you got the car is 1/2 respective to doors 1 and 2 (its equal for both). So, its absolutely same if you change your opinion or no, from the aspect of possibility theory.

[Cen]

I expect answers like the one from extasy (in that form). Ty

[eXtasY]

Can we say he will fuck you up on purpose and open goat whatever you chose? :D

[efko.wbs]

this one was here cca 2 years ago :D

[-KaMiKaZa-]

no no no,the host will always play on the "human greed ans self insecure" card,if the player has guessed the prize in his 1st hand,on the other hand he will offer something low/cheap (w/e)if the players guessed the goat (in this case)on his 1st try.

Ex: door 1(players choise (car inside)),door and 3 goats.
Player choose door 1,the host knows that the car is in door1 so he offers smth that can tempt the player to change the door...on the other hand he doesnt need to offer him nothing if he guessed the goat.

[Cen]

1. Both goats and the car are randomly placed behind the door.
2. When you pick a door, host will always open the door with a goat behind.
3. Host always offers you to switch or not to switch.

[MiZiGe]

Well.. Considering you already missed one goat possibility that you got the car is 1/2 respective to doors 1 and 2 (its equal for both). So, its absolutely same if you change your opinion or no, from the aspect of possibility theory.

I hope you do not study math :D

@the original problem: first of all, cen, you want an answer, that is situated into a "real" situation, but you present a theoretical problem. There is a large discrepancy between what the theoretical outcome is (in theory yes, you should switch), and the practical/statistical outcome. The best answer would be to study previous cases, and create a percentuall success rate of "switching". The next thing you need to know in praxis are the laid down rules of the gameshow producers, to see if they alter the game hosts behaviour in any way. Therefore, speaking in praxis, the answer cannot be given based upon your incoherent and insufficient data /suck that!/

[mestar.]

There is a serious math behind this problem, and the answer is that you should switch doors. On wikipedia is alot about it.

But you can also look at this problem like this (easier to understand but not totally right):
If there is 2 goats and 1 car that means that at start I will have 2/3 odds that I will choose wrong. But after he opens one door and asks me if i want to change my choice then the odds have changed and now i have 1/2 chance to pick wrong. So yes I would change my choice.

[eXtasY]

Actually Mizige, i passed both possibility theory and statistics exams with high grades. What i wrote is correct from that aspect, but considering Cen posted it here, as a riddle, im almost sure there is some trick behind that will totally change concept of the problem, maybe as kamikaza said. Also as most of problems of this kind, it can be watched on few ways even from math aspect what will bring different results.

I can watch it that in first attempt i had 1/3 chance to hit the car, while in second i got 1/2 considering i got only two options, so its better to change opinion since 1/2 > 1/3.

But its so stupid to watch like that since even if i chose NOT to change the opinion i still did pick one door again, just the door i chose is the same as in first attempt so it takes 1/2 possibility too.

Now if you work with conditional possibility, in first attempt chance that you miss one goat, what you did, is 1/3 (1 - 2/3), and to hit the car when you change your opinion is 1/2. When you multiply that (conditional possibility) you will get 1/6 what is less than 1/3 in the first attempt so its better not to change.

So, it only depends on way you watch.

Now im really, really wondering how the creators watched on this :)

[Cen]

For Mizi:

Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

THis is purely mathematical description for those who like to complain. ;)

[LeCron]

Actually, the host always try to make audience, so the game show cannot end that way, if the car is (or not) behind door number 1.

So he play with your mind (and audience´s mind)... Open a wrong door, with a goat inside... show some commercials... make some money... and return with two other choices.

Number 1 ou 2... which one has a car behind? So it´s up to him manipulate you the way he wants to... It can´t be answered by math. It´s more a marketing situation.

* Sometimes a guy will have a car, because if nobody never wins that game, gradually the show loses audience and ends.

* Sometimes (most of) a guy will have a goat! Nobody can always give cars... the host would be losing money and trust me.. that´s not his point/will...

So... you have to be very lucky. You have to count with:

1) Your choice (your own. That way you can win or lose, but it´s your own... ignoring what´s he saying to you)... because you can pick up the right door (number 1), and he can show you a wrong door (3) and still that way your don´t change your door and win a car... or the car is behind door 2, and you still thinking about a wrong door... and get a goat. :)

2) The host... if he wants you to win ou lose...

2.1) It´s your lucky day! The host wants (needs) you to win the car (it´s time to somebody wins to fake he´s a nice and good one who gives money and cars to everybody), you pick up the wrong door, he show you another wrong door and make you change your choice... so you pick up the door number two and win a car. (you´re so weak... change your mind "so easily"... but you won a car! :D)

2.2) Your unlucky... you pick up the right door (1), he pretends to be your "friend", show you a wrong door (3) and makes you change your mind... so you pick up door number 2 and get a goat. (you´re so weak... change your mind "so easily"... and get a goat! :))

Maybe it´s some math form to solve it, but It´s not the right way to see it. (My opinion)

____________

Sorry for the mistakes in writing... I just woke up and I´m pretty lazy to check if something is wrong, but I think you can understand my point (if you have patience to read everything xD)

Have a nice weekend!

[]´s

[MiZiGe]

no, this is the mathematical expression for it (http://en.wikipedia.org/wiki/Monty_Hall_problem#Mathematical_formulation) (extasy will read this, and then go and erase your grades in statistics :D )
all in all, it is a famous practical application of the game theory (functionalism/systematic approach, my favourite way to analyse systems!!)

PS: do not hate me extasy <3

[eXtasY]

Jeezaz, i so failed....

The key of misjudging this is fogeting the fact that host knew where to goat is, as i did and that is following explanation:


This is different from a scenario where the host simply always chooses between the two other doors completely at random and hence there is a possibility (with a 1 in 3 chance) that he will reveal the car. In this instance the revelation of a goat would mean that the chance of the contestant's original choice being the car would go up to 1 in 2. This difference can be demonstrated by contrasting the original problem with a variation that appeared in vos Savant's column in November 2006. In this version, the host forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch"

[Cen]

87% of people who were asked this said it's 50% - 50%, just like you. I thought the same when I first got to it. It's because you think like "he showed me a goat, now I have 2 doors and it's 50-50 lol, gg owned"... in fact, you must not simply erase the first part of your choise, where you have 2/3 chances to get the goddamn goat.

[[RO]Claudiu]

i'd say no and go for number 1 just because he ignored my first choice. if i picked 1 and IF it was a goat behind it he would have no interest to give me another chance.

this has little to do with mathematics and more to do with psychology.

[Fika[F]]

in start you have 1/3 chance on every door to get the car while having 2/3 chance on the other two doors to get the car, so when you picked the door you had 1/3 chance to get the car, while the other two doors held 2/3 chance for the car together, after the host did not open your 1/3 chance door and opened one of the other two (in witch there was another goat), the combined chances on those two doors stay the same witch is 2/3, but now we know in one of those is a goat, so yes, it's better to switch because if we switch we have 2/3 chances of getting the car, and if we don't we have 1/3

this kinda sounds stupid, because I know it's obvious you have 50%-50%, but it's the only explanation I could think

[MiZiGe]

btw., I would prefer the goat to the car...

[eXtasY]

Its just a proof how our mind is limited, and how its hard to imagine even this simple problems :)

And then wonder why we cant understand things as endless universe, death, illusions of time etc etc...

Im almost sure that almost all of those 13% who answered correctly did so only because of very good knowledge from theory of possibility, not logical thinking or intuition.

[Fika[F]]

tbh I don't see how any knowledge can be applied here... it's just how well can you play with your mind and think outside the box ;)

in other words .p Fika

[eXtasY]

Nah, its math. Its Bayes's formula if im not wrong ,check the link they gave, all those explanations are mathematical. And be real, if you didnt see this as solution you wouldn't even try to think in that direction. As you saw in my first post i wrote three different solutions and they all do have logic in themselves, but two of them are somehow wrong from math aspect.

Same goes with all unnatural problems to our mind. We wont even get idea to think in other direction since the one in front of us will be most understandable and normal for our mind.

The biggest proof are illusionists. Our mind simply focuses all resources on our seances and empirical knowledge that is blocking our more wide thinking, what is used by illusionists to hide things from us.

You see, if no one would tell you an illusionist is making a trick, when you see a guy cutting a woman on half, your mind wouldn't say "hey its a trick" but it would say "hey that guy killed a woman". Even if you somehow manage to realize what he did, what is extremely hard, you will do it only because you actually know its a trick and you did focus your mind on finding other solutions to thing in front of you.

Ofcourse, there are very few exceptions, because without them we wouldn't have science at all. But again lets say one such guy, uber important for theory of possibility science, still didnt come to that stage from nothing. He started by throwing a coin million times in concentration camp through years and writting results to make sure he will really get 50-50 results so he forced his brain to start thinking on that way.

Get what i try to say?

[Fika[F]]

I get your point, but I also say that even a person from the outskirts of civilization that has never seen math or similar things could solve this riddle if someone explained it to him. But he couldn't solve an equation with two unknowns in it. Bayes just discovered this first and mathematicaly explained it, becouse it is math of course but not the math you are thinking on...
If I say to you that the whole world around you could be mathematicaly explained you wouldnt believe me probably, but EVERYTHING is math, so this discusion kinda has no sense...
It's just the question will knowladge from math help you here more, or logic thinking outside the box, I think the other...
Only knowledge that could help you in this one is if you encountered a problem like this before.

[Aj1234]

I have a lot of Budda mini statues in my cabinets and i believe in luck.
Im a retard so ill go with number 1, what could possibly go wrong ? :)