Is the Monty Hall problem an idiot detector?...

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Is the Monty Hall problem an idiot detector? Like, anyone who cares about it is just a try hard deep thinker right? Not even trolling. I was just thinking to myself, "I'm pretty sure if I explain the Monty Hall problem to someone and their first reaction is 'this is stupid,' then I'm probably not going to get along with them."

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>>576266

Honestly it's just a really fucking stupid argument either way.

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>>576266

>caring a solved problem

what does this even mean you fucking tryhard?

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>>576266

The whole argument was stupid. Probability would adjust itself. I wouldn't say that it's an "idiot detector", as it is a "pretentious deep thinker detector".

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OP here, meant to say "and their first reaction isn't"

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ITT: retards that still don't really get the correct answer and are massively butthurt about it.

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>>576266

>implying a straightforward probability problem as if it's some sort of filter

>not the sleeping beauty problem, which has actually different nontrivial probabilistic interpretations

Why are OPs in /his/ always so fucking stupid?

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>>576266

what is your point and how is this at all related to /his/?

>inb4 math is old

>inb4 math is phil

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Take this crap to >>/sci/ since it deals with prob&stat.

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>>576330

So you have no understanding of basic probability. Fucking pathetic.

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>>576266

The solution is.

It is in your solution not to switch because if you fail anyway your reaction is going to be like

>Ooooh better luck next time

But if you switch and fail you're going to be kicking yourself for the next while.

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>>576266

>Is the Monty Hall problem an idiot detector?

No, it’s a fun logic puzzle that demonstrates the counter intuitiveness of probability

>Like, anyone who cares about it is just a try hard deep thinker right?

No, nobody “cares” about it

>if I explain the Monty Hall problem to someone and their first reaction is 'this is stupid,' then I'm probably not going to get along with them."

So you have terrible teaching skills. How does that reflect on the MH problem?

And what do you mean by “stupid”? That the math is wrong because you fail to grasp it?

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>>576292

This. Also, people forget that at least one source of this "paradox" came from a TV game show. You know, where they would want to make the probability confusing so they did not have to give away the prize.

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>>578361

Of course it's solid math, but there's still that probability that you're wrong.

And I'd rather be the lad that stuck to his guns and lost than to change my mind and lose anyway.

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>>576292

>Probability would adjust itself.

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>>576266

Math major here, it's basic probability theory and cuts straight through statistics and thus all science.

Only retards don't get it.

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>>576292

what the fug does this even mean

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>>578652

That's a bit mean.

History major here that stopped at high school math, it's not that hard.

You have three doors, one has a prize behind them. You are asked to pick one of them.

There is a 33.333 recurring percent chance that the door you picked has the prize behind it. There is a 66.666 recurring percent chance one of the other two doors has the prize behind it.

The "host" opens one of the doors you didn't pick. Note (and this is crucially fucking important) he could NEVER, ever, ever, ever have picked the door you originally chose or the door with the prize behind it.

There is still a 33.333 recurring percent chance you picked the right door initially. There is NOW a 66.666 percent probability the other, remaining, door is the correct one.

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>>578681

Uh huh. Good job, you're not an idiot!

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>>578705

Thanks bro! :-)

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>>578681

what stops the one you've allready picked being the right one?

Since logically it'd be 50%/50%

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>>578799

Not him, but because you've selected one option out of three, the chances of picking the correct answer are 1/3. That doesn't change even when you remove the other door.

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>>578831

Why not?

It's just as if you picked from two doors from the start

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>>578799

You're making a classic mistake and not understanding the basic premise of the problem. If you account for all probabilities, then getting the prize is a 50/50 chance. But the question is not "what chance is there you'll get the prize?", it's "is switching better than staying?".

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>>578799

>>578841

>Oh hey anon, you picked the right door to start with

>any gameshow ever

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>>578705

No he is right.

>>578799

>what stops the one you've allready picked being the right one

Nothing. That still has a 1/3 prob.

>>578841

>It's just as if you picked from two doors from the start

No it is not. You are given information about one door. That is not the same as if the door was never there

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>when you try to explain the two envelopes problem to a normie but they don't understand it

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>>579010

>Praise Jeebus and fuck maths and books and science.

>implying there aren't people on /his/ who honestly believe this

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>>576266

>I'm probably not going to get along with them

If you bring this up the first time we meet I'm probably not going to get on with you either

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>>578930

>No he is right.

Reading comprehension is not your strong suit

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>>576266

How do I maximise my chances of getting a goat, and living in goat tower, and discovering the secrets of goat tower?

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>>578851

> If you account for all probabilities, then getting the prize is a 50/50 chance.

What's this even supposed to mean? The whole point is that even though there are two doors remaining, one of which has the goat, your odds without switching are still the one you picked out of the three you picked from.

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>>578851

You're stupid as fuck. The probability that you will get a prize is 2/3 if you always switch.

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>>579355

> Yea I'll have a big mac c/o thank you very much

> You see, I've hidden it under one of these 3 cups. One of them have it, one is empty, and the other one have fries.

> Ok I pick this one

> Before that, this is the ones with fries

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>>578841

Think of it this way: The number of possible situations where the door you picked is correct are less than the number of possible situations where a door you did not pick is correct (because there are more doors that you did not pick than you did pick). However, switching is normally bad because even if you knew for sure that the door you picked had no prize, you still wouldn't know which of the other two had the prize. So when the host eliminates one option, all you know is "the door i picked is probably wrong, and there is only one other door option"

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>>579545

Excuse me, anon.

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My favorite explanation of this problems is the 100 door version where there are 100 doors and you pick 1. Then the host opens 98 of them to reveal all goats. It's pretty obvious at this point why you would want to switch doors everytime

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I understand it, but I still wouldn't change my choice.

The host could be trying to trick you out of your prize.

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>>580528

By opening the door with the car 2/3 of the time?

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Why does the probability not change?

Why does the probability remain at 33.3333% instead of the 2 doors being counted as a new scenario?

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>>580743

2/3 of the time you will initially pick a goat. So in 2/3 of the cases the game host can only open one of the two doors you didn't select because the other contains the car.

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>>580747

Okay, so if I count sticking as just picking a new door wouldn't that just make the probability 1/2?

>So in 2/3 of the cases the game host can only open one of the two doors you didn't select because the other contains the car.

Obviously that's what game shows actually do but I'm not quite getting the real logic of the situation.

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>>580749

You're not picking a new door then, you just accept your 1/3 chance of getting it right on the first try if you don't switch.

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>>580747

It just clicked for me. Thanks, anon.

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>>578002

Please. They were just trying to mess with the contestants heads to add a little entertainment value. They didn't know the odds would change.

The rest of the show was about decisions that you don't have helpful information for. "Do you want to keep this prize, or take what's in the box?"

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There are 3 doors and there's a car behind one of them. What's so difficult to understand about this. It doesn't make a difference if you change the door or if you don't. The car isn't moving.

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>>576266

it has nothing to do with pretension or deep thinking, or even the humanities really. it's just a quirk of statistics (probability) that a lot of people without study in the area intuitively get wrong

so what

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>>580812

There's a 2/3 chance you picked a door with a goat behind it though. You don't want to improve those odds at all?

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>>580812

Actually nevermind.

I just grasped it.

You should always change.

If you didn't choose the car in the first try then he'll always be on the door the host didn't get open.

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>>580758

But you may as well be. If the scenario was every so slightly different and you did get to pick a new door but picked the same one anyway this wouldn't mean that magically one door has a 1/3 chance but one has a 1/2 chance, that's fucking retarded.

Neither the doors nor the car have moved, and there isn't some bizarre 16.6% chance of something new randomly jumping out of either of them. It literally is a 50/50 bet.

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WHAT THE FUCK

THIS MAKES NO SENSE

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>>580842

If you pick a goat then there are two doors left, one has a car and another one has a goat. The host can only open the goat door in this case.

If you pick a car initially the host can open both of the two remaining doors since they both have goats.

The chance of initially picking a goat is 2/3, therefore the door that is left unopened contains the car in 2/3 of the cases, which is why you should switch.

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Say the car is behind door 1. Then there are 3 possible scenarios:

You pick door 1. The host reveals a goat behind door 2. If you switch you lose.

You pick door 2. The host reveals a goat behind door 3. If you switch you win.

You pick door 3. Th host reveals a goat behind door 2. If you switch you win.

You win 2/3 of the time if you always switch

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>>580842

>It literally is a 50/50 bet.

You literally failed the test.

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>>580842

Try thinking about your choice in terms of your initial odds. They do not change once a goat is revealed. There is still a 2/3 chance your first choice of door was one with a goat behind it, so the odds of the other one hiding the car are substantially improved.

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>>580869

I get what you're saying. Originally the door you picked had a 1/3 chance, and the two you didn't collectively had a 2/3 chance. Then one of them was showed to have a goat in it.

I don't get why the math doesn't change. Now there are two doors so rightfully both of them should have a 1/2 chance (game-show logic aside) rather than the remaining unpicked door somehow still has a 2/3 chance.

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The Truth Shall Come
2016-01-20 09:06:22
Post No.580889

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You are not as bright as you want to believe. This problem is flawed and is used to determine who refuses to accept authority. The "popularity" of this problem is artificial, as so is used to test what I said across the internet. Translation: you are being data mined.

I might give arguments about this, but no, you are smart enough to understand it. Besides, the dataminer is probably going to deny it.

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>>580889

I'd believe this before I'd believe the so-called real answer.

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>>580886

the math does not change because your choice does not exist in a vacuum

imagine there had been not three, but thirty or maybe a thousand doors

the chances that you picked the correct one out of all those is very slim

and now if the host opened all but two (your choice + one another), that does not make the probability _that you had picked the correct door in the first place_ different

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The possibility was 1/2 all along. The third door is merely an illusion. R-right?

fuck i don't understand this. but i would get along with OP

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>>580895

if the scenario was 3 doors initially, 1 door was eliminated, and I had to choose again, but I chose the original choice a second time, would that change the ods

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>>581159

odds*?

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>>581159

the odds that you had picked the door with the prize stay the same no matter what you do - the entire switching or staying merely changes whether you exchange the worse probability of having picked the prize door from several doors, with the better probability of the prize being in one of the other doors (the remaining door retained by the show master)

IF, and this is a _different scenario_, as in probability of a different event, you were to walk into a room and saw the experiment being performed, and saw only two doors remaining, and only knew a car was behind one of those, then YOUR chances of correctly guessing where the car is would be 50/50

however, the chances of the participant having picked the correct door would be as in the first paragraph - remember, this again all boils down to the original chance of having picked the ONE correct door out of SEVERAL

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>>580895

Yes but all but two of those doors are totally irrelevant, from the information you're given only 2 of those doors have any mystery to them.

So for all uncertainty it only comes down to two. It can only be a 1/2 choice.

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>>581002

imagine this with more doors

like 123 doors

what are the chances you pick the ONE door with the prize out of 123? very low

so you pick a door

then the game show host, who knows where the prize is, opens ALL DOORS but one + the one you picked

meaning that either the prize is the door you picked OR the door he did not open

except when you were picking your door, you only had a 1 in 123 chance of picking the correct door, so the chances of the prize being in your door are exactly that low - and chances of the prize being in the other are the rest

so you switch and win (most of the time)

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>>581186

Except when it comes down to it at the end you're essentially being asked to pick between two doors, the innumerable duds are irrelevant.

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>>580492

I understand it just fine in this instance but I've never seen how the fuck it scales down.

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>>580492

Nevermind just got it.

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>>580889

It is just always poorly fucking explained by assholes trying to sound smart rather than offering the extra mote of logic that does not occur to most people.

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>>581196

you are indeed asked to pick between two doors, but each door has a different probability of having the prize behind it

your originally picked door retains the 1 of 123 (to use the previous example) chance of having the prize behind it

the other door, by virtue of the knowing game host removing other doors, now has the (much) greater chance of having the prize

this is a very simple problem once you apply larger numbers of it - imagine two groups of 300 people, one switchers, the other non-switchers

each group of 100 picks either A/B/C and then behaves accordingly to their switching preferences, with the prize being behind door A

you will find that with the non-switchers, only those who had picked A will get the prize (100 people), but with the switchers, it is those who had picked B and C who win (200 people)

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>>581210

But it doesn't.

One door has car behind it. One door has a goat behind it.

The odds of either of the three doors having a goat behind it is 2/3 with the remaining 1/3 having a car behind it. If you elimate one of the goat duds you're left with 2 doors, each with a 1/2 chance of having either a goat or a car behind it.

I don't understand why if you remove the element of initially picking a door the chances are 1/2 for either. But if you've already picked a door it suddenly becomes 2/3 vs. 1/3.

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>>576292

>pretentious deep thinker detector

This.

Fuck this problem and anyone who wastes time on it.

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>>581226

but that is exactly the core of the problem - you are picking out of many doors, not the remaining two

remember, do not mix up the various events or probabilities - you are interested in the probability of having picked the prize door out of many doors in the first place, and that chance is low

again, imagine it with a much larger number of doors

>If you elimate one of the goat duds you're left with 2 doors, each with a 1/2 chance of having either a goat or a car behind it.

eliminating the goat duds does nothing to your (low) chance of having picked the correct door

you are still standing in front of one door out of many (again, imagine this with a hundred doors) which you have picked and hope for the best

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>>581234

But you are, the whole premise of the problem is that all but 2 doors you know for a fact are duds.

This is why choosing to stay or swap is exactly like just picking between two doors with a 50/50 chance. Whilst initially you were taking a pure 1/3 shot in the dark, now that you know one is a dud you're essentially being asked to pick between two options only knowing that one has a car and one has a goat but no way of knowing which so it's 50/50.

The opening premise of the situation just make it deliberately confusing, those two doors are all that matter.

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>>581176

So the original participant gets a 1/3 chance on his original or a 2/3 chance on the remaining, but an observer who also gets a choice has 1/2 for each door? Is this testable or just a thought experiment based on the way probability mathematics operates?

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>>581247

You can test it with online simulators or with just 3 cups and a penny.

When I tried it I got the exact opposite of the expected result, staying seemed to generally be the better option.

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>>581248

How manyb instances if the test did you perform

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>>581249

Like 12.

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I’m going to give it one last try:

Think of it like this:

>When you pick a door you lay down the odds and *they never change during the game!*

You pick a door and that door has 1/3 chance of a car. And 2/3 of a goat.

The other 2/3 chance of a car now resides in the two other doors. Combined.

Because we have no further information it is fair to equally divide those 2/3 among the two doors. Giving each 1/3

Now one door is revealed to have a goat.

All this does is give you information about the distribution of the 2/3 chance of a car.

The odds did NOT change. The 2/3 chance of a car is still divided among the two doors. Only now you have information about HOW this is divided. You now know that one door has 0 probability and the other door has (all of the) 2/3. That’s the exact same 2/3 you first assumed was equally divided among the two doors.

So, if the scenario is pick a door; have a goat revealed; choose “stick” or “change”:

changing will double your chances of winning the car (from 1/3 to 2/3)

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>>578799

Think of it this way:

There are 100 doors. You pick one, and then the host opens 98 other doors with goats behind them. Now you are offered to switch or keep your current door after the other 98 were opened. Is the chance still 50/50?

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>>581245

no, i am convinced you are being deliberately obtuse or trolling, there is plenty of food for thought in this thread or on the internet in general, including simple calculations which will prove the truth to you

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>>581362

And as far as I can see it's all wrong.

The "logic" here is Alice in Wonderland tier nonsense.

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>>581370

again, simply imagine the exercise with a hundred doors

if what you were saying was true, then your chances of picking the one single correct door out of a hundred would be 50%

which clearly is not the case

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>>581380

No, I'm saying 98 of those doors don't make a difference because you already know what's behind them. The only doors worth considering are the remaining two, so it's obviously 50%.

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>>581399

>you already know what is behind those doors, but you did not know when you picked your door

As I say, the premise of originally picking a door just makes it deliberately confusing. When it comes down to it you're picking between two doors.

>and since you still appear to claim that picking one door out of a hundred is a 50% chance of picking the correct door,

But you aren't picking between 100 doors. You're picking between two.

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>>581418

>>581391

>>581247

>>581245

You are picking between two doors, but the chances of the Car being behind one door (the one you picked) are 1 in 100. While the chances of the Car being behind the other door are 99 in 100. Why? Because originally you had picked a single door out of a hundred (1 in 100 chance). Meaning that only one person out of a hundred competing would have had picked the Car, let's say the Car is hidden behind door number 49 every time and the hundred people competing in separate rooms each pick a different door from one to a hundred. Now 98 doors are revealed, only the participants' choices and number 49 remaining, showing Goats only. Out of those hundred people participating, only the person who had originally picked door number 49 would win. While the ninety-nine who had picked doors other than 49 would win by switching.

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Ah, now it makes sense.

No matter what your chances of picking a goat are 2/3 and no matter what Monty Hall HAS to reveal the other goat. So since it was so likely you picked a goat it makes sense to switch.

Why are all the posts ITT trying to explain it making it so complicated?

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>>581436

>So since it was so likely you picked a goat it makes sense to switch.

yes

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>>576298

it is just a small fun puzzle, hardly takes up any time, if someone believes it makes them a super-genius they are trying too hard but it isn't a big deal

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Literally the answer can be explained in one sentence.

The only way to lose by switching is if you got to car, which you probably didn't.

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It is this thread that makes me feel like an idiot.

I don't understand what is going on, from OP to people explaining it, and people saying they don't get it, and the replies.

Why would people believe the problem is benchmark for either intelligence or tryhard?

It's a tricky counter-intuitive problem so simply at first sight that lots of intelligent people fall for it

Once you know there's a "twist" to it, the explanation is so fucking simply even stupid people will get it

Not giving two shits about the problem does not make you shallow in any sense

And the problem (and what leads to the common mistake) is in itself intersting to analyse and take apart, without amking you a tryhard

So how on Earth can you conclude anything from someone's attitude towards this problem?

I know the world is scary place full of uncertainty, but you are trying to find meaning in so little.

Also, there are seven different explanations, you have no excuse not to search the solution online.

Have another one:

>When you choose the first door, you are creating two sets of doors: one set with the single door you chose, and another with two doors. Probs are 1/3 and 2/3 of the car being in each.

>Given the chance, you'd choose the set with two doors, obviously, even after seeing which one of the two has a goat

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>>581949

Think of it with boxes instead of doors.

There's three boxes, two of which have small prizes and one of which has the keys to a new car. You pick one. Then, without you seeing, they dump the contents of one the two remaining boxes into the other.

So then, one box contains two of the three prizes, and your box contains one. The Monty hall problem is 100% exactly like this problem.

Or, even better, imagine there were only two boxes with three prizes distributed so that every box has at least one prize. And then, imagine every time you pick, you're told you picked a box with just one item, and you can switch to the box with two items.

That's the Monty Hall problem as simple as possible. Whether you "know" what one of the prizes was doesn't matter.

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>>581949

OP is wrong maybe

OP is one of those types to whom absolutely anything other than pop culture is boring and magically wrong somehow.

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>>581949

>So how on Earth can you conclude anything from someone's attitude towards this problem?

you cannot its just the op being a fag and most people itt ignore his "points"

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>>580889

>thinks this "authority" is arbitrary

>thinks he has a better formulation of probability than Kolmorogov

>implying he isn't just another dumbass shitposter

Typical /his/.

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>>582780

It looks more like some weird conpiracytard /pol/posting to be totally honest, familia.

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>>581949

You probably didn't pick a car the first time around so switch.

Everyone ITT is thinking about it too hard.

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>>580846

Look it's all in the grammar of the problem.

They only EVER flip a door with nothing behind it. If you picked one door, and they randomly flipped one of the other two, and that one HAPPENED to be empty, it would be a 50/50 shot. But in that case, sometimes they'll flip a a door to reveal the car. That chance that they would reveal the car, but don't, is why you have a better shot switching. But the way the problem is worded, instead of ever flipping the car door, they only flip one that's empty.

It's a grammar trick.

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>>581391

After the host has eliminated the other 98, there are 2 remaining.

The one you picked, or the one the host has been specifically avoiding. Why has he not picked this one? either it's random and you happened to guess right the first time (1% chance)

Or he has been avoiding it because it has a car behind it (99% chance)

I don't know how to make it any more simple than this. The host isn't opening doors at random, he's opening ones that you did not pick and that did not have a car behind them.

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>>580864

you forgot one you idiot

>You pick door 1. The host reveals a goat behind door 1. If you switch you lose.

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>>585616

The host doesn't open the door you pick, dumbass.

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>>585616

>you idiot

ha haha

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>people prefer a filthy common car to a Great Of All Time like pic related

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>>584112

>that one HAPPENED to be empty, it would be a 50/50 shot

No. That would also be 2/3.

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>>584112

>It's a grammar trick.

no, it's a math test.

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>>585863

Nope. It would be 1/2.

Because sometimes they'll flip ope the door with the car, in which case you're stuck with loser options. That cuts down how often you can be right to 50/50

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0.999... = 1

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I hate how such a fun problem to discuss was started by a goddamn retarded OP.

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>>586471

Yes.

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>>585929

>>0.999... doesn't equal one!

>what is infinitesimal

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why is this being discussed. There have been simulations that prove you should switch.

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saw a myth busters episode about this once, it was clearly statistically better if you switch every time, I refuse to think any deeper into the matter after seeing it.

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>>586606

B-but it does

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>>586606

1/3 = 0.333...

3 × 1/3 = 3 × 0.333... = 0.999... = 1

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>>586606

An infinitesimal is not a number.

There's a well-known theorem that between any two distinct real numbers there's a rational number. Show me the rational number between 0.999... and 1, and I'll believe you.

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>>586738

This I like.

Do you have the name of said theorem?

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>>586747

https://math.dartmouth.edu/archive/m54x12/public_html/m54densitynote.pdf

Density of Rational Numbers in the Reals

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>>586747

Also, if you have a notion of a LUB, and inclusive and a non-inclusive interval on R will have the same LUB, which is essentially what it means to say 0.999...=1

If you take [0,1] and [0,1), you'll realize you can't find a LUB for either that is distinct, even though [0,1) is a proper subset of [0,1]

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nice /his/ thread laddies

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The whole problem boils down to what you pick at the beginning. You are more likely to pick the goat, so you are more likely to have the other goat when the goat is revealed. Because you probably have the goat you should switch.

You can do it on your own if you like. Its easy to do. Cups and coins. Work it out.

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>>586810

>You can do it on your own if you like. Its easy to do. Cups and coins. Work it out.

It can take hundreds or thousands or millions of tries to get close to the right odds. You need large numbers, which is why they usually do this stuff on computer simulations to be sure.

I tried 20-30 times and the switch was effective 90% of the times, when it should be closer to two thirds.

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