/sci/ - Science & Math

>monty hall doesn't make intuitive sense

I'm sick of this shit. Just do it with 100 doors.
Then it'll make perfect sense intuitively.

>>14956391
a goat is much more useful than a car, so the problem's solution is clearly wrong

>>14956391
Its not the same fucking problem at all at that point lmao. How the fuck can you be so disingenuous?

>>14956426

>>14956535
You're right. I'm retarded.

>>14956361

the faggot show host only reveals the goat never the car so switching gives more expected value

>>14956588
yes, fuck you

Do you know how to fucking count?

>>14956361
>people actually think their odds of flipping tails twice in a row is 50%

>>14957013
The doors are blind except the goat door which you can safely exclude, so out of the 2 doors each one has a 50/50 chance of being a car. Switching doesn't make one more or less likely, because you can't tell which is which.

>>14956361
/sci/ you've been training for this

>>14957019
>you can't tell which is which
But the show host can. Your original odds are 1/3, but if you change you're upgrading them to 1/2.

>>14957019
You take one 33/66, and then can choose to stay or take another guess for 50/50. Switching logically always has better odds.

>>14957019
It's more like every door has a 1/3 chance. If you set a door aside, the door you pick, the other doors have a 2/3 chance as a group. Eliminating one door in the group doesn't affect the group's probability. So if there's only one door left in the group it retains the full 2/3.

>>14957034
>>14957036
The goat door was never in play because you didn't and can't pick it. The nature of the problem forbids you from ever picking the goat door.

>>14956775
uhhhh wat tha fuk

>>14957032
>walks directly over to the switch and ignores the bullshit

>>14957032
This is the sort of problem that would have an asterisks near it with

>*This problem is actually easy if you think about it.

>>14956775
What about if where you're from doors were never invented? As in prior to colonialism your (people?) just had like.. archways maybe. Some type of raised mud ditch?

So doors are actually like a kind of futuristic technology and when you *BASH* them that is religiously significant or some shit?

>>14956361
>1/3rd chance that your door has the car
>2/3rds chance that the other two doors has the car
>goat door opened, removing that one
>your door still has the same chance of having the car
>remaining other door is now 2/3rds chance of having the car

>>14957221
>you can never pick the goat door
>50/50 chance of picking the car

>>14957221
He removed the third option. there is only 2 left. He selected a door without confirmation so he basicly didnt open any door and the presenter removes a choice. 2 options availlable, 50/50. the previous statement of 3 doors is now obsolete and doesnt count anymore because it was for a previous situation that existed but not anymore.

> " Do I still have a chance to speak to my dead grandma that died several years ago?"
does oblivious person thinks to himself.

no, chances dissapear, you cant reselect a thing that is already gone.

perhaps if he was superstitious, he would had have a chance within his mind.

>>14957321
Do you think the odds are the same for this question?

100,000,000,000 doors
You pick door 1
Host opens 99,999,999,998 other doors, leaving two unopened (your choice and one other)

Would you switch?

>pick a door
>4chan told me to switch
>i switch
>lose because it wasn't guaranteed I would win just by switching
>don't get a fancy new luxury car
>don't have a farm, dunno what to do with the goat, live in an apartment
>don't get to play the game ever again
>decide to keep goat
>best bud, total bro
>funny guy blaaaaah lmao
>get a girlfriend
>girlfriend thinks goatbro is cute
>years go by
>goatbro getting old
>haha. But remember the good times. Goatbro still a bro of all time.
>goatbro dies
>depression
>girlfriend becomes depressed too
>alcohol, drugs, anything to fill the gap
>girlfriend breaks up with me cause she wants to f niggers and do heroine
>i just want to do heroine
>keep goatbros ashes and urn next to my at all times
>haha remember the good times
>stare blankly at the tv turned off for hours every day
>haha
>happy i switched
>happy
>haha

>>14957338
2 choises yeah really. its not a question for the host its a question for you. The host had many options, but not you, he left you just 2 choises.

>>14956391
The 100 doors shit doesn't make sense intuitively. What does make sense intuitively is realizing the host's actions don't impact your choice at all as switching will always switch between two options (you will never switch between a got and a goat)

>>14956361
I have 88 buckets in my basement

69 have become cumbuckets.

I call my girlfriend, she comes down and I explain her the situation. I tell her 69 of the 88 are cumbuckets, and then tell her I am about to remove 10 buckets full of cum with 100% certainty in front of her. She cant loot into the buckets to know which buckets are full of cum or which not. I then proceed to ask her:

> "how much of a chance do you have now in >selecting a cumbucket out of all the buckets?"

(I dont have a gf)

Ah, monty hall thread on /sci/. Who would have guessed

>>14957416
Monty hall threads don't have the staying power anymore. You gotta go two coins and dress it up with a disguise. Make it boxes instead of coins. 300 replies every time

>>14957372
>The host had many options
Except for the door with the car. He eliminated every single door containing a goat except yours and one other. Here's how it works out:

Your odds of picking car behind 1st door: 1 / 100,000,000,000
Host odds of leaving car behind 2nd door: 99,999,999,998 / 100,000,000,000

Odds of car if stay: 1 / 100,000,000,000
Odds of car if switch: 99,999,999,998 / 100,000,000,000

>>14957377
Try doing pic related with 100 doors

Instead of having a 1/3 and 2/3 chances.
You have a 1/100 and a 99/100 chance.

>>14957435
wrong, my odds of picking car behind 1st door was never 1/100,000,000,000. You are selecting a scenario that doesnt exist anymore. Then the question would more be like if it was at the beginning or the end scenario. However the question layed in the last 2 doors, not previous stage.

>>14957447
it was only 1/100,000,000,000 if the host was shot dead making him unable to open any other doors leaving the 100,000,000,000 choises unaltered. the host changed the rules, very simple.

>>14957377
pick car, stay, win
pick car, switch, lose
pick goatA, stay, lose
pick goatA, switch, win
pick goatB, stay, lose
pick goatB, switch, win

pick door, host reveals goatA
>switch: win, you had goatB
>switch: lose, you had car
>stay: win, you had car
>stay: lose, you had goatB
pick door, host reveals goatB
>switch: win, you had goatA
>switch: lose, you had car
>stay: win, you had car
>stay: lose, you had goatA

what is the probability you picked goatA?
>33%
>if picked, switching wins
>if picked, staying loses
what is the probability you picked goatB?
>33%
>if picked, switching wins
>if picked, staying loses
what is the probability you picked car?
>33%
>if picked, staying wins
>if picked, switching loses

Can you pick both goatA and goatB simultaneously?
No.
You have a 66% chance of not picking goatA.
>pick car/pick goatB = goatA is revealed
You have a 66% chance of not picking goatB.
>pick car/pick goatA = goatB is revealed
You have a 66% chance of not picking the car
>pick goatA = goatB is revealed
>pick goatB = goatA is revealed.
Possibilities:
Pick 1 door. GoatA is revealed
>you either picked goatB or car
>50% goatB; 50% car
>you absolutely did not pick goatA
>goatA cannot be acquired
>only goatB or car can be acquired
>you either (do) or (do not) have goatB
>you either (do not) or (do) have car

Pick 1 door. GoatB is revealed
>you either picked goatA or car
>50% goatA; 50% car
>you absolutely did not pick goatB
>goatB cannot be acquired
>only goatA or car can be acquired
>you either (do) or (do not) have goatA
>you either (do not) or (do) have car

50/50
choice doesn't matter. just makes you feel undeservedly bad if you chose wrong and lost, or undeservedly good if you chose right and won. If you did not already know where the car was because of insider information or even fucking psychic dousing, you are a retard.

>>14956396
based Uncle Ted

>>14956647
holy shit
is that real?
I've never seen a cat do that

>>14957447
>wrong, my odds of picking car behind 1st door was never 1/100,000,000,000. You are selecting a scenario that doesnt exist anymore.
The host opening doors does not change your odds with the original door. You made your choice with 100,000,000,000 doors to choose from. Only if you switch will your odds change.

>>14957495
it does? I shoot my dog and not my cat. do I still have to feed my dog and cat or just the cat? the first choise didnt mattered, he stopped you before making a definite call and removed all the other options and then reasked it again.

>>14957502
>it does?
Yes.

>the first choise didnt mattered
It matters in that you were choosing from 100,000,000,000 doors. If you refuse to switch, your odds remain the same, whereas the host knows where all the goats are, and where the car is, and opened every door without a car behind it. I really can't believe you don't see how switching is the better option. By staying you're essentially taking one door, whereas planning to switch (even before hand) means you get every other door. Who has better odds, the person who picks 1 door, or the person who picks 99,999,999,999 doors?

>>14957495
>You made your choice with 100,000,000,000 doors to choose from
where did that happened? it started with 100,000,000,000 doors, he removed all 99,999,999,998 doors and left just 2. then asked you which of the 2 doors he had a thing. There *was* a choise of 100,000,000,000 however not given to you.

>>14957517
>then asked you which of the 2 doors he had a thing.
But the doors are not weighted equally.

>There *was* a choise of 100,000,000,000 however not given to you.
That's still the choice if you refuse to switch.

Let's word it differently:
The host asks you to pick one door. He then says that instead of keeping that door, you can instead choose to have ALL of the other doors? Do you switch?

That is the exact same question, only with different wording.

>>14957510
>If you refuse to switch, your odds remain the same*
in the odds where he just left one other door? he didnt left the 99,999,999,998 alone now did he? or did you forget he just got rid of them

>>14957528
>in the odds where he just left one other door?
But that one other door has a near 100% chance of having the car. Your door has almost a 0% chance. It's not a coin flip.

>>14957524
weighted equally to a previous stage that doesnt exist anymore. yes. Like I had 2 milkbottles yesterday to choose from but now are gone due roomates, to then think you have still the choise of picking one of the 2 bottles which are clearly consumed already.

>thats still the choise if you refuse the switch

so basicly you keep referring to a older question dillema to a new one, although is has no significance anymore. yeah he "had" more choises back then. but "now" he doesnt, he switches or he keeps his choise. basicly 2 choises, theres not a third or fourth single or 0 choises, just 2 options with either win or no win.

>>14957546
>just 2 options with either win or no win.
But you know one door is a near 100% win, so you're a fucking moron if you stay. If a person has two cups, puts $100 in one cup (with you watching), and tells you that you can keep the $100 if you pick the cup with the bill in it, would you say your odds are 50/50 because there's two cups, or are you going to use your brain and choose the cup you watched him put the bill in?

>>14957533
fine, that one made sense.

>>14957533
yeah my loss. thanks fren for pointing that out clearly. selective picking is what I forgot

Which alternate univeree are you from /sci/?
A)
>you have a 66% chance of picking a goat
>you have a 33% chance of picking a car
>you're more likely to pick a goat. switching generally wins.

B)
>you have a 100% chance of picking a goat or a car if you pick a door
>you have a 0% chance of picking the specific goat the host reveals
>you're equally likely to have picked the other goat or the car. choice to switch or stay doesn't matter.

C)
>there are 2 game possibiities
>game1: you have a 50% chance of picking the goat1/car setup where the host reveals goat2
>game2: you have a 50% chance of picking the goat2/car setup where the host reveals goat1

game1:
>goat2 is inaccessible
>picked car, switch loses by switching to goat1
>picked goat1, switch wins by switching to car

game2:
>goat1 is inaccessible
>picked car, switch loses by switching to goat2
>picked goat2, switch wins by switching to car
game1+game2:
>picked car, switch loses by switching to goat1 from car, goat2 inaccessible
>picked car, switch loses by switching to goat2 from car, goat1 inaccessible
>picked goat1, switch wins by switching from goat1 to car, goat2 inaccessible
>picked goat2, switch wins by switching from goat2 to car, goat1 inaccessible
>2 cases switch wins
>2 cases switch loses
>4 cases total
>2/4 switching wins
>1/2
>50%

D)
>goats are more valuable than cars

E)
>win by default of playing. goats and cars are equally valuable prizes, doesn't really matter which prize is received.

>>14957579
Kudos, it's rare to see someone change their mind on here.

Where is Paul Erdos when we need him? Fuck all of you

>>14957559
Not the scope of the question.

>>14957811
The scope of reality > the scope of the question. This is about a practical solution.

>>14956391
>there a 100 doors, 99 doors with a goat and 1 door with a car
>you select some door, initially your chance of winning is 1/100
>Monty opens 98 doors to reveal a goat behind each one.
>only 2 doors remain, the one you initially selected and some other door
Would you switch?

>>14957013
>he thinks there are such things as odds and it's not entirely dependent on random luck

>>14957584
The conclusion of B doesn't follow from the premises.

C is using backwards logic. Just because there's a 50% chance of Monty revealing ghost 1 or 2 doesn't mean either is "inaccessible" when you make your choice.

>>14956361
You can't lose, to be honest.
I wouldn't mind a free goat.

>>14956396
I would rather have a goat friend than a car but that doesn't make the solution wrong, because the solution is based on the premise that the intention is to choose the car door. While not everyone would desire that, it doesn't make the premise wrong.
>>14956361
If the person who opens the door opens an unchosen door without knowing who or what is behind that door, and as a matter of chance, a goat is behind the door, then switching door choice does not affect probability of choosing goat versus car.
If the person opening the door is an omniscient observer who intentionally opens an unchosen door behind which is a goat, then switching door choice doubles the remaining likelihood of car door while halving the remaining likelihood of goat door.

>>14956647
what the fuck is that real

>>14957479
>>14959091

>>14958344
it is random to an extent, but we can know those extents and make deductions from there

If the first door you picked is a goat (2/3 outcomes) then the host has to reveal the other goat. This means that there is a 2/3 chance that the remaining door is the car.

>>14958691
any door has a 33% chance of being the car door.
you can only pick 1 door which you will have the possibility of winning with, either the initial door, or the swap door.
here are the games
let game1a= [GoatA, HostGoatB, Car];
let game1b= [GoatA, Car, HostGoatB];
let game1c= [Car, HostGoatB, GoatA];
let game1d= [Car, GoatA, HostGoatB];
let game1e= [HostGoatB, GoatA, Car];
let game1f= [HostGoatB, Car, GoatA];

let game2a = [HostGoatA, GoatB, Car];
let game2b = [HostGoatA, Car, GoatB];
let game2c = [Car, GoatB, HostGoatA];
let game2d = [Car, HostGoatA, GoatB];
let game2e = [GoatB, HostGoatA, Car];
let game2f = [GoatB, Car, HostGoatA];

if for example, you pick door 1, then the amount of playable games reduces to only the games in which option 1 does not include a HostGoat choice, because the host cannot choose to reveal the door you picked and must choose door 2 or 3

>pick 1
>possible games:
>game1a= [GoatA, HostGoatB, Car];
>game1b= [GoatA, Car, HostGoatB];
>game1c= [Car, HostGoatB, GoatA];
>game1d= [Car, GoatA, HostGoatB];
>game2c = [Car, GoatB, HostGoatA];
>game2d = [Car, HostGoatA, GoatB];
>game2e = [GoatB, HostGoatA, Car];
>game2f = [GoatB, Car, HostGoatA];
there are 8 possible games for any door pick.

in this example of having picked door 1, staying with option 1 shows that there are 4 of the 8 games in which staying with door 1 will win, and 4 of the 8 games in which staying with door 1 will lose. switch or stay has no consequence, so it's 50/50 whether staying or switching matters, and ultimately only a 33% chance of winning outright regardless if switching or staying.

There's a really intuitive explanation.

If you picked a goat (odds: 2/3), you will switch to the car. If you picked the car (odds: 1/3), you will switch to a goat.

>>14956396
You don't get to keep the goat

>>14956361
Massive time wasting problem.
Here is the solution:
Yes, first we must address the fact that if you have two doors, and one has a goat and the other a car, then there is a 50% chance of either, you do or you don't...

BUT, you need to realize that's not all to the equation, because BEFORE you reached this situation is when you made your choice, you are NOT picking between two doors, you already picked your door BEFORE reaching the decision whether to switch. And when YOU picked your door, there were THREE options. Now let that sink in, you picked from three doors, that's a 1/3 chance. The reason you are left with two in the end is because the host removed one of the wrong options, BUT there was a 2/3 chance he removed one of the goats, because there were two goats you could have picked and two chances for you to fuck it up.

So when you get to the last two doors, you must not forget what happened prior to this situation, and the best option is to switch, because in two out of three timelines you picked one of the two goats, and the host revealed the other. He can't reveal the car because then the game would be over, that's not part of the rules, so there is always a 2/3 chance your original guess was wrong, because you just need to remember you started with three options to pick from, not two. That's not 50/50, that's 33/33/33.

The only use of the Monty Hall problem was to prove that some people default to invalid reasoning, like assuming that two doors means 50%. Because they can't process more information than that. And they don't realize in this case the decision was made between 3 doors, not 2.

It's really that simple. They aren't capable of understanding the consequences of the original guess being made between 3 doors, they completely ignore the conditions of the experiment and only acknowledge the final dilemma of two doors.

>>14959886
values : car, goata, goatb
leading letter : y = your pick, h = host's pick

let game1 = [ycar, hgoata, goatb] //stay win
let game2 = [ycar, goata, hgoatb] //stay win
let game3 = [ycar, hgoatb, goata] //stay win
let game4 = [ycar, goatb, hgoata] //stay win
let game5 = [car, ygoata, hgoatb] //lose stay
let game6 = [car, hgoata, ygoatb] //lose stay
let game7 = [car, ygoatb, hgoata] //lose stay
let game8 = [car, hgoatb, ygoata] //lose stay

let game9 = [ygoata, car, hgoatb] //lose stay
let game10= [ygoata, hgoatb, car] //lose stay
let game11= [hgoata, ycar, goatb] //stay win
let game12= [hgoata, car, ygoatb] //lose stay
let game13= [hgoata, ygoatb, car] //lose stay
let game14= [hgoata, goatb, ycar] //stay win
let game15= [goata, ycar, hgoatb] //stay win
let game16= [goata, hgoatb, ycar] //stay win

let game17= [ygoatb, car, hgoata] //lose stay
let game18= [ygoatb, hgoata, car] //lose stay
let game19= [hgoatb, ycar, goata] //stay win
let game20= [hgoatb, goata, ycar] //stay win
let game21= [hgoatb, car, ygoata] //lose stay
let game22= [hgoatb, ygoata, car] //lose stay
let game23= [goatb, ycar, hgoata] //stay win
let game24= [goatb, hgoata, ycar] //stay win

there are 24 possible game sets based on staying as a strategy.
the various permutations of which goat or car is behind which door and which door you picked plus which door the host picked. Of the 24 possible games, 12 win by staying and 12 lose by staying (AKA 12 win by switching), so 12/24 win by staying.

Are you saying it is not equally likely that any possible game is played? Don't you have a 1/24 chance of playing any of the game sets?

please remember that you can pick the car but the host never can, while both you or the host could potentially pick either goat.

the real answer is to pay attention to which direction the goat is facing after the goat is revealed, cause it likely probably wants to be with the other goat and can smell the other goat, so you should be able to determine which door has the car because the goat wont be facing that direction (unless the car smells like goats)

>>14959991
TL;DR.
Once the host has revealed a goat-door, switching doors is equivalent to changing the nature of your original pick. You had 2/3 chances of choosing the goat originaly, so you have 2/3 chances of switching to the car once the host reveals a goat-door. It is really that simple.

>>14959996
you had a 33% chance of choosing a goat originally. you had a 33% chance of choosing the car originally. you had a 33% chance of choosing the other goat originally, too. you have a seemingly 66% chance of choosing a door which contains either of the goats, but you also seemingly have a 66% chance of choosing a door which contains either a car or one of the goats.

The goats are not a single entity.

>>14960004
(You) must be trolling.

>>14960004
rather than goats, lets say the prizes is money.

prize 1: $200
prize 2: $50
prize 3: $40

you pick a door
the host reveals a different door.
the host reveals $50
you either have the $200 or the $40 door

which one were you more likely to pick?
did you have a 66% chance of picking the $40 door?
nah, you had a 33% chance of picking the $40 door. and you had a 33% chance of picking the $200 door. so given there are only two doors left and they both had an equal percentage chance of being picked... see?

>>14960011
the goats are not a single entity, you mongoloid

>>14957429
With these probabilities ones I am just convinced that our understanding of probability as a math is wrong.

>>14956361
So has anyone done a real world actual study of this?
Because with these probability pranks, this one and the one with two coin flips, while sure if you break it down like a probability equation you get what people say is the correct answer.

But what about real life?
Are people who stay with the door they chose actually less likely to win than the switchers..

>>14960014
I don't get it.
Why does the probability carry over to the other door?

>>14960018
They correspond to the same outcome. You should spend your energy doing other things than math, like herding goats. I'm sure you would be great at it. You would recognize they are not a single entity, and that would make them really happy. :^)

>>14960030
This guy is legitimately retarded. Don't listen to him.

>>14960025
You can run a simulation...

https://www.mathwarehouse.com/monty-hall-simulation-online/

>>14960030
because it is in the same group as the opened door

>>14960032
>>14960014
>>14960035

here's the problem retardo
there are 3 doors
there are 3 prizes
prize1: $100,000
prize2: $100
prize3: $1

you probably want $100,000
you are told to pick a door, and because you're a big bitch who does what they're told to do, you in fact pick a door. behind each door is one of the individual prizes.
I reveal one of the prize doors. Let's say I reveal the $1 prize door.

There are now two doors, and you are given the understanding that these two doors contain the prizes of $100, and of $100,000. You are given the understanding that you are allowed to stay with your initial door pick, or swap to the other unopened door. You are also given the understanding that you are not allowed to swap to the opened door.

Your initial picked door could either have $100,000 or $100 behind it, right? It can't have $1. surely we agree on the definitions so far.

so is it 66% likely that you picked the $100 door?
why does the $100 door specifically somehow attain a weighted likelihood of being picked?
Wouldn't it benefit your brain if you stopped lying to yourself and simply accepted the fact that you had a 33% chance of initially picking the $100 door and an equal 33% chance of having picked the $100,000 door?

See how this problem starts to make more sense when you don't disingenuously believe all goats are a single entity, but individual values, just like these money prizes are individual values?

all of these are rhetorical questions, do not bother answering them.

>>14960297
>>14959991

https://openprocessing.org/sketch/1724632

>>14960292
what number door is that with the animal? tell door 5

Is there a problem which superficially looks a lot like monty hall but the correct answer is to NOT switch? Would be funny to trip up people who have just rememberd "ah right you have to switch".

>>14959836
>switch or stay has no consequence, so it's 50/50 whether staying or switching matters
This doesn't follow. You assumed that just because you listed out some possible scenarios they are all equally likely. They are not, since that would mean your initial choice had a 50% chance of being a car, even though you said at the beginning it's 33%. This is the most common mistake made by novices in probability theory. Lists of possible outcomes are non-informative if you don't properly assign probabilities to those outcomes. Each of your possible games beginning with a car are half as likely as those beginning with a goat, because Monty having a choice between two goats to reveal does not increase the likelihood of that game.

>>14959991
>Are you saying it is not equally likely that any possible game is played?
Yes. The chance of you choosing a car is 1/3 and the chance of Monty then revealing a goat is 1, so the chance of being in a game with ycar in it is 1/3. The chance of choosing a goat is 2/3 and the chance of Monty then revealing a goat is 1. So the chance of being in a game with ygoat in it is 2/3. Same number of games, so each ycar game is half as likely as each ygoat game.

>>14960591
>They are not, since that would mean your initial choice had a 50% chance of being a car, even though you said at the beginning it's 33%. This is the most common mistake made by novices in probability theory.
This is a common mistake made by people who lack logical thinking. In this thought experiment there is never a scenario where the door the host picks will be chosen. There are only ever 2 doors you can choose from, one door with a bunk prize, and one door with a car.

>>14960626
>In this thought experiment there is never a scenario where the door the host picks will be chosen.
Non sequitur, I said nothing to the contrary.

>There are only ever 2 doors you can choose from, one door with a bunk prize, and one door with a car.
Yes, and is twice as likely you chose the bunk prize at the beginning, so switching is twice as likely to get you the car.

It would be nice if you could respond to anything I said. Monty revealing a goat does not affect the chance that you chose the car, because he would reveal a goat no matter what. It does however pinpoint where the car is if you didn't choose it initially, which again is twice as likely as choosing it. Thanks for admitting I'm right.

>>14956361
(even before the game starts) You know that there are 2 goats and 1 car, and you also know that whichever door that you choose, there will be at least 1 door that has a goat behind it:
1) if the door that you choose has a car behind it, the other 2 doors have goats
2) if the door that you choose has a goat behind it, there is still one other door with a goat.
So you always know that the host will open a door with a goat, no matter what, but also you know (even before the game starts) that there are 2 goats and 1 car, so the chance that in your first choice there is a car behind the door is 1/3, and 2/3 for goat.
Since you know that your first choice has higher chance of being a goat than a car, and since you know the host will always opens a goat, and since you know all of these even before the game starts, you have to change.

>>14958330
This is how I came to understand it too. Pretty straight forward once you realize swap is correct when because your first choice had bad odds, whether we are exaggerating to 1/100 or if 1/3 as it's written

>>14960600
but it's not just ygoat, it's ygoata and ygoatb. two goats.
they're individual prizes, just like the car is an individual prize. just because the car has a presumed individual value seemingly greater than either goat, does not collapse the goats into a single net outcome of "undesirable".
33% desirable prize (dp) [a car]
33% undesirable prize (udp) [a goat]
33% unwanted prize (uwp) [another goat]

you believe that the goats combine into a single generalized outcome of probability
>33% dp
>66% udp+uwp
and so you wager you're more likely to have picked udp or uwp compared to dp's 33%
>33% dp
>33% udp (probably picked this)
>33% uwp (or probably picked this)
So you've seemingly arbitrarily grouped two different outcomes into a single unlikable outcome, and so assume to have picked two door values for having picked a single door value

What if it were like this?
>33% dp (probably picked this)
>33% udp (or probably picked this)
>33% uwp
or
>33% dp (probably picked this)
>33% udp
>33% uwp (or probably picked this)

so along with the original group combo, you have a 33% chance of having picked the door combos which will win 0% by staying, and a 66% chance of having picked the door combos which have a 50% chance of winning by staying.
Now the percentages of what you picked have changed.
You're more likely to have picked an outcome where the choice doesn't matter, than having picked an outcome where the choice to switch does matter.
But this is entirely disingenuous. The choice always matter because it is presented, and it is chosen to STAY or chosen to SWITCH.

game1
>dp (probably picked) [definitely picked]
>udp (probably picked) [definitely didn't pick]
>uwp
game2
>dp (probably picked) [definitely didn't pick]
>udp (probably picked) [definitely pick]
>uwp
game3
>dp (probably picked) [definitely picked]
>udp
>uwp (probably picked) [definitely didn't pick]
...
which leads to the 24 game payout table of >>14959991
and each game is just as likely.

For anyone who feels dumb for not getting why it's a 66% chance of success if you switch, Paul Erdős refused to accept the answer until he was shown a computer simulation.


Probability and the human brain do not mix

>>14956361
Just do the same with 10, 12 doors and you get the logic

Many-doorfags, answer this:
There are 100 doors, 99 with goats and 1 with a car. You pick the door which you guess conceals the car. Monty then tells you that, without changing your pick, you can choose any number of other doors and he'll reveal their contents. You choose 98 other doors and find goats behind all of them, leaving only your original pick and one other door. Monty tells you that you can switch your pick to the other door if you wish. If you do switch, what's the probability that your new door has the car?

>>14961656
50/50 at that point since you were randomly guessing and ended up at two doors. It's different with Monty since he knows which door hides the car. Also, the odds that you'll manage to pick 48 doors in a row with a goat are slim.

>>14961559
dp = desired prize
udp = undesired prize
uwp = unwanted prize
(you probably picked) = ypp
[you definitely picked] = ydp
{host probably picked] = hpp
{host definitely picked] = hdp
>ydp + dp = win
>ydp =/= hdp
>hdp =/= dp

g1 win
>dp | ypp | ydp
>udp | ypp | hpp
>uwp | ypp | hpp | hdp
g2 win
>dp | ypp | ydp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp
g3
>dp | ypp
>udp | ypp | hpp | ydp
>uwp | ypp | hpp | hdp
g4
>dp | ypp
>udp | ypp | hpp | ydp
>uwp | ypp | hpp | hdp
g5
>dp | ypp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp | ydp
g6 win
>dp | ypp | ydp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp
g7 win
>dp | ypp | ydp
>udp | ypp | hpp
>uwp | ypp | hpp | hdp
g8
>dp | ypp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp | ydp

8 games, 4 win by staying

dp = desired prize
udp = undesired prize
uwp = unwanted prize
(you probably picked) = ypp
[you definitely picked] = ydp
{host probably picked] = hpp
{host definitely picked] = hdp
>ydp + dp = win
>ydp =/= hdp
>hdp =/= dp

g1 win
>dp | ypp | ydp
>udp | ypp | hpp
>uwp | ypp | hpp | hdp
g2 win
>dp | ypp | ydp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp
g3
>dp | ypp
>udp | ypp | hpp | ydp
>uwp | ypp | hpp | hdp
g4
>dp | ypp
>udp | ypp | hpp | hdp
>uwp | ypp | hpp | ydp

4 games, 2 win by staying

>>14961676
(accidentally had doubles)

>>14960590
If the goal is you want a new friend instead of a piece of consumerist garbage, then the correct answer is to not switch

I figured it out

>>14956361
mythbusters explained this in the most retard-friendly way possible
i'm sorry if you just too stupid to understand it

>>14957429
¼?

>>14957429
It's 50%. If at least one of them is heads, and there are two coins, one of them is definitely heads, the other could be heads it tails.

>>14959886
this

>>14956361
---|--------|---
| | <<<------ if jesus returns
| | kill him again.jp

>>14957546
let's say your retarded nigger ass has three milk bottles in your kitchen and you need to choose one of them to drink tomorrow. you make a choice and then cover them with a blanket. while you were asleep, one of your roommates drank two milk bottles and then covered them back up.

when you wake up, you go to your milk bottles and your roommate reveals that one of the bottles you didn't pick is now empty. do you think you have a 50/50 chance of your original bottle being empty or full?

>>14960297
congrats nigger you just lost 100k

>>14961666
>It's different with Monty
nah

>>14960433
Aww what's the matter stupid? Can't keep up?

>>14962705
You can die in your dreams for the next week and wonder why someone on 4chan can dictate your life.

>>14957429
This is the best shit, i used to troll american manchildren with this in gay discord servers, once I told a mod "who was going to uni studying maths" that he's gonna be a forklift driver if he keeps this up and he sent me a formal DM complaint warning me that if I keep being antagonistic there will be consequences. Non americans usually admit they dont know how to calculate the probability but something about american education makes mutts seethe when you question their laughable competence.

>>14962738
(your pick)
[host pick]
>1: (100K), [100], 1 win stay
>2: (100K), 100, [1] win stay
>3: (100K), [1], 100 win stay
>4: (100K), 1, [100] win stay
>5: [1], (100K), 100 win stay
>6: 1, (100K), [100] win stay
>7: [100], (100K), 1 win stay
>8: 100, (100K), [1] win stay
>9: [1], 100, (100K) win stay
>10: 1, [100], (100K) win stay
>11: [1], 100, (100K) win stay
>12: 1, [100], (100K) win stay

>13: 100K, (100), [1] win switch
>14: 100K, [1], (100) win switch
>15: 100K, [100], (1) win switch
>16: 100K, (1), [100] win switch
>17: (100), 100K, [1] win switch
>18: [100], 100K, (1) win switch
>19: (1), 100K, [100] win switch
>20: [1], 100K, (100) win switch
>21: (1), [100], 100K win switch
>22: [1], (100), 100K win switch
>23: (100), [1], 100K win switch
>24: [100], (1), 100K win switch

24 games, 12 win by staying, 12 win by switching
it is not possible to have a different game setup and outcome than these 24. all are equally likely to occur. Roll 4 standard dice to get which game you could play.
you do not understand probability.
you are a filthy plebian brainlet.

>>14962738
possible door arrangements
>1: goat1, goat2, car
>2: goat2, goat1, car
>3: goat1, car, goat2
>4: goat2, car, goat1
>5: car, goat1, goat2
>6: car, goat2, goat1

>1a: (goat1), [goat2], car win switch
>1b: [goat1], (goat2), car win switch
>1c: goat1, [goat2], (car) win stay
>1d: [goat1], goat2, (car) win stay

>2a: (goat2), [goat1], car win switch
>2b: [goat2], (goat1), car win switch
>2c: goat2, [goat1], (car) win stay
>2d: [goat2], goat1, (car) win stay

>3a: (goat1), car, [goat2] win switch
>3b: [goat1], car, (goat2) win switch
>3c: [goat1], (car), goat2 win stay
>3d: goat1, (car), [goat2] win stay

>4a: (goat2), car, [goat1] win switch
>4b: [goat2], car, (goat1) win switch
>4c: [goat2], (car), goat1 win stay
>4d: goat2, (car), [goat1] win stay

>5a: car, (goat1), [goat2] win switch
>5b: car, [goat1], (goat2) win switch
>5c: (car), [goat1], goat2 win stay
>5d: (car), goat1, [goat2] win stay

>6a: car, (goat2), [goat1] win switch
>6b: car, [goat2], (goat1) win switch
>6c: (car), [goat2], goat1 win stay
>6d: (car), goat2, [goat1] win stay

inb4 c&d are somehow the same game and should only be counted once
>a: car, (goat1), goat2
>b: car, goat1, (goat2)
>c: (car), goat1, goat2

>you have a 66% chance of picking 2/3 values durr

>ab: car, (goat1), (goat2)
>ac: (car), (goat1), goat2
>bc: (car), goat1, (goat2)
ab = 66% chance of happening!!!!! stay win 0%, switch win 100%
ac = 66% chance of happening!!!!! stay win 50%, switch win 50%
bc = 66% chance of happening!!!!! stay win 50%, switch win 50%

1: ab = 33% chance, stay win 0%, switch win 100%
2: ac = 33% chance, stay win 50%, switch win 50%
3: bc = 33% chance, stay win 50%, switch win 50%

inb4 2&3 are somehow the same game and should only be counted once

1: 33% chance, stay win 0%, switch win 100%
2: 66% chance, stay win 50%, switch win 50%
you are more likely to play #2 where you're (un)ironically equally likely to have picked the car as either goat, because each door is 1/3

>>14956391
it makes intuitive sense but doesn't make mathematical one

if instead of 3 doors, it was 9 doors, but you get to choose 3 doors, and there are 8 goats and 1 car, this is how it would look

>1 2 3 4 5 6 7 8 9
>pick 3
>[1] [2] 3 4 [5] 6 7 8 9
>host reveals 3 goats
>[1] [2] 3 g [5] g 7 8 g
>doors 4, 6, and 9 were goats
>[1] [2] 3 [5] 7 8
>host asks if you want to stay with [125] or switch to [378]
>possibilities:
>[c] [g] g [g] g g || win by staying
>[g] [c] g [g] g g || win by staying
>[g] [g] c [g] g g || win by switching
>[g] [g] g [c] g g || win by staying
>[g] [g] g [g] c g || win by switching
>[g] [g] g [g] g c || win by switching

you were (1/9) likely to have picked the car when making the first pick of door 1.
you were (2/9) likely to have picked the car when making the second pick of door 2.
you were (3/9) likely to have picked the car when making the third pick of door 5.

you were (3/8) likely to have picked the car when the host revealed door 4.
you were (3/7) likely to have picked the car when the host revealed door 6.
you were (3/6) likely to have picked the car when the host revealed door 9.

this is fundamentally the same problem as 3 doors + 1 pick, just multiplied by 3 evenly; to get 9 doors + 3 picks. Just as the host reveals 1 door which wasn't your pick and wasn't the car, now the host reveals 3 doors which weren't your picks and wasn't the car.

if you want to use goofy logic:
[1,2,5] = 33% likely to have the car
[3,7,8] = 66% likely to have the car
any door has an 11.111% chance of being the car door, or an 88.888% chance of being a goat door
any 3 doors have a 33.333% chance of having the car, or a 66.666% chance of being goat doors
( 1, 2, 3, 4, 5, 6, 7, 8, 9 )
( [11%], [11%], 11%, 11%, [11%], 11%, 11%, 11%, 11% )
( [11%], [11%], 11%, goat, [11%], goat, 11%, 11%, goat )
( [11%], [11%], 22%, [11%] 22%, 22% )
why does the value of all unpicked doors go up, but not the value of any picked doors.
Isn't that awfully arbitrary?

BTW, why is the 366th day of a leap year at the end of February?

>>14963022
because you were only 3/9ths as likely to have picked the car door, so switching would be 6/9ths as likely

>>14963031
Any set of 3 doors is 3/9ths as likely to have the car door. How does switching from one set of 3/9ths to another set of 3/9ths suddenly mean the other set is actually 6/9ths?

>>14961559
>but it's not just ygoat, it's ygoata and ygoatb. two goats.
That doesn't contradict anything I said. There being two goats is the reason why the chance of choosing a goat is 2/3.

>just because the car has a presumed individual value seemingly greater than either goat, does not collapse the goats into a single net outcome of "undesirable".
It doesn't matter how you group outcomes, if the math is correct then the conclusion will be correct regardless. Your math was incorrect because you made choosing a car twice as likely as choosing goata and twice as likely as choosing goatb. Get it?

>33% dp
>33% udp (probably picked this)
>33% uwp (or probably picked this)
No, those are equally likely.

It's fine to say it's twice as likely you chose the car or goata than goatb, but so what? That doesn't change the conclusion either.

>Now the percentages of what you picked have changed. You're more likely to have picked an outcome where the choice doesn't matter, than having picked an outcome where the choice to switch does matter.
No, they're the same. Switching wins when you have a goat. You have a goat 33%+(66%)(50%) = 66%. Correct math is consistent.

>>14961676
Again, you incorrectly assume all games you listed are equally likely. They aren't. If they were equally likely, only 1/3 of the games can begin with a car. The issue is that you treat Monty choosing randomly between two goats as separate games, which artificially inflates the chance of you choosing the car. Get it?

>>14962827
>all are equally likely to occur.
No, you have 12 games beginning with you choosing $100K. They are half as likely as the other games.

>>14959115
WITCHCRAFT

>>14956361
pick the goat

(Strategy A) Switching doors:
(1) if you picked the car you will land on a goat;
(2) if you picked a goat you will land on the car.
(Strategy B) Not switching doors:
(1) if you picked the car you will stay on the car;
(2) if you picked a goat you will stay on a goat.
Your odds of winning the car in Strategy A are 2/3. Your odds of winning the car in Strategy B are 1/3. Therefore the best strategy is switching doors.

>>14963079
>>14963081
>random
lel

anyway

doors are labeled with letters, L-, M-, and R- for left, middle, and right respectively.
games
>1. L-car, M-goat1, R-goat2
>2. L-car, M-goat2, R-goat1
>3. L-goat1, M-car, R-goat2
>4. L-goat2, M-car, R-goat1
>5. L-goat1, M-goat2, R-car
>6. L-goat2, M-goat1, R-car

choices are labeled with letters, -y and -h for your pick and host's pick respectively
> L-car-y, M-goat1-h, R-goat2
> L-car-y, M-goat1, R-goat2-h
>>you treat Monty choosing randomly between two goats as separate games

they are separate games.
in one reality, you picked the car and monty revealed goat1
in another reality, you picked the car and monty revealed goat2
just as well as in yet another reality, you picked goat1 and monty revealed goat2
or just as well in a further reality, you picked goat2 and monty revealed goat1.

you treat picking the car as two different realities collapsing into a single reality where, for example, goat1 was revealed, and there no longer exists any reality where goat2 would have been revealed instead.

alternatively, you treat picking the car and monty revealing goat1 to be subdivision of a joint quantum reality where you picked the car and monty revealed either goat, a seemingly inefficient extension of the logics of reality to merely accommodate two individual realities for lesser values.

>[16%] 1a) your car, host goat1, goat2 || win stay
>[16%] 1b) your car, goat1, host goat2 || win stay
>[33%] 2) car, your goat1, host goat2 || win switch
>[33%] 3) car, host goat2, your goat1 || win switch

do not collapse realities
do not divide lesser realities into alternative realities
humanity, singular or collective, are not an authority.

>2022
>people are still getting filtered by the Monty hall problem
The absolute state of nu-/sci/

>>14963181
>they are separate games.
When you choose a car, Monty has a half chance of revealing one goat and a half chance of revealing the other goat. In every other case, he is forced to reveal the only remaining goat. If they are separate games then the games you listed aren't equally likely. If you want to list games that are equally likely then they aren't separate games. Choose one.

>in one reality, you picked the car and monty revealed goat1
in another reality, you picked the car and monty revealed goat2
>just as well as in yet another reality, you picked goat1 and monty revealed goat2
As I've shown you several times, these scenarios aren't equally likely. The first two are half as likely as the third. The first two have probability (1/3)(1/2) while the third has probability 1/3.

Again, as long as your math is correct, you will get the same result regardless of how you describe our group outcomes. Your math is incorrect and you have no response. You just repeat the same mistake over and over.

>>14963185
I think it's mostly /v/, /pol/ and reddit invading. Fucking pea brains

>>14956647
wtf is that gif real?

The Monty Hall problem is a perfect dividing line to separate intelligent people from everyone else. It's pretty beautiful for that purpose alone.

>>14963294
do not collapse realities, you turbofucking retard
do not divide lesser realities into alternative realities
you are a goddamn human lmao

i bet you believe the speed of light is real and atomic clocks are real
i bet you're a fucking stupid motherfucker who believes anything so long as it's in book
i bet you believe books lmfao kys

I am infinitely likely to always pick the car by random chance and win the car through staying without even knowing ahead of time the prizes behind the doors. 100% win rate. Where does that add up into your sense of mathematics? You assume it can't happen because you're a fucking retard who commits the sin of bearing false witness by assuming your insignificant and worthless imagination is instead actually a real observable view of reality in totality.

Look in the goddamn fucking mirror. Look at you lmfao.

>>14964067
i bet you never take a shower

>>14956391
>there are 100 doors
>some of them have goats some have cars and some have rapists with knives
>20% of the doors are opened and 7 knifed rapists run into the audience and begin raping
>1 rapist begins killing and raping the goats
>do you switch doors?

>>14964067
when im farting and shitting on the toilet i like to masturbate to anal porn because the odor adds another layer of reality

>ctrl+f "bayes"
>0 results
lol

>>14964700
>>14956535

>>14956361
>>14956391

Initially you have a 2/3 chance of picking a goat.
One goat gets removed.
You were more likely to pick a goat at first which means switching would more likely give you the car.

>>14956535
>total number of doors: 3
>player selects 1 door (33%)
>doors remaining: 2 (66%)
>monty opens 1 door (*retarded noises*)
go on
>>B6: doors remaining: 1 (33%)
>>D6 = 0.333 / 1

>66% per unrevealed door
>2 unrevealed doors = 133%
math is more than excel and shitty calculators

>>14964456
God frowns upon your sorry excuse for an existence

>>14963294
QUESTION:
Is it equally likely that monty reveals goat1 compared to revealing goat2 when you pick the car door?

Is it equally likely that monty reveals goat1 when you pick the goat2 door, as it is when you monty reveals goat2 because you picked the goat1 door?

>pick car : 50/50 whether monty reveals goat1 or goat2
>pick goat2 or goat 1: 50/50 whether monty reveals goat1 or goat2

>pick any door: 50/50 whether monty reveals goat1 or goat2
>car door: 33% of the time. monty will reveal goat1 or goat 2
>goat doors: 66% of the time. monty will reveal the goat you didn't pick

>a: 33% x 1/2 = pick car, monty reveals goat1
>b: 33% x 1/2 = pick car, monty reveals goat2
>c: 33% = pick goat2, monty reveals goat1
>d: 33% = pick goat1, monty reveals goat2

it's a 33% chance you picked goat2, specifically goat2. not double goats.
you know of one other situation where monty reveals goat1, besides picking goat2. and that's if you picked the car.

Do you know, with certainty, whether you picked goat2 or the car?
it could be 50/50 whether you have one or the other.

is it 16.66% likely you picked the car? or is it 33% likely you picked the car?
if it were 16.66% likely, that would mean there were 6 doors and only 1 door had the car.

Is it 33% likely you picked goat2? or is it 66% likely you picked goat2?
there are not two goat2s. There is one goat1 and one goat2.
car = 33%
goat1 = 33%
goat2 = 33%

whether you picked the car or goat2, monty is equally likely to reveal goat1.
You had an equal chance to pick the car and goat2. Both are 33%.

I'm not asking if you believe in 66%
I'm asking whether or not you exactly know what door you picked. You're guaranteed to win if you know the prizes behind the doors are before you make your choice.

You're unlikely to win if you don't know, the least reason being because you've forfeit any greater understanding to higher powers of luck or unknowns.

Words can kill.
that being said

niggers

>>14964067
>do not collapse realities
Why not?

>>14964954
>Is it equally likely that monty reveals goat1 compared to revealing goat2 when you pick the car door?
It doesn't actually matter, since he always chooses a goat. The probability of choosing a car and then Monty revealing a goat always adds up to 1/3, regardless if he is biased to one goat or not. Since you don't know which goat Monty would be biased to, this gives you no information.

>Is it equally likely that monty reveals goat1 when you pick the goat2 door, as it is when you monty reveals goat2 because you picked the goat1 door?
Yeah, it's 1.

>Do you know, with certainty, whether you picked goat2 or the car?
No. You know with certainty that there's a 1/3 chance you chose the car. If you didn't, you are guaranteed to get the car by switching, because Monty singles it out for you by revealing the remaining goat. So switching is more likely to get you the car. Not that hard to understand.

>>14964913
>can't use a 5-line excel correctly
lol idiot

>>14956361
it's 50/50

>>14957013
gambler's fallacy

>>14957251
either you change, or you don't, 50/50

>>14963898
are these people even real? I see people talking about 100 doors, cum buckets, alternate realities. bruhs yall are on a level beyond monty hall

>>14956361
>>14956391
Hey, gang, so I was wondering: does the fact that the universe is NOT locally real have any bearing on the idealized 2/3 favorable probability involved in switching doors?

>>14967372
No. Are you retarded?

>>14967373
Don't hate on a science enthusiast for asking questions, my man.

>>14967375
Yikes. Let's unpack your problematic proposition, my guy. Why would the fact that the universe is NOT locally real have any bearing on the idealized 2/3 favorable probability involved in switching doors?

>>14967378
If I knew, I wouldn't be asking.

>>14964988
feel free to commit suicide

>>14967425
Why can't you answer a basic question?

>>14956361
The thing I don't understand, is that this show was on TV for over 30-years, and NOT one statistician used his advanced mathematical knowledge to game this system and win prizes consistently.
https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal
Were people just plain retarded back then? Or was everyone smart too busy working for NASA and other space contractors??

>>14970007
Because the problem is contrived and the conditions necessary for the 2/3 answer to be true were probably not present in the actual show, namely, Monty is not forced to reveal a door.