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Monte Hall Problem - A paradox in how the simulation is programmed?
Basically the Monty Hall problem comes from an old game show hosted by a game named Monty Hall. The gist of it is as follows:
>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?
Turns out statistically the answer is "yes", even though it would seem indisputable that you've got a 50/50 chance when choosing between 2 doors.

I think this seeming paradox is an intrusion of higher dimension (more complex) reality onto our reality via poor programming. Whoever created this simulation PROBABLY didn't expect there to be a gameshow called "Lets Make A Deal" and thus presumed nobody would have noticed. I dunno.

Basically I need /x/'s thoughts on the paranormal implications of this and I would plead in vain that you pretentious mediocre fedora wearers out there refrain from the stupid "Well, I TOTALLY knew that the odds were better if I stayed with the original choice!" because, you know, you didn't. If you were being honest you would just admit that you didn't.
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>>22513774
>guys why is this paranormal
nonono that's your job op
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>>22513774
>Turns out statistically the answer is "yes"
And fuck me. It turns out the answer is "no", I meant to say. The answer is to stick with your original choice. Oh well. I fucked up the entire OP cuz of one little stupid dyslexic word, but you get the idea. Any input on this is appreciated.
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>>22513779
Fuck off loser this is a board for discussion about these topics. Perfectly reasonable post on my part and obviously it's not low energy "how do I summon an incubus" or whatever.
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>>22513780

you peanut
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>>22513796
I feel really dumb about it, if that makes any difference. Anyway still a good post for this board and really want some answers. It's a clear paradox. It's one of the most clear and glaring paradoxes of logic that we can see. It makes no sense. To anyone. The human mind is not capable of processing how these two things are simultaneously true at the same time. You have a 50/50 chance at something, but yet you simultaneously don't. Clearly this has to be a window into a higher reality and a far more complex version of physics.
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>>22513774
I'd rather have a goat
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>>22513782
no u
>I don't understand statistics
isn't paranormal
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>>22513916
It isn't statistics, it's a plain as day paradox right in everyones view.
You have 2 doors. The odds of you getting it right should be 50/50 no matter what choice you make. They aren't though. That's a paradox. There's no way around it. It's a paradox. And BTW one that is impossible for the human mind to process.
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>>22513924
>>22513916
and it's because of the way our reality is programmed. There are tension points in the programming, as have been pointed out by so many. That's how we know we're living in a simulation. This is one of them. This is one of the tension points in the programming. There's no way you can realistically say it makes sense to have 2 doors and not have a probability of 50/50 that what you want is behind either one.
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>>22513774
>He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
No, because if the doors are as close together in your pic you can't fit a car behind door 2 without it being visible partially from both doors 1 and 3 or even more so from one of doors 1 or 3. This means the car is behind door 1 if you know the goat is behind door 3 and you can't see the edge of the car.
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>>22513934
heh autism'd 'em
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Actually, the thing is you have two goats and one car so you have 2/3 chance to get a goat instead of the car on the start.
Since you already have one of the goats, the show guy can only open one of the doors, that means that the next door is for sure the door that has the car inside if you picked the goat from the start.
Do you understand now op? Since you only have 1/3 chance to pick the car on your first pick, it is much more likely (75% - 25%) that you will pick a goat instead of the car, thus when the other goat is removed from the game you are left only with the car, so it's more of a 65/45
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>>22513947
but muh simulation REEEEEEEEE
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>>22513947
>>22513951
I am the OP and it's not me who doesn't understand, it's you guys.
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>>22514121
>>22513951
>>22513947
You guys have to understand it's a paradox, OK? It's a flaw in the programming of the rules that define our world.
It's like if you're playing GTA 5 and all the sudden there is a glitch and you start floating or something.
You idiot fedoras think you're so smart explaining this shit but you're not. It's not hard to understand, what takes some more thinking is to recognize what is happening here and see that it gives you a glimpse into the faulty nature of physics, math and our reality. Fucking losers.
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>>22513947
This. Just because you retards can't grasp this doesn't make it paranormal or a glitch in the matrix or anything idiotic like that.
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>>22514131
That's not the faulty nature of reality, physics, or even math. Anyone who understands statistics understands that it's all subjective bullshit mascarading as mathematics. There's a few accurate statistical methods like for analyzing normal distributions and chi square and standard deviations - but beyond that it's only charlatans who attempt to portray it as math (this is why it is used abundantly in economics, psychology and sociology studies.)
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paradox can only truly exist with 2 opposing ultimate outcomes ie:there cant be life without death.
also the varriant of the third party (the host) and possibly being bias or not and unpredictable as a conscious sentient being throws this whole thing off. sorry to say it here pal but life is just whacky. can we get a ghost story now? or is this not /x/?
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The answer is obvious if you expand the problem. Imagine there are a million doors instead of 3.

You pick one door. The host opens all the remaining doors except for one, showing them to be losing doors.

In this example it is obvious that the chances of finding the prize if you switch choices are overwhelmingly higher.

By opening a specific type of door (no prize) we are presented with additional information. This changes our initial assessment of probabilities.

It is counterintuitive but not paranormal.
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>>22514188
>>22514159
>>22514146
>>22514144
You people are so fucking dumb.
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It would be 50:50 if Monty Hall would occasionally open the door and take the prize for himself.

Since we know he will only open a losing door that gives us additional information and changes probabilities in favour of switching.
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nah bruh ur the dumb one.. ever heard of the schrodinger's cat theory btw?? just an fyi its better than this nonsense.
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Try the opposite of this problem. Monty Hall has 3 pills. 2 are made of sugar and one is made of cyanide.

You choose one pill. Monty Hall says he knows which pills are which, eats one of his pills and doesn’t die.

Would you agree to eat his remaining pill instead of the one you picked?
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>>22513947
This anon described it perfectly and it is not that hard to understand. OP you were right when you innitially said you should switch.

And yeah there are synchronicities and parts of reality that make no sense, and I do think we are in a simulation of some kind, but the Monty Hall problem is actually pretty straightforward.
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again the human variant take out the unpredictable variant of human nature it is not paradoxal nor is it worthy of being even mysterious maybe... or even sinical but not something worth review again with schrodingers cats... the possibilities are infinite and will remian so until an option is selected and there fore not selected will remain forever both true and false at the same time. this bs with human varriables though is sad to read so just stop
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>>22513774
The monty hall paradox is easy to explain. You choose 1 of 3 doors, they open one that is always NOT the right one, then they let you choose again. Since you had a 1/3 chance of guessing the first time, the odds of it being one of the other doors is 2/3, when they open the empty one, you still have a 2/3 chance that it is the door they didnt open.
Think of it like this, let's say it was 100 doors, you choose one, they open. 98 doors that aren't the right one, then offer to let you switch. Obviously you only had a 1% chance of your door being right the first time, now that they've eliminated 98 doors for you, the remaining one is 99% likely to be the one with the prize.
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>>22513780
you're supposed to switch doors. there's a 67% chance your first answer was wrong so 67% of the time the correct answer will be a different door. it's essentially an option to throw out one of the three doors and make your choice 50/50 instead of 33%. 67% of the time your 50/50 choice will pay off, so it's all god and I am God.
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shit wait duh i see it now

ok in that case the odds change to 50-50 with the rule that if any of the options with attached value of odds gets eliminated the remaining options with set odd values must change their odd values by evenly dividing the previously eliminated value to be distributed evenly to remaining set odd values... right?
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>>22514208
>t. schizo who failed math
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>>22513912
Fuck off Muhammad
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>>22513774
No the odds are better if you switch you dingus, think of it this way, the game show host gives you 100 doors, you say fuck me thats a lot and just choose door 1 knowing you wont get the car. The hose removes 98 doors and asks you if you want to change your chosen door, now its super fucking obvious that changing your door choice gives you better odds
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>>22513774
It doesn't matter if you stay or switch after he opens up a door to a goat. No matter your first choice, there will always be a door with a goat. Regardless of whether you choose right or wrong to begin with, the host knows exactly which door he needs to open to reveal a goat. But you don't know if you choose a goat or not a goat. So switching at that point is just as random as picking a door in the first place. Go ahead, stay or don't, it doesn't matter.
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A more interesting problem would be if the host had the option to reveal a losing door to you, but he did it at his discretion, knowing what is behind each door from the start.

Then it becomes a game theory problem. If he did reveal a losing door, is he trying to trick you to change your mind? Or is he trying to trick you to stick with your first choice by pretending that he is trying to trick you to change?
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>>22514554
He does reveal one losing door but because of the simplicity its still 50/50 if you decide to change your door
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>>22513774
I've always hated this problem. It's a classic example of how stupid "smart" people are.
And also of how huge populations of human beings seem to collectively omit important information because it perpetuates some idea that they find attractive (in this case they find the idea that the monte hall problem is a mystery to be attractive so they perpetuate it).
The same bullshit happens even in rigorous scientific disciplines, and it's honestly depressing.

Sorry for ranting, but once I'm done explaining to you how this works I think you'll feel silly for every believing the monte hall problem was a paradox.

The KEY to the whole damn thing is a missing ingredient. It was only ever interesting as a game show BECAUSE the ingredient was missing, and it's only still thought of as an interesting problem because all descriptions of the game still omit the vital ingredient.

So let me make this extremely clear:
If the host reveals his door at random then the whole thing falls apart, and you do NOT increase your odds by switching doors. And that's provable.
But if you read the games description you never see it mentioned whether the host chooses the door at random or not, right?
That's why the whole thing is stupid. Everyone acts like you have to be some genius to figure it out on your own, but anyone who comes to the "correct solution" must make an ASSUMPTION here.
The key to the entire thing is the (assumption) that the host will intelligently avoid revealing the car door, but that piece of information is never told to you.

Once you know that though it becomes intuitive. It's no longer all random chance, there is additional intelligent information being fed into the system when the host reveals a door. If one of the 2 remaining doors is a car then it's guaranteed the host will reveal the goat door instead. That happens 2/3 of the time, so 2/3 of the time the remaining door is guaranteed to be the car.
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>>22514571
The host always picks the door with a goat. Why would he show you the door with a car? Then you are only left with goats. Are you seriously this dumb?
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>>22514538
Think about it this way. You had a 2/3 chance that you chose a door with a goat behind it on the first guess. The host then has to open a door with a goat behind it, but not the one that you selected, so he only has one possible door to open, with the other door being the one with the car. This means you have a 2/3 chance of getting it right if you switch.
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>>22514604
No. You could very well have choose the car first, so the host is just opening a door with a goat, regardless of what you think you choose. Changing your initial choice does not improve your odds of picking the car because you have no idea what you choose in the first place.
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>>22514596
Yes, it's extremely obvious once it's stated out loud. But when it's unstated people don't focus on that fact, and I hope you're intelligent enough to realize that that fact _literally_ changes the odds.

That's my whole point. It's a simple problem that only seems difficult at first because a simple, yet _provably_ crucial, factor factor is never revealed and lies hidden underneath subconscious assumptions.

If you think I'm wrong, then go explain the problem to someone who's never heard it before and make sure to explicitly state that the host will NOT choose at random, but will intentionally avoid revealing the car in the case that one of the remaining doors is a car.
And I bet you they'll immediately get the right answer.
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>>22514571

Great explanation.

In real game shows they will open the losing door and try to change your mind. But they will not do it every single time.

The problem of real game shows is a game theory problem where the host is trying to trick you to lose.
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>>22514624
You could have chosen the car first, but the odds are 2:1 that you didn't. Nobody ever said you will always get the car 100% of the time. But you will get the car 2/3 of the time if you switch.
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>>22514634
You only get 1 choice though. Pick wrong, and no car for you. You don't get to keep coming back and rolling the dice again, hoping you get lucky this time. What you're falling into is gambler logic, and it isn't correct unless you can cheat the system.
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>>22514628
But if he shows the door with a car, then you lose either way...that's the point I'm making. He isn't opening the door that has a car because it's a game show, and he basically just dabbed on you and ruined the suspense of possibly switching away from a car, or not switching to a car.
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Not paranormal
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>>22513774
Go back to >>>/sci/
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>>22514645
You only get one choice, so you should make your choice be the one that is statistically most likely to be correct. You could switch doors and end up with a goat, absolutely. But you're twice as likely to switch and get the car.
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>>22514571
so basically you're saying (I'm not very good at math but basically) if they guy is against you, then there's a chance that he avoided the third door deliberately, giving that a higher chance of being the car. but that doesn't make sense, wouldn't it still be 50-50? I always thought the idea that it was 2/3 this alleged paradox was actually an example of the gambler's fallacy.

frankly at this moment I cannot think of any theory that makes it not 50-50 regardless of the game show host's motives
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>>22513774
It's not a paradox, it's probability. It goes against your instinct and common intuition but it makes perfect sense. Your first pick had 33% chance of being right. Since one guaranteed failure is removed your chance by switching is 50% rather than the initial 33%. You can't force it to make sense if that doesn't spell it out for you. But it is in no way a paradox. A paradox would be that switching or staying the same guarantees failure.

In the future don't correlate ignorance with the paranormal. This is just math.
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>>22514679
It isn't statistically more likely though. No matter what your first choice is, there will always be a goat left over for the host to show you. It doesn't change that your first guess had a 1/3 chance of picking a car. No matter what, a goat will be shown to you. This isn't new info that makes your first choice any less likely of being correct.
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>>22514655
I know that anon. I know it's obvious and nobody would ever deny that that's how it works once the question has been raised right?
THAT'S how they get away with keeping it a mystery.
Because I believe there are basically 2 types of people when it comes to this problem: Those who've consciously realized that it works that way, and those who haven't yet consciously realized it.
Because if you don't take that fact into account when you're reasoning it out then you WILL get the wrong answer.

But that fact is left out of descriptions of the problem because psychologically it works in favor of the problem seeming like a paradox when it's not.
Once everyone is aware of it then it's no longer a mystery.
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Good to see there are still some intelligent minds here still.
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>>22514688
It's a troll paradox, in that, only trolls bother to continue pretending the answer isn't this >>22514690
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>>22514688
That's a fallacy because it designates switching as a choice, but not staying. Staying is also a choice. They've baited you into ascribing the probability of his previous choice to pick between three to the second case, when in the second case, whether he stays or moves, he's still picking between two.

It's like a trick question to trap people that can do math but are retarded

I have to thank you for answering this question >>22514687 though, after seeing you explain why you believe this I understand the fallacy

Stay woke
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>>22514687
>then there's a chance that he avoided the third door deliberately
Not a "chance", a guarantee.

Look, just write out the probabilities, and keep track of the goats by saying "goat A" and "goat B":
Case 1: Your first choice was the car - staying with your choice wins 1 time.
Case 2: Your first choice was "goat A" - now the host WILL reveal "goat B" and the remaining door WILL be the car - switching doors wins 1 time.
Case 3: Your first choice was "goat B" - now the host WILL reveal "goat A" and the remaining door WILL be the car - switching doors wins 1 time.

That is all the possibilities that exist. There are no others. 2 of the outcomes win when you switch doors, and only 1 outcome wins when you don't.
Note: if the host can potentially reveal the car then the odds change. So the key to this whole thing is knowing that the host will never reveal the car.
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It's like an inverse of Clarke's Law:
Any sufficiently low intelligence will declare basic fucking knowledge to be magic/paranormal.
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>>22514701
>Staying is also a choice
There. Now I don't know how it could be made more simple than that. Yes, you have a 50% chance of choosing the car after he shows you the goat, but staying is a choice that is just as likely to give you a car as switching.
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>>22514705
oh fuck

this does kind of break my mind a little
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>>22514690
You don't have to take my word for it, there are a million simulations of it on the internet you could look up and see that switching gives you a 2/3 chance of getting the car, and you could run it yourself and see that that is the result.

It also doesn't help that there are people like >>22514688 who say that it somehow gives you a 50% chance. That is wrong. Switching gives you a 2/3 chance of getting the car, which really comes from the 2/3 chance that you have of picking a goat initially. If you picked a goat initially (2/3 chance) then the host must open the other door with a goat leaving only the car left over. If you picked the car initially (1/3 chance) then it doesn't matter which the host opens because there is a goat behind each door, but remember you only have a 1/3 chance of getting to that point.

The question is really "given three doors, 1 with a car and 2 with goats, what are your chances of finding a goat".
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>>22514719
It's not a 2/3 though. You mention simulations on this internet thing; well, those are running this little nonsense problem over and over again, then saying "he look, it shows that 2/3 of the time, switching gives you a car, so it must be 2/3 chance every time! YAY SCIENCE!". But that's moronically incorrect. You only get 1 chance, not infinite chances to improve your odds. In that 1 chance, you don't improve your odds by switching. Staying or switching; it doesn't matter, both give you just as much likelihood of hitting the car.
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>>22514725
Have you read this post? >>22514705
You're correct only if the host reveals a door randomly and can potentially reveal the car. But that's not how the game works.
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>>22514705
Same guy here, I understand now. If the rules of the game are that the host chooses randomly, then this wouldn't be the case. It's just what you said, it depends on omitted information about the rules. If it's accepted that he chooses between the available goats, rather than the available remaining doors, the math is different. You're right, it's not even interesting, it's just a trick question
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>>22514725
What do you think statistics is? Where do you think that 2/3 number comes from? It objectively does improve your odds to switch. As I've said, that doesn't mean that given 1 chance you will succeed, it just means you are more likely to. I think it is generally wise to do things that increase your chances of success.
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>>22514744
>You're right, it's not even interesting, it's just a trick question
Exactly. I'm glad someone else get that.
And calling it a "trick question" is a good way to put it. That's basically what it is.
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>>22514747
>>22514725
I should should have said probability instead of statistics. It's getting late and I'm getting sleepy.
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>>22513774

33% of people are tranny demons. That's what the goat really means. Baphomet.
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The problem shows how people oversimplify problems. They become focused on this one possibility with door 1 and 2 and think it's either a car or a goat and they're right. It is 50/50 but only for this possibility. They don't consider all the other ones.

To approach it in a general way there's 3 possible doors the car can be behind, times 3 possible choices, so 9 possibilities that need to be considered. Switching only loses for 3/9 possibilities you choose the car. Which door the car starts behind though doesn't affect the game, only the choices do, so people are reducing it to 3 possibilities.

The paranormal implications of this is that people make bad decisions they believe are good and feel like a magic force is sabotaging them. What's insidious about this fallacy is that people rarely realize the choices they made were bad until shown all the possibilities. People feel trapped exhausting seemingly good decisions and get incredibly depressed.

To understand this with a real world problem consider two amateur artists trying to sell their services. One artist has twice the talent and a hundred times the social media reach and struggles hard all week to sell a few commissions but the less talented artist makes several sales by the end of the first day. How can that be?

People like to blame things and call it bad luck, but the artist struggling in this example just posts messages and new art on social media feeds hoping for a bite. In reality people don't spend much time there and there's too much noise to compete against. The successful artist on the other hand is engaging with fans directly and has a far higher likelihood of being noticed and selling a commission. To the struggling artist it seems like magic when they don't understand how the other is succeeding, but it's simply being aware of the possibilities. An introvert might not consider talking to people and miss those opportunities, just like people get stuck on seeing door 1 and 2 as 50/50.
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>>22515361
If you do believe in the occult, perhaps wizards use this human fallacy to put thoughts in people's heads and suggest them into taking seemingly good decisions that are actually bad. Unless a person can step back and take into account the greater possibilities, they will be unable to disagree with the suggestion from their current level of perception. Maybe that's the higher dimension intrusion you're looking for?
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>>22514571
So your problem is that something that is stated needs to be stated. OK. Very interesting perspective.
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>>22515383
Except that it's not.
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>>22513924
Holy fuck you’re retarded. The problem is very simple and has been explained many times.

Look, imagine it with 100 doors. You pick 1/100 and then the host opens 98 to reveal them as empty, he asks you if you’d like to switch... Do you think it’s 50/50 that you just happened to pick correctly out of 100 doors?

Fucking moron.
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>>22513774
It's not paranormal, it's just not clear how it works because of the numbers used. If I ask you to pick the ace of clubs out of a deck of cards without looking, then discard every card in the deck except one after you've picked, and give you the option to switch, OBVIOUSLY you'd switch.
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>>22515977
>>22515999
Based gets explaining simple probability to retards.
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>>22516003
I didn't used to understand it either, the deck of cards explanation was what helped me get it. The three doors scenario only has one false option removed, and I think that's what makes the statistics hard to understand there.
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>>22513780
The official statistical answer is "yes", you dingus, look it up, you didn't fuck up the OP.

You start off with a 1/3 probability, but after one goat has been revealed, you have a 2/3 chance to get the car which you can make use of only if you switch, otherwise you have gambled with only 1/3 chance of winning.

1/3 = knowing only one door can have the car
2/3 = knowing two doors can have the car

Sure, you may have picked the right door all along, but the point is about gambling with better chances.
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>>22514725
Not switching is like playing with 2/3 chances for a goat.
I think those who say switching doesn't change anything conveniently forget how they were initially making their choice among ALL the doors, including the one which got revealed as the wrong one.
Switching is like getting to make a choice among narrowed down options, you're thereby moved closer to the winning door. It's somewhat confusing because switching seems to force a particular door on you, but it is not a guaranteed win anyway, just better chances due to how it alters the gambling situation.
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>>22515361
The problem is people are horrifically bad at probabilities. We aren't wired to think about them properly. This is why the Gambler's Fallacy is a thing. This is why the Monty Problem is a problem at all. This is why people can freak out over terrorist attacks while paying no heed to speeding without a seat belt with their phone in one hand and a lit cigarette in the other.
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>>22515580
I suppose you might need to understand English to understand. Keep studying. You'll get there eventually.
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>>22514146
This
>>22514535
But it doesn’t change your odds.of winning at all, to say otherwise is magical thinking. It is still one of two doors left, you have NO NEW INFORMATION ON WHICH of the two. You are still judging picking on or the other at random, opening the other doors doesnt change anything because you didn’t pick them.
>>22514571
Bait
>>22514688
Probability is junk science.
>>22514719
And here is why.
>simulations
Probability only works with LARGE data sets, it can tell you NOTHING about the next event. Same with flipping a coin twice in a row and the first flip is tails staring the odds the second flip is less lie,lay to be tails is retarded. The second coin flip is always 50%. It is the same coin, to state otherwise is magical thinking.
What you mean to say is if you took 10,000 flips %50 would be tails so now that one is tails the odds are less the next will tails. BUT THIS ACTUALLY PROVIDES NO INFORMATION ABOUT THE NEXT FLIP. Only about 10,000 flips
>>22514725
This
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>>22513774
If you remove the middle door, 2, and choose between 1 and 3, you have a 100% chance of choosing right and wrong, simultaneously. Choosing the second door is admitting defeat.
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>>22517373
>it can tell you NOTHING about the next event
>The second coin flip is always 50%.
So it clearly CAN tell you something about the next event. It can tell you the probable results of the next event.
How amazing - probabilities can tell you probabilities.
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>>22517412
Um no probability would tell you the next flip would be 25% tails, which is retarded
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>>22517432
>probability would tell you the next flip would be 25% tails
Only to an idiot who has no understanding of probability. Makes sense why you would think so.
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I think anyone who claims that changing the door is always the better option, is completely incorrect. You're looking at this through the perspective of bs hypothethical maths.
You have 3 choices, however it is guaranteed that one will be eleminated and its not the one you picked at first, which makes it a 50% chance from the start. When the door is eliminated you are still counting it in the probabilities, which is incorrect.
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>>22514571
This is the classic answer.
Its also not stated whether the host normally opens the door or not though. Perhaps the host knows you understand probability in which case he might open the door to throw you off only if you picked the car at the beginning.
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>>22517482
Tell you what, I'm thinking of a number between 1 and 1000. I'm going to let you pick a number and then eliminate 998 of the remaining numbers. I'm then going to give you the option to swap or not.

What will you do?
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>>22517540
I increase my bet but I don’t change my pick, changing my pick does nothing, I have ZERO information on which of the 2 numbers left it is, what changed is my odds of winning went from low to 1 in 2, NOT my odds of randomly picking from 2 numbers
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So is /x/ all tuckered out of excuses on why they don't understand probability? Want to try another? A simpler problem for you to contemplate:

>100 passengers board an airplane with exactly 100 seats.
>Everyone has a ticket with an assigned seat number.
>The first passenger has lost their ticket and takes a random seat.
>Every subsequent passenger attempts to choose their own seat, but takes a random seat if their’s is taken.
>You are the very last passenger to board the plane.

What is the probability that you will get your assigned seat?
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>>22517548
Ok, whats the number you're guessing then? I've written the number I'm thinking of down on a piece of paper here.
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>>22517553
1/2
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>>22517606
The anon explained it pretty well. You're not giving a good example because you are artificially decreasing the chance to win from 1 in 3 to 1 in 999 which is not the point of the problem. The point is what are the odds that you will choose the right option. And if you know that one of the options will be eliminated, and you will be left with only 2, then your chance is always 50%.
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>>22517671
Then give me a number if you're so convinced.
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>>22517683
Can you read our replies? Read again what me and the other anon explained to you about how increasing the options does not correlate with the monty hall problem's purpose. Not every mathematical problem is comparable to others. This problem is very much a paradox. . I'm done responding to you, I hope you understand the inconsistencies in your argument.
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>>22517743
It is not a paradox. It is simple if you take the time to go over it in your mind. You're only limiting yourself by remaining ignorant.
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>>22517606
You have to tell me the the numbers you eliminated brainlet
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>>22517785
Not him, but do you even understand the process?
There are 1000 numbers to choose.
You give your guess.
He will eliminate all but your guess and one other number.
You have the option to stay, or switch.

Give your number.
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>>22517785
I can't tell you that until you tell me what you guessed as I can't eliminate yours.
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>>22517801
256
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>>22517802
256
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>>22517811
Ok, all but 256 and 732 are eliminated. Want to switch to 732?
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>>22517815
No.
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>>22517815
Yes
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>>22517811
I mean, you'd be mad not to. Seeing as there's much higher probability that 732 is the number I was thinking.

IF you still don't get it then we should swap. You should think of a number and I'll guess.
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>>22517482
The one eliminated will not be the one you picked at first, but that's irrelevant, because at the beginning you're making your choice among all three - you're blind to which one is going to be eliminated when it comes to your choice.
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>>22517815
An you repeat the question?
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>>22517836
>there is a higher probability... ... number I was thinking
That is just psychology, not probability. There is just as good a chance I picked right the first time and you are trying to trick me
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>>22517842
Put yourself in the position of the gameshow host.

Lets do it with 1000 doors because its much easier to understand.

I guess a door. You open 998 other LOSING doors. This is not done randomly. You only open LOSING doors. So basically, the one you leave closed is only going to be a losing door if I correctly guessed the door with the car at the beginning (1 in 1000 odds). Otherwise, the one you've left closed is the car (1-1/1000 = 999/1000)
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>>22517857
yes, I did also write that earlier:

>>22517490

It certainly isn't a paradox though, either way you argue it.
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>>22517877
Or I picked right the first time and you opened the other doors to try to trick me and entice me to pick a new door. If I had picked wrong the first time you would have no reason open more doors because I had already lost,
lLLLLlLLLllLLlllLlexcept you could not do this /every time/ because people would pick up on the pattern so you would still have to open other doors sometimes when Players were winning to keep it random. Psychology not math.
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>>22517902
>to try to trick me
Where are you getting this "trick" from? The process is the exactly the same no matter what you pick.
>you pick wrong, host opens 998 losing doors
>you pick right, host opens 998 losing doors
Where is the trick? the only psychology here is you not getting probability and desperately reaching for any other reason to explain your lack.
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>>22517902
Yea or maybe you just need to read more carefully. I explained I would eliminate the numbers in advance.

>>22517540

If I had not done, then there is the option I would try to throw you off and only eliminate numbers if you guess correctly. But those were not the terms.

Either way it certainly isn't 50-50
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>>22517932
>(Picking from two numbers is not 50/50 due to pretempoal events)
This is magical thinking.
if you have to eliminate 998 out of 1000 numbers, that leaves 2 numbers. It DOES NOT effect if my number was already right or not, to say otherwise is magical thinking
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>>22517956
No, it doesn't affect whether its right or not. And it doesn't affect the PROBABILITY of it being right either. Thats the whole fucking point.
The host increases the probability for the other door but not the one you chose.
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>>22517972
>The host increases the probability for the other door but not the one you chose.
Nope
The host increases the probability of *both* doors to exactly 1/2
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>>22517992
Are you actually trolling now? You are wrong.

Just go through the motions. You're the host. Write a number down on a piece of paper between 1 and 1000. I'm going to guess what that number is. You're then going to remove 998 numbers (you cannot remove mine) making sure that at least one of the numbers is the one you were originally thinking of.
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>>22518013
one of the remaining numbers*
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Perhaps if people stopped thinking about it as discrete options, and looked at it as groupings.
You have two groups:
>options you picked (P)
>options you did not pick (NP)
At the start, all the options have not been picked, so the chance of the winning option being in that group is 100%
>P = 0%
>NP = 100%
You then choose one out of however many options there are. IT DOES NOT MATTER HOW MANY OPTIONS THERE ARE. Let's try it with 3, 1000, and X. You choose one option, so the odds that you choose the winning option is 1 out of the number of options.
>P = 1/3, 1/1000, 1/X
By simple math, we know the remaining odds are the opposite. Also, since we are treating all the options not chosen as a single group, we can state these are the odds of the entire group. Thus, the odds of the entire group that is "not chosen" are:
>P = 1/3, 1/1000, 1/X
>NP = 2/3, 999/1000, (X-1)/X

Next, we take the NP group, and we eliminate all the options besides one, making sure to not eliminate the winning option IF it is in the NP group. But here's the freaky part people are missing: THE ODDS OF NP AS A GROUP DO NOT CHANGE. So after we eliminate all but one option in NP, the odds are still
>P = 1/3, 1/1000, 1/X
>NP = 2/3, 999/1000, (X-1)/X

So what DID change with the removal of all those options? Because something certainly did change. It was the odds of the options being a winner WITHIN NP AND ONLY WITHIN NP.

With the three options, the odds of each option WITHIN NP went from (1/3, 1/3) to (1/2).
With 1000 options, the odds of each option WITHIN NP went from (1/100, 1/100, 1/100,....) to (1/2).

But outside - looking only at the groups P and NP, the odds never change. It will always be
>P = 1/X
>NP = (X-1)/X
because these odds are completely independent from what is going on inside of NP.
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>>22518046
>With the three options, the odds of each option WITHIN NP went from (1/3, 1/3) to (1/2).
>With 1000 options, the odds of each option WITHIN NP went from (1/100, 1/100, 1/100,....) to (1/2).

It doesn't go to 1/2. In your second option it goes to 99/100.
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>>22518074
sorry, if its 1000 options it goes to 999/1000. (if 100 it goes to 99/100)
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>>22518046
>So what DID change with the removal of all those options? Because something certainly did change. It was the odds of the options being a winner WITHIN NP AND ONLY WITHIN NP.
>With the three options, the odds of each option WITHIN NP went from (1/3, 1/3) to (1/2).
>With 1000 options, the odds of each option WITHIN NP went from (1/100, 1/100, 1/100,....) to (1/2).
Looking back over my rant, this is wrong. The odds of each option in NP being a winner would be the total NP chance (X-1)/X divided again by the number of options within NP.
So if there is only one option - such as when all the others are eliminated, that one option would have 100% chance of being (X-1)/X% chance of being right. If there are 2 options in NP, each would have ((X-1)/X)/2% chance of being the winning option, and so on.
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>>22518046
You can’t convince smart people that between two random choices the odds are not 50/50, no matter if the host paints one door with gold and shits on the other or does nothing.
Between two random choices the odds are 50/50,, all you are proving is stats and probability is a junk science
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>>22518107
>You can’t convince smart people that between two random choices the odds are not 50/50
But you CAN convince a smart person that what is being described isn't two random choices. Sadly, you remain unconvinced...
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>>22518046
Oh right, I just reread, yea I get what you've written now. Its correct.
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>>22518114
How is it not random? The winning door was picked before the host did anything
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Let's try to remove some confusion.

Let's say the host doesn't get rid of any doors. The game is now this:
There's three doors.
You pick one
You now have the option of switching between the one you picked, and the two you did not.

Do you switch?
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>>22518107
Sometimes it helps to go through it. Seriously just write a number down on a piece of paper. It'll become very clear to you if you do the eliminating.
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>>22518129
God you are dumb, get your head out of the math book and THINK.
Here, I will use your own logic Against you.
At first I have 1/1000 chance of right door. Maybe I picked right door, maybe I did not.
Now, you take away 998 losing doors. Now I have 1/2 of having picked the right door. The other door DOES NOT go from 1/1000 to 1/2. There are two cases.
Case a.
A. Where door 256 is 1/1000 and door 732 is 1/1000
Case b.
B. Where door 256 is now 1/2 and door 732 is now 1/2
There is NO
case C. Where door 256 stays 1/1000 and door 732 is now 2/3 or any other case c. I hope this makes it clear, you go from case a, to case b, your odds are the same in each case to stay with your door because both numbers change
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>>22518179
...
there are only 2 options, the probabilities need to add up to 1.

Stop theorising BS at me and go through the actual exercise. Have you written a number on a piece of paper yet?
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>>22518179
There's three doors.
You pick one
You now have the option of switching between the one you picked, and the two you did not.

Do you switch?

Or with the numbers.
Pick one number out of 1000
You now have the option of staying with the number you picked, or going with the entire other 999 numbers.

Do you switch?
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>>22518199
We already did that.
>>22518205
Why would I switch? First pick I have a 1/1000 chance of picking the right door. No matter what door I picked
Second pick I have 1/2 of picking the right door. No matter what door I pick. I stay with my door it is 1/2 to be right, I pick other remaining door it is 1/2 to be right. I gain nothing from switching because either door is now 1/2. I lose nothing from switching either.
Brianlets trouble with temporal, 4d thinking it seems.
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>>22518236
I'm asking you to be the host. Hopefully that way you'll get it.
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>>22518240
God you are dumb. Fine. Pick a number
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>>22518236
>Why would I switch? First pick I have a 1/1000 chance of picking the right door. No matter what door I picked
This is correct. What is the chance the correct door is NOT the one you picked? That would be 999/1000, right?
So your option is between 1/1000 chance of getting the right one, and 999/1000 chance of getting the right one.

Do you switch to the 999/1000 doors, or do you stay with the 1/1000 door?
I'm not removing anything. I'm giving you the option of one door, or the entire group of 999 other doors. Which do you pick?
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>>22518257
524

What are we left with?
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>>22518260
But that’s wrong. You are presenting effectively a new case of two doors.
I had a 1/1000 chance of picking right removing the other doors does not change that 1/1000 pick. Either I was right or I was wrong. The new case is not my door vs 999 doors. It is my door vs one other door. The other door is 1/1000 and my door is 1/1000
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>>22518265
357 and 524, do you switch?
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>>22518284
>But that’s wrong. You are presenting effectively a new case of two doors.
No. Not at all. New game. No removal.

We have 100 doors.
You pick one.
You have the option of staying with that one door, or switching to the ENTIRE GROUP of 999 doors.

Do you switch?
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>>22518293
Chances:
1/1000 that 524 is correct
999/1000 that 357 is correct

I swap to 357
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>>22518294
For everyone not trolling, it's pretty obvious that the group of 999 doors will have the better chance of containing the winning door.

So next step, same game but with one addition.

1000 doors.
Pick one.
I remove from the group not picked a single door that I ABSOFUCKINGLUTELY GUARANTEE is the wrong door.
You have the option of staying with one door, or choosing the group of 998 doors (minus the door that is absofuckinglutely NOT the right door).
Do you switch from one door to 998 doors?

Same thing again, except now I remove two doors that are the wrong group, and you choose between your one door, or the group of 997 doors.

Anyone with half a brain can see where this is going.
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>>22518298
Wow, you got a 1/2 chance right, it is not impressive. You are still wrong.
If you think your math is right, just go to Vegas and bet on blackjack, because if you count cards you will know when good combos will come up, lmfao
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>>22518322
we can do it 50 times and I'll likely be right 50 times. Do it yourself if you can grapple with playing both roles at once.
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>>22513780
kys
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>>22513774
Its not even a paradox, it just takes advantage of poorly describing the "game" and the problem. Its just brainlets being clever and a way to trick people.

If you can switch to ANY door obviously it doesnt become 50/50. It relies on 'but for the 2nd round the game show host will pick the car if you picked the goat or will pick a goat if you picked the car but you then can ignore a door XD"

This problem can suck a dick.
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>>22519269
I can understand people not understanding the math. But people not even getting the basic setup completely baffle me with their stupidity.
THE
HOST
DOES
THE
SAME
THING
NO
MATTER
WHAT
YOU
PICK
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>>22518322
how are you still not getting this
that anon was nice enough to fucking walk you through it and you still don't get it
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>>22514417
But if you choose to stick with your original choice, aren’t you actually making a new choice between two options which, now that the other wrong options are eliminated, each have an even chance of being correct? You’re odds have changed since you’re actually making a new choice.
I’m not arguing, but I wish I could actually understand.
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>>22517548
If both remaining doors are goats, the host picks at random. However, if only one is a goat, the host must pick that door. That means there are two scenarios in which the host eliminates a losing door, and one in which he gives you no new information. This means that he is more likely to eliminate a losing door than give you no information.
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>>22514538
I bet it's all the womens fault you can't get any pussy and not yours at all
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>>22514571
You are stupider than all the people you think are stupider than you.
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>>22519603
>now that the other wrong options are eliminated, each have an even chance of being correct?
This is what is tripping you up. Consider my "new game" I tried with someone else.

1000 doors
Player chooses 1
Player has the option to choose between the chosen door, or the entire group of non-chosen doors.

The odds of this switch are 1/1000 being correct for chosen door, and 999/1000 being correct for the group of 999 doors. Do you agree?

Now here's the rub - that group of 999 doors that has a 999/1000 chance of being the right pick.
Why would its chance of being right change if you remove all the wrong options?
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>>22520377
>Why would its chance of being right change if you remove all the wrong options?
Even better. Don't think about "removal" at all. The groups stay exactly the same:
>1 door
>999 doors
But now, I've shown you what you already know - the group of 999 MUST have at least 998 doors that are empty. (998 wrong + 1 right, or 998 wrong + 1 wrong) I merely show you what you already know must be true, so you're left with this:
>1 chosen door, 1/1000 chance of being right
>999 doors, 999/1000 chance of being right, now visually confirmed to include 998 empty doors
Would you decide to stay with the the one door, or choose the group of 999 doors, with 998 that MUST BE and have been physically confirmed to be empty?
Why would physically showing what must be true about the entire group change the odds of that group?
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>>22520416
Thank you, reading these posts I do actually get it, and it makes total sense. Sorry about how stubborn that other anon is being.
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>>22513829
Dude, maybe YOUR mind is incapable of grasping this simple example of something seeming to be counterintuitive (not insulting you) but it's not that mysterious, my man.
Even just reading the wikipedia article on it made it very simple to understand.
Whether or not 'higher realitys' (whatever that means) exist or not, it has nothing to do with this simple brain teaser.
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retards. this shit is real.
you can run a script to solve this problem and you'll always have higher chances of winning by changing choices.
it's the part of digital RNG that leaks out to IRL RNG and it's fascinating.
though people already abused such by doing animal sacrifice lomg ago so it's less likely to have your livestock die out of nowhere because you're controlling reality (while human sacrifice is still a thing to cults).
also you can play a game of chances, lets say the game lets you win premium stuff by opening treasure boxes with 20% winning chance which is 1 out of 5 chance.
the boxes price also varies and if you want to win easily, just go for a 4 streak lose on the cheapest boxes and finally the open the most priced box one so you'll get 100% chance that it wins. RNG hacking.
same shit happens with lottery.
if you have a number you've been saving and isn't winning forever and one day forgot to buy yourself a ticket it might have higher chances of winning right then as the number appeared frequently and reality assumes it should appear 'again' so it appears the moment you stopped buying lottery tickets. duplicates/coincidences are very hard. the more the same combinations appears the less chances it will appear. this is why you can't run a RNG program and expect it to show repeating digits.
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>>22515977
What if there are 2 people who each pick a door and the host reveals 98 as empty. Is person A or person B more likely than the other to win the prize? Or is is a 50/50 chance.
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>>22520977
"The reason they increase their chance of winning in the standard edition of the game is that they pick a door from a set about which the game host has given some information. In this case, with the suggested play that two contestants pick two out of three doors, it might be that players A and B have both selected a goat in their first pick, and then the game show host would be forced to open the remaining door with the prize car. This makes the game less interesting. Even if you extend the game to have four doors, one of which has a car behind it, the game host would only ever open one of the two doors that are not picked by either A or B in step one of the game, so the players have information about those doors and can increase their chances of winning by changing their pick to the only remaining unopened door. Picking the other players door gives the same probability as the initial pick, which is no improvement. The reason the probability for the other players initial pick does not change is that the players are not given any information about that door. Notice that all of this changes if the game host is ignorant about the players picks and opens a random goat door — it's all about the players being given information about a subset of the doors, and picking a door from that set now is less probable of containing a goat."
-some guy at some page

This should explain two player mode.
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>>22520977
This will only happen like 1 in a hundred times you dingus, and ya it’s 50/50 in that case.
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One thing I've yet to see in this thread is any of the tinfoil hat wearers explain how this math problem is a paradox or how a paradox like they claim could exist.
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>>22513924

You're forgetting the host knows which door the prize is behind. The host wont open the door with the prize behind it. The monty hall problem is a way to remove an incorrect answer. The chances of you getting the correct answer overall was always 50% if you change and 33% if you dont because the host would always remove an incorrect door

It's not a paradox, it's psychology mixed with statistics
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I mean your right but I’ve done the problem before. You have a greater chance initially at picking a goat, and switching is always the best option because you probably initially picked a goat. Honestly the option of switching and comparative odds will mess with people the first go around. But if you had 100 doors had someone pick one then opened 98 doors to show goats and asked if they wanted to switch to the still closed door people would catch on better to the trick. It’s not so much a paradox other than people just naturally thinking unintuitively.
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>>22523760
>50% if you change and 33% if you dont
What result is the other 27%? 27% chance that the world dissolves back into void?
You have a 66% chance if you switch, not 50%. Look at the pic above your post. Three end results with a switch - only one results in losing. That's 2 out of 3 odds of winning - 66%.
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>>22523920
>27%
17% I can maths.
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>>22513774
Door 1 is Providence, you expect something (the science of good and evil)
Door 3 the Goat that climbs the highest peaks of the rockiest mounting just by will of light (lucifer)

Door 2 ? Rise from death
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>>22513774
>/x/ trying to take on monty hall problem
This going to be good
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>>22513780
>>22513829
Rest of your OP post shows you are more of brainlet than simple fuck up of words yes and no
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>>22513774
>I would plead in vain that you pretentious mediocre fedora wearers out there refrain from the stupid "Well, I TOTALLY knew that the odds were better if I stayed with the original choice!" because, you know, you didn't. If you were being honest you would just admit that you didn't.
I admit I didn't know because this problem fooled me but I got it explained in way every non brainlet should get. In way like this >>22515977
>>
post the fucking specifications that were originally printed shithead
>The host must always open a door that was not picked by the contestant (Mueser and Granberg 1999).
>The host must always open a door to reveal a goat and never the car.
>The host must always offer the chance to switch between the originally chosen door and the remaining closed door.
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>>22514571
>Everyone acts like you have to be some genius to figure it out on your own, but anyone who comes to the "correct solution" must make an ASSUMPTION here.
Bullcrap, its obvious thing and you should see it as obvious regardless if you figure it out or somebody explain it to you
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>>22517553
You intentionally added pic like this so people look at unrelated numbers, get influenced by them and confused
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>>22518322
Somebody need to screencap entire conversation
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>>22524282
No, I put the pic because I wanted a plane image, couldn't find a graphic of the prolem showing the plane, and thought relative safety of various plane seats seemed the most relevant to /x/. But it doesn't matter. The only other response got it right and no one else bothered to talk about it. Move past it.
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>>22513774
The problem with the monty hall problem is that it ignores the fact that even after a door is eliminated, choosing to keep the same door is still a choice and therefor is still 50/50.
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>>22513774
>Whoever created this simulation PROBABLY didn't expect there to be a gameshow called "Lets Make A Deal"
that's the whole reason for the simulation. so novel things can happen and we can be there to observe them. the monty hall problem is just unintuitive to the human mind. humans are stupid and have monkey brains, math is pretty complex; don't read too much into it.
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>>22524889
No. How are you so dense? Reread this thread, or the wiki page on it or watch one of the dozens of YouTube videos that exist explaining it. The host has knowledge of all the doors and MUST reveal a goat, odds are the you picked a goat the first time (2/3) so by switching youre more likely to get the car.
There are literally only three winning scenarios -start with the car and stay 1/3 odds you got it right.
-start with goat A and switch 2/3 odds now that the host has refined the data set for you and removed the other losing option.
-start with goat B and switch same as above.
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>>22513774
Your initial choice is not a probablilty issue there is no analysis to be made it is simply an action required by this game in order for the host to give you the 50/50 it was always going to be.

Think instead of odds of winning this game with each step think of losing with each step.
1st Choice - 100% will not lose game
2nd Choice - 50/50

I understand the idea of your first choice being a 33% chance assuming you dont know the host will always reveal a goat door but the other door is also a 33% chance of being the winning door. Both raise to 50% when its between the two.

Am i seriously missing something here?
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>>22526746
Yep, that the host know which door is which.
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>>22526752
Why does it matter what he knows though, why would that effect your choice?
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>>22518318
Okay but isnt the OPs question more like pick 333 doors you remove 333 doors do i swap to the other 333 doors?
There is no significant difference between those 333 and my 333 its still a random block of equal size equally capable of containing the winning door
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>>22518340
>>22524889
>>22526310

Of course you'll be right if you have a 999/1000 chance of getting the wrong number initially. Barring a 1/1000 chance you got the right number first go, of course you'll swap if the other number has better odds because NEW INFORMATION has been revealed. You have not diminished the odds from 1/1000 to 1/2. You are making a choice between the likelihood that you got a 1/1000 chance correct on the first try vs a 999/1000 chance of getting it wrong on the first try, and it's better in this situation to believe you made the wrong choice initially.

I'm assuming in the OP's example the host does not terminate the game if you choose the door with the car on the first go. The next step will be the same regardless of a correct or incorrect initial decision. If you choose the car, he will open one of the two doors which the goat is behind. If you choose one of the goats initially, then he will simply reveal the other goat to you. You have no new knowledge which door is more likely to hold the car, unless you know in advance he will try to make you call his bluff or that he will simply reveal the car to you immediately if you got it correct. Neither of these factors apply. We have not opened 998/1000 doors to reveal goats as in the previous example. Before the host opened the door, we still had a 1/2 chance of choosing the right/wrong door because the second goat- the one the host revealed- was never part of the odds to boot.
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>>22526852
The host opening the door does actually reveal new information, because in 2/3s cases it reveals which door holds the car. It took me a long time to understand this also.
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>>22513924
2/3 chance of winning sticking with your first choice.
This is a simple math problem old af you moron.
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>>22526872
What?
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>>22526746
Just read the thread, imagine there is a hundred doors, or even millions of doors. You pick one with say 0.00000001% chance of it being the car. The host opens all the other doors and leaves you with two. You can be sure one of them is a car according to the rules. Do you really think you have 50% chance of winning when staying with your previous choice?

In this case, overwhelming majority of people will not chose the correct door initially. If they switch, they will win. About every millionth person will chose the car on their first try and switching doors will make them lose. That's why the initial choice matters and you definitely have to account for it if you want to understand why switching gives you better chances.
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>>22515977
I'm this anon>>22526852 btw
In the example you're trying to compare OP's problem to, you don't have the same amount of new information as if there were 100 doors and the host eliminated 98 because you could infer that your probably chose incorrectly the first time.

In the Monte Hall paradox, the host will opening a door with a goat leaves you with as much new information as if there were 100 doors and the host only opened 1. You have no grounds to say switching to another door is a better decision. If you had 4 doors, and the host opened 2 with goats behind them, then you are choosing between a 1/4 chance you got the car first go or a 3/4 chance you got it wrong the first go. of course, the odds are still smaller than if it was a 98/100 chance you got it wrong, but the possibility, period, is introduced as an object of consideration whereas it is not in OP.
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>>22526882
in 2/3s cases it directly implies that the door neither of you chose holds the car.
>>
I'M A GOAT
I'M A GOAT
I'M A GOAT
ASS ASS ASS ASS
ALL I WANT TO DO IS EAT ASS
GRASS GRASS GRASS GRASS
ALL I WANT TO DO IS EAT GRASS
I'M A GOAT
I'M A GOAT
I'M A GOAT
>>
>>22526852
Think of it this way: you are more likely to pick a goat (2 of 3 doors) as your first choice than you are to pick the car (1 of 3 doors) the host then removes one of the chances of losing so switching is more likely to win
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>>22527087
Ah shit, I get it now. And it is basically the same principle as if it was 1000 doors instead of 3
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>>22526852
>You have no new knowledge which door is more likely to hold the car
Yes, you do. The odds that you chose the wrong one don't change, which neccesarily means the odds of the non-chosen doors are redistributed. Regardless of how many options you have, if all but the one you picked and one other are removed, then the chance of every unpicked door being the right one gets added into the remaining unpicked door, resulting in the odds that the remaining unpicked door is correct being 100% - (percentage that the door you picked was correct). If you've got 100 doors, then the remaining unpicked door will be the right door 99% of the time. If you've got 3 doors, it will be the right door 66.666...% of the time.

tl;dr: the odds that the remaining unpicked door is correct is the sum of the odds any specific unpicked door was correct.
>>
Joke's on you. I wanted to win the goat.
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>>22527140
you are destined to conquer Asia
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>>22526842
No, second choice is always when I are reduced to 2 choices from whatever number of initial choices were.
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>>22526842
>you remove 333 doors do i swap to the other 333 doors
Forget about "removal." This is throwing people off, as it is meant to. Monty Hall was intentionally playing on people's misunderstanding of statistics.
There is no "removal."
The choice is your pick of 333 doors, or switching to the other 667 doors.
The only thing is that before you choose to switch or not, I merely open 333 of the 667 doors, confirming them to be empty - as they MUST be.

Again, your choice is not 333 vs. 333. Your choice is 333 vs. 667 (333 of which you have confirmed to be empty doors). Confirming that there are empty doors does nothing to change the odds between 333 v 667.
>>
Okay so I think a lot of people here are over complicating things. Lets parse this out and boil it down to help some anons wrap their minds around it.

-You have a 1/3 chance of picking the car on your first try because there is 1 car, 3 doors
-You have a 2/3 chance of picking a goat on your first try because there is 2 goats, 3 doors
-The host will only ever remove a goat from your options but don't worry about this too much yet
-You are NOT making a new selection between two options
-You are choosing to stay with your first pick either the car (1/3 odds you got this at the start) or a goat (2/3 odds you got this at the start)
-Now because the host removed a goat this means that there will always be one winning door and one losing door during the time you may switch
-it is more likely you choose a goat to start because there were two of them (2/3)
-Therefore you have better odds when switching
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>>22513774
It's because of the omniscience of the host and the host's willful choice to choose a door with a goat, you absolute retard. I would not change my answer because I value goats more than cars. Same reason I'm vegan. Animals' lives and freedom are more important than cars and our tastebuds.
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>>22514705
Ok so Common Core raped my understanding of basic math- please for the love of god walk me through it like a brain dead cripple 8 year old. I feel like I am close to understanding.
Ok so 3 doors, 2 goats, 1 car. I pick randomly a door, and the host reveals a different one, which has a goat. I can either keep my original choice, which either has the other goat or the car, or I can switch to the remaining door, which also could have the goat or the car.
That's as far as I got. Please don't get mad I've already admitted to being a mathtard. But I can remember anything I've read and apply it.
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>>22513774
>>22513947
It's a dumb fucking question because it baits you into using the standard logic of "I have the same chances no matter what happens next"
The problem is with the Host ""selecting"" a door to open, because he has backstage knowledge of which door to show. You can use that to your advantage, despite it being less intuitive. That's the whole reason why this question is a bait and it solely relies upon that assumption. An assumption that is typically ignored or overlooked.
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>>22524970
it's because it uses gameshow logic and rules instead of being a real game of chance
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>>22531455
Lay out all the options possible. What are all the results that could happen if you switch? Seriously write them out, and see how many possible results end in winning.
If you just want the answer, the pic here >>22522223 lays it out for you.
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>>22531893
This makes more sense. I guess I wasn't quite "feeling" the statics behind it but now from a numbers standpoint I get it.
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>>22514571
No.
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If you don't switch, you win if you picked the right door. Chance = 1/3
If you do switch, you win if you picked a wrong door. Chance = 2/3
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>>22513774
After the third door has been opened, you've got a 50% chance of attaining the price. It doesn't matter if you switch your choice. Imagine you only have two doors in the beginning, so 50/50 chance of getting the car. Opening one bad door is basically removing it. It's not a paradox what the fuck.
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>>22531959
The paradox is how people can believe a 1/3 chance magically turns into a 1/2 chance despite dozens of people all explaining in different ways why this is wrong.
>>
Perhaps it will make sense to people if you play the game in reverse.

Let's say there are two doors, one car and one goat. You choose one door. Everyone agrees that the chance of winning at random is 50%, right?
OK, so two doors, choose one. Now I ADD 99 empty doors to the mix. Do you think the odds of your first pick being the car went from 50% down to 1%?
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>>22531455
Does it help if you imagine there are more doors? Lets say there are a million doors and only one of them has a car behind it. So, your chances are one in a million at the beginning. Next, the host opens 999,998 goat doors so that we are left with only two doors. Would you switch your door or keep the original, one-in-a-million one?
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>>22531959
You're right in that it's not a paradox but you're drooling on yourself retarded in terms of math. Really reread this thread, for your own good
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Gonna boil this down so absolutely the most retarded person can understand it.

1) To win a car, your aim is first to choose the INCORRECT door because that is more likely than choosing the right one.
2) 2 out of 3 odds are still better than 1/3 odds.
3) The host is cooperating with you to help you win the car.
4) The host eliminates one incorrect door. Unless you are a cocky fucker, it's safe to bet you probably chose the wrong door initially because 2/3 is more likely than 1/3.
5) If you chose the wrong door initially, and the host reveals the other wrong door, then by swapping you are more likely to have chosen the car.

The most important part to understanding this is realising the aim of the game is to choose the goat because it's more likely than choosing the car.
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>>22513774

>play the game 100 times
>chose door
>other doors remain closed
>open choice
>win 33 cars on average

>play another 100 times
>chose door
>other door with goat is opened
>stay with choice, open
>now win 50 cars on average
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>>22534404

>play another 100 times
>chose door
>4th closed door is added
>open choice
>win 25 cars on average
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>>22513774
>because, you know, you didn't

My highschool monography was on this problem and about 10% stayed with the original door, although the great majority of then didn't know the reasoning behind their answer.

Now, then you went on with with the higher dimension and that kind stuff. It's a tought experiment that was meant to confuse us (even Erdos, one of the best mathematicians of his time, couldn't possibly understand the answer), it's is not a paradox (such as the Banach Tarski paradox, a paradox in the sense that our understanding of the "real world" isn't the same as our mathematical knowledge, which depends solely on the axioms we are using) because it does not presents us a flaw that originates, let's say, in the Kolmogorov axioms, but the confussion it's only there because of our understanding of statistics and not because statistics are flawed themselves. It is, in a sense, a language problem (completely circunstancial) and not a mathematical one.

If this is making you thing of the paranormal then you will go completely nuts when reading about the Agrippa's trilemma or the Gettier problem.
>>
OPs example is dumb and gay but are there any other interesting "error in the simulation" theories?
>>
What everyone arguing that the second choice is still 50/50 aren't seeing is that this isn't an isolated choice, it's a sequence.
This is like rolling a 6D dice and saying the chance of getting a 6 is always 1/6.
It isn't, because what are the chances of getting a 6 one time? That's 1/6. But when you roll it again, what's the chance of getting a 6 twice? It's 1 in 6x6, so it's actually 1/36
If you roll it again, getting a 6 the third time again you're at 6x6x6, the chance is extremely small. There are no isolated chances, statistically it's always a sequence.
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>>22513774
Still don't get how its statistically better

When the host asks if you want to change, you're not actually altering anything, you're making a new choice of 2 equal doors. Everything else is irrelevant
You can't assume the hosts intention
You're previous choice doesn't matter
The eliminated door is meaningless

The only thing that matters is which of two doors you want to open, one wins, one goats, 50/50
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>>22534619
>When the host asks if you want to change, you're not actually altering anything, you're making a new choice of 2 equal doors.
That's not true. You had a 1 in 3 chance of picking the right door, initially. That hasn't changed, which means the other door has a 2 in 3 chance of being the right door.
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>>22518127
It doesn‘t matter, retard. Whether you switch or not, each door has an equal chance of being the correct one.
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>>22534731
but I already picked 1 out of 3 doors. That chance is gone
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>>22513774
does the host wants me to win or lose?
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>>22534544
Point the fingertips of your pointers at each other, an inch apart. Then hold that an inch away from your eyes. A whole new finger appears! Where does it come from? Glitch.
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>>22534992
But anon, it looks more like a hot dog than a new finger. Mmmmmm.... hotdogs.
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>>22532148
After 3 bowls of weed I get it now thank you everyone who spelt it out to me.
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>>22526975
>. If you had 4 doors, and the host opened 2 with goats behind them, then you are choosing between a 1/4 chance you got the car first go or a 3/4 chance you got it wrong

You are really close to an enlightening discovery
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>>22534919
You are given the option between one door and two doors. You don't think two doors have a greater chance of containing the winning door than one door?
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>>22532020
thats not how statistics and probabilities work anon. You have to be able to choose from all 100 doors at the beginning.
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>>22537735
You deon't understand my point. Let's work through it step by step. Forget absolutely everything else but this post on:

2 doors, 1 wins, 1 loses. You get to choose one. What are your chances of picking the winning door?
>>
Where'd you go, anon? Why say something is wrong and then just disappear? Don't you want to understand? Or conversely, don't you want me to understand? Let's work through this and you can show me exactly where in my steps I make a mistake.

2 doors, 1 wins, 1 loses. You get to choose one. What are your chances of picking the winning door?
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File: 1555546952792445.gif (1.61 MB, 338x250)
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1.61 MB GIF
Here's a good way to visualize it, I think -

Let's say that SECRETLY you pick one of the three doors and Monte doesn't actually know which one you picked

One possibility is that he's going to reveal to you the door you secretly chose and let you see that it was in fact NOT the right door, this is where the statistical advantage comes from but you feel like you're denied it.

Your choice is actually meaningless and I think it's the human ego that makes this problem difficult to understand. If you're looking for a paradox in this THAT'S it
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>>22537783
Since that anon is a troll or a coward, I continue for others who might not be.
>2 doors, 1 wins, 1 loses. You get to choose one. What are your chances of picking the winning door?
Hopefully we all agree that the odds are 50/50.
Now let's try this - remember I am not dealing with the Monty Hall problem at all. I am creating new scenarios to show the mechanics of determining the probability.
New Scenario:
There are four doors. Two blue, two red:
>B1 B2 | R1 R2
One door wins, three lose. But this time, you are choosing between the GROUPS, not the doors. You choose the red group, or the blue group.
What are your chances of choosing the winning GROUP (not the specific door)?
The answer is again 50/50:
B1 - 1/4
B2 - 1/4
R1 - 1/4
R2 - 1/4
Choose blue, you get B1 & B2, 1/4 + 1/4 = 1/2. Choose red, you get R1 & R2, 1/4 + 1/4 = 1/2.
Everyone with me so far?
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>>22537851
uhhh yeah sure, but I don't know where you're heading
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>>22537851
Third Scenario:
There are eight doors (1 wins, 7 lose), two groups:
>B1 B2 | R1 R2 R3 R4
In this scenario, you are again choosing a GROUP, and it is axiomatic and 100% true that the winning door will either be in blue or red. In other words, the odds of each GROUP is fixed at 50/50.
Since we KNOW that the blue doors have a 50% of winning AS A GROUP, and the same for red - what are the odds of the INDIVIDUAL DOORS?
>blue = 50%, two doors in blue, so each has half the chance of 50%
>B1 = 1/4
>B2 = 1/4
>red = 50%, four doors in red, so each has one quarter the chance of 50%
>R1 = 1/8
>R2 = 1/8
>R3 = 1/8
>R4 = 1/8
When you fix the percentage of the GROUP, then the odds of the doors within that group MUST total the group's odds. Make sense so far?
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>>22537870
but why should it be 50/50 between the red and blue group? There are 4 red and two blue doors if the car is randomly put behind one of the six doors, chances are 2/6 for blue and 4/6 for red. UNLESS you first decide on either red or blue group by throwing a coin
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>>22537870
Fourth Scenario:
>B1
>R1 R2 R3 R4 R5 R6 R7
Choose a group, each group has a 50% chance of being right.
>B1 = 50%
>R1 = 1/(50/7), R2 = 1/(50/7), and so on
To reiterate, once you fix the odds of the GROUPS, the number of doors in that group DOES NOT CHANGE THE ODDS OF THE GROUP.
>>22537888
>but why should it be 50/50 between the red and blue group?
It is axiomatic. It's true for this scenario AND ONLY for this scenario because it's truth is set from the very beginning.
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>>22537888
>if the car is randomly put behind one of the six doors
Ahh, I see where you got sidetracked. In my scenario, this is not the case. It is randomly put in one of two groups, AND THEN randomly put in one of the doors in that group. I am guaranteeing that the odds between red/blue is 50%.
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>>22537899
ok sure, you can do it like that by flipping a coin and heads >blue tails >red but thats not how it is done in the original problem where every single door has 1/3 chance at the start
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>>22513774
It's a 33 percent chance of picking the right door but each time you choose wrong it ups your chances. It's not intuitive plus probabiliy is basically not present in the macro scale universe

So yeah op you're kind of right
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>>22537906
Continuing, two groups of doors, you choose a group, then I arbitrarily change the number of doors in a group. Let's say I add three doors to blue
>B1 = 50%, blue total is 50%
>R1-7 = 1/(50/7)%, red total is 50%
Make a choice.
Then add three
>B1-4 = 1/(50/4)%, blue total is STILL 50%
>R1-7 = 1/(50/7)%, red total is STILL 50%
>>22537909
>thats not how it is done in the original problem
I know. I said that.
>remember I am not dealing with the Monty Hall problem at all. I am creating new scenarios to show the mechanics of determining the probability.
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>>22537919
ok sure, adding goat doors doesn't change the probability between the group s. what do you want to show?
>>
Let's put it different and say you and the game master are both playing the game but the game master just a has an unfair advantage. While you get to pick only 1 door from the 3 he gets to pick 2. So he has twice as much probability to get the right door.

He opens one of his doors and reveal there's a goat. His probability of winning the car remains the same 2/3.

Thus his remaining door has a 2/3 chance of having the car while your door still has the 1/3 chance. Picking the game master's door is twice as likely to win you the car.
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Sorry for double posting, don't worry I saged.

Say if there were 100 doors, you get to pick 1 door while the game master chooses 99.

He opens 98 of his door and they all reveal goats.

Do you seriously think you picked the one door out of a hundred that had the car?
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>>22537919
NOW I will relate all this to this Monty Hall problem:

We have one group of three doors. Each door has a 1/3 chance. We make a choice, CREATING TWO GROUPS WITH SET ODDS.
One group (blue) is the single door we picked - odds are 1/3
One group (red) is the two doors we did not pick - odds are 2/3.

Now let's go back to my scenarios, except instead of 50%, we have new odds.
>Blue = 1/3
>Red = 2/3
>B1 = 1/3
>R1 = 1/3, R2 = 1/3, R1+R2 = 2/3
And we can arbitrarily change the number of doors in the GROUPS, without changing the odds of each group.
>B1-4 = 1/(3/4)%, blue total is still 1/3
>R1-100 = 2/(3/100)%, red total is still 2/3
or, going back to Monty Hall's doors:
>B1 = 1/3
>R1+R2 = 2/3
remove one red door
>B1 = 1/3
>R1 = 2/(3/1) = 2/3
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>>22537941
yeah, so if I switch to red I have a higher probability of winning? I guess thats right
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>>22537951
>so if I switch to red I have a higher probability of winning?
As long as you know the host cannot remove the winning door, which is axiomatic to the scenario, yes.
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>>22537961
ok I think I understood it now :^)
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>>22537967
Great! It's not paranormal, but probabilities can get so unintuitive they almost might as well be, and they're really interesting in either case.
>>
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The host knows what door the car is behind, and opens a door with a goat 100% of the time. He eliminates one of the wrong choices after you chose one of the three doors at random. There may as well be no 2nd goat, and no 3rd door at all. The only reason the 2nd goat and 3rd door are there is because the host ALWAYS NEEDS TO open a "wrong" door, 100% OF THE TIME, and will NEVER open the door containing the car. Your chances of winning are 50/50 no matter what you do. Stop overthinking this. It doesn't really matter. There may as well be only two doors from the beginning, one with the car and one with the goat, and no need for the host to fuck with your lizard brain. Bullshit like this >>22537938 does not apply
>>
So let's have some fun with my red/blue groups and look at weird door combos.
>There are 100 ungrouped doors, you get to choose 15 doors to put into your blue group.
>After you choose, the doors in blue are reduced to 5, and the doors in red are reduced to 20 - ONLY removing guaranteed losing doors.
What are the odds of being the winning door for EACH INDIVIDUAL door in blue? In red?

>100 doors
>choose 15
>15 blue, 85 red
>reduced blue to 5, reduce red to 20
>odds of B3 winning = ?
>odds of R7 winning = ?
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>>22538040
Advanced question:
If you had to choose ONLY ONE door from either blue or red - would you choose from blue, or would you choose from red?
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>>22538030
brainlet
>>
>>22538040
>>22538056
Since no one else finds this fun, I'll answer my own questions. Let's do blue first.
>15 doors chosen out of 100, each with 1% chance = 15% total chance for blue
>blue reduced to 5 doors, still 15% chance
>each blue door = 15%/5 = 3% chance to win for B3
And now red
>85 doors left out of 100, each with 1% chance to win = 85% chance for red group
>reduce to 20 doors, still 85% chance
>each red door = 85%/20 = 4.25% for R7 to win

So there would be definite advantage to choose the red GROUP over the blue GROUP. But if you are forced to choose only one door within a group, there is only a 1.25% better chance to win if you choose from red than if you choose from blue.

Follow-up: Can you reduce the 15 blue group and the 85 red group such that the chance of EACH INDIVIDUAL DOOR is the same no matter which group you choose from?
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>>22538310
>Follow-up: Can you reduce the 15 blue group and the 85 red group such that the chance of EACH INDIVIDUAL DOOR is the same no matter which group you choose from?
Why yes you can.
>blue group, 15% chance
>reduce to three doors
>15%/3 = 5% chance for each blue door

>red group, 85% chance
>reduce to 17 doors
>85%/17 = 5% chance for each red door.

And hey, look at that. Blue group has 3 doors, red group has 17 doors. That's 20 doors, with each door having a 5% chance to win. What is 5x20? 100.
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>>22534976
Goat and car are not randomly change places before second choice. They stay in same place when they were before one goat was removed.
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>>22538030
Post like these can be most annoying. Start like you get problem and what is going on but in end you just dumbass dont get it at all no matter what explanation



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