The monty fucking hall problem.

to put it simply the reason the second door is 2/3 is because monty knows where the car is and the fact that he decided to show you the goat in the 3rd doors means it is more likely there is not a goat in the 2nd door. the way you worded the problem in the first post fails to mention that monty knows where the car is and deliberately showed a goat, without this information I assumed that monty chose to open the 3rd door without knowing where the car was, in which case the two remaining doors would have an equal chance 1/2. I don’t think this is a problem in human reasoning but more like a lack of information and failure to properly state the problem or perhaps my failure to assume the actions of monty were deliberate, either way it’s kind of a stupid problem, at least in my opinion

edit//nevermind i’m dumb.

is this the problem from the movie 21?

here’s how that one goes down

there are 3 doors and one winner

your only choice is to pick a random door.

you pick door 1 lets say.

the host says, but wait a second, and reveals door 3 to be empty.

next he offers you a chance to switch your answer from door 1 to door 2.

the question is why is that a good idea.

the answer put simply is this.

when the game show started there was a 1/3’d chance of the winning door being door number 1, and a 2 third chance of it being door number 2 or 3.

with the disposal of door 3, door 2 now represents the probability of it being in door 2 or 3 which is higher than it being door one.

variable of change or something it is called.

if the gameshow host knows whats behind the doors, switch.

if he doesn’t know, it’s the same odds.

The part that I have a hard time with is, what if we add another contestant or viewer partway through?

Suppose the scenario all plays out just as described in the example, and after that I turn on the TV and start watching. For me, I see 2 doors and a goat. From the two of them talking, I get the general idea that there’s a car behind one of the two doors, and a goat behind the other. It seems like in that situation, I’d have a 50/50 chance of picking the right door, if I didn’t know which one the contestant picked originally. Right?

Can someone explain to me how discovering which door the contestant picked would provide information that makes one door more likely than the other? What is it about the contestant picking door 1 that makes me go, “Ah, it’s probably door 2!”

Has anyone read ‘The Man Who Only Loved Numbers’? Some good stories in there about how some of the finest mathematical minds of our century couldn’t grasp this. For my part, I understand the proof I saw, but its still very counter-intuitive. If Paul Erdos didn’t understand it, I don’t feel so bad.



How about looking at it this way…?

Three doors: 2 goats, one car - you choose one. 66% you chose a goat.

ie: You prolly did.

So, gameshow guy is left with two doors. According to the above there’s a 66% chance you’ve left him with a door with a car, and a door with a goat.

Obviously, he can’t open the door with the car. Cos he’d get fired. So, 66% of the time, he has no choice about which door to open.

Ergo, if you choose the door the gameshow host didn’t open - you’ll get the car, 66% of the time.

Not bad odds really - 2 in 3, certainly better than the 1 in 3 you started with.

Not so unintuitive if you look at it backwards.

I understand the mathematical proof, I just place no stock in mathematical proofs concerning probability.

Likewise, a lot of people do this intuitively. As such, it isn’t that they ‘don’t get’ the answer, it’s that they don’t believe in it.

??? You’ll hafta 'splain the last bit.

Fair enough, sometimes common sense ain’t enough, but then that’s what makes aquiring uncommon sense all the more worthwhile, no…?

Be simple enough to test with 2 people and a deck of cards, wouldn’t it? The stats aren’t just numbers in space, if the example is right, switchng really should get you the car (or ace) 66% of the time.

someoneatwhatever is always making absurd and nonsensical claims that he doesn’t even try to justify. Of course his beliefs are irrelevant, its not just numbers in space, which anyone intelligent enough to operate a deck of cards should be able to find out for themselves. His beliefs won’t alter any probability when making the choices or the statistical outcome. Don’t expect any coherency besides complaints about my repeated use of the word ‘absurd’ sad and pathetic.

people don’t believe it only because they don’t ‘get’ it. It works out that way in the real world, regardless of personal opinion. thier lack of belief doesn’t change the probability difference between picking thier card or the non revealed. if they don’t believe, they don’t get it, because thats just how it works out. again master the playing card and get back to us.

:laughing: P’raps we should give SIATD the benefit of the doubt… Maybe he’s operating in an alternate reality, philosophically at least.

siatd makes perfect sense to me

an unjustified prediction is an unjustified prediction

-Imp

How can a prediction be “unjustified”? It’s either going to turn out accurate or inaccurate between subjective opinions based upon the criteria it self-describes.

Men only gather around the predictions that keep proving themselves true, which is the error of taking science as a faith…

it begs the question or it does not.

invalid assumptions are not justified.

-Imp

Justice is ambiguous then … it always gets stuck in hypothetical contexts.

But isn’t that what all predictions are, hypothetical? (until they manifest) So then – what is an “invalid assumption” in context to the hypothetical?

This is interesting, because this logic seems flawed to me when it can’t be practical in any sense whatsoever.

no, logic itself is flawed.

-Imp

That’s exactly the definition of ambiguity – whatever a person is compelled to do is whatever a person is compelled to do.

The situation says nothing until beforehand or afterward in context, until it is discussed and made sense of, otherwise we’re just being. Actions speak louder than words, yes, but what are we doing here on this forum – acting or writing? Where do word acts begin and end? Is this even the problem at hand?

The hypothetical is a memory of something that may or may not be real, according to fiction or nonfiction. Predicating events based on hypothetical contexts are what men instinctively do in order to anticipate the exchange of gunfire. The hypothetical can be true when what is “true” is definitely going to happen (like that I’m going to drive my car within the next two hours).

I want some clarification…

Skepticism & Nihilism continually beg the question. Pragmatism ends it, so it also forces men to decide what is “valid” and what is “invalid”.

It’s only as flawed as flawed men allow it to be. The fallacy of logicians (and most other logically predicated sciences) is that they don’t know how, where, or when to update their language after mistaking it as an absolute authority. I won’t speak for others, but my authority rests in the same place I put my faith…

as a question of faith, it is no more valid as a belief in any god…

-Imp

Ihate my threads degrading to this drivel. This is a testable prediction, people who don’t believe simply can’t wrap thier heads around it, as the same statistical results or close enough happens consistently in the real world WHEN TESTED. leave the BULLSHIT run of the mill arguments against science/statistical predictions until you can show that in the real* world they don’t routinely come true.

again i suggest a deck of cards for those people too incompetent to do the mental math if you don’t ‘get’ it grab some cards if the people in question thinks its faith 200 rounds with a deck will prove them wrong, the correct card *will be in the dealer’s hand consistantly enough to say the prediction is correct.

seriously not all my threads need to be dragged down by philosophy based on the standards of a seven year old. real world ideas have testable predictions, the worth of claims depends on the accuracy of those predictions, not any mental midget’s ideas about thier worth…