/sci/ - Science & Math

>>9837694
Imagine 999 goats 1 car
You pick a door 998 doors get opened
Do you switch or not?

>>9837694
>But the key thing that these videos intentionally ignore is that the moment that the host opens a door, the probability changes.
No.
You're just a brainlet.

>>9837718
Does the host know where the goats and car are? If so, it doesn't matter if you switch.
I've always hated the, "hurr imagine if there are more doors" explanation, it's poor and doesn't make sense.

>>9837750
You're probably one of those who think 0.99999... =/= 1and infinity is just an extremely large natural number.

>>9837750
>Does the host know where the goats and car are?
Yes, he does. Which is why he will only open a door to a goat.

The door you picked was probably not the car.
The door the host opens is definitely not the car.
Therefore, the door the host doesn't open is probably the car.

There, you don't even have to think about it from a statistics point of view.

>>9837750
Just because you dont get it doesnt mean wrong.

You can literally do this experiment yourself. With enough trials you'll see the probability is correct

>>9837758
>you don't even have to think about it
Your explanation only include the first prompt.
Remember, there are two prompts, so there are two sets of probability, 33/33/33 and 50/50. The first set is replaced by the second set. That's why you get 50% chance regardless if you switch or not.

>>9837762
>do this experiment yourself
If you do this in a spreadsheet. You'll see that it's 50/50.

>>9837694

>>9837775
If you don't pick before a door or 998 doors are revealed that is correct. But because you're picking before the chance that you pick a wrong one is 66.6% so switching doesn't decide between just two doors because you aren't just picking between two. You're picking between the one that has a 66.6% chance to be a goat and the one that has a 33.3% chance to be a goat.

>>9837775
>Your explanation only include the first prompt.
It literally doesn't matter.
>Remember, there are two prompts, so there are two sets of probability, 33/33/33 and 66/33.
Yes.

>>9837775
You're approaching this from the perspective of
>there are three doors, one is open with goat behind it, one has a goat behind it and one has a car. what is your probability of picking the car?
That's wrong. You're ignoring the first prompt.

When you are first asked to pick a door you have a 1/3 chance of picking the car. You are more likely to pick a goat.
The host opens a door to reveal a goat.
The host then asks if you want to change your choice to the other door.
The probability of your first pick being a goat HAS NOT CHANGED. You are still just as likely to have picked a goat, all that has changed is that you now know which of the other doors is definitely a goat.
Armed with this knowledge your best bet is to change your choice because your original choice WAS STILL MORE LIKELY TO BE A GOAT.

>>9837782
But you get to pick again!
The first time you pick a door is now irrelevant.
What really counts the the second time, which is 50/50.

How about this.
Let's say you pick from three doors. One is open. So, there are two closed doors left. One is a goat, one is a car.

But something happened, the studio catches on fire and everyone has to evacuate, and the show is postponed.

The next month. The show continues in a new studio. This time you're given two trailers instead of two doors. Do you see now that it's 50/50?

>>9837694
I know this is b8 but it's literally possible to prove this by testing it yourself
>Proof: https://www.youtube.com/watch?v=o_djTy3G0pg
Stop being a lazy nigger

>>9837803
>The first time you pick a door is now irrelevant.
Wrong.

>>9837806
Staged.
Do it yourself and it's 50/50.

>>9837817
Incorrect.

>>9837694
Choice is an illusion, everything is predetermined by the conditions at the Big Bang. Probability of all events is either 100% or 0%.

>>9837694
What's with all of these posts on sci? Who is behind all of these misinformation?
Yes, you got a 50% chance of getting the right answer from two choices.
But the key thing that these posts intentionally ignore is that because the host opens a door, the probability is changed.
It's not an option among two symmetrical choices, which you got a 50% chance. It's between two choices which were influenced by the hosts actions, which you got 33% chance if you dont switch.

A = "Your initial choice was correct."
B = "Host opened a goat door"

[eqn]P(A|B) = \frac{P(A \cap B)}{P(B)} [/eqn]
[eqn]P(A \cap B) = P(A) = \frac{1}{3} [/eqn]
[eqn]P(B) = \frac{2}{3} [/eqn]
[eqn]P(A|B) = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2} [/eqn]

What is so hard to understand about that?

>>9837694
It's so easy to test!
Grab a friend (your mom works too if you have none) and try doing the monty hall problem with them as an activity. All you need are three cups and a small object like a quarter.

1). Have one person put the quarter under one of the cups while the other person looks away.
2). Have the person whom looked away choose a cup (without lifting the cup).
3). Have the person who put the quarter under one of the cups lift up one of the cups that doesn't have a quarter and wasn't chosen.
4). Offer the person whom looked away, a chance to choose a different up (excluding the one that was lifted already).
5). Finally lift the cup that was chosen by the person who looked away; revealing either a quarter or nothing.

Do it many times and write down the stats.

>>9837694
suppose I play a game with you
there are 3 doors, with an empty jar behind a door, another empty jar behind another door, and a jar of money behind the remaining door. They are randomly assigned between game rounds, so you won't know anything about their positions at the beginning of each round. In order for you to play a round, you will need to pay $1. When the round starts, you will pick one of the three doors. In response, I will check behind the two doors that you didn't pick, and I will open whichever door has an empty jar behind it (or, if both doors have empty jars behind them, then I will just open one of them at random). Now there are only two closed doors remaining, the door you picked, and the door you didn't pick (and that I didn't open). One of these doors has the jar of cash behind it (worth $1.50), and the other has an empty jar behind it. If you KEEP your selection, then I will open your chosen door, and you will get to take any money that you find inside your chosen door's jar, but you will not pocket any cash from the two jars that you didn't pick (this round). If you want to SWITCH your selection, then you forfeit, and you don't pocket any money (this round). If you win the $1.50 jar, then, after you pocket your cash, the round will end, and I will put another $1.50 in the jar, and I will randomly assign the three jars behind the three doors. If you win the empty jar, the round will end, and I will randomly assign the three jars behind the three doors. If you don't have enough cash on you to play another round, then you can still play, but the $1 entry fee is charged to your tab. If your tab is non-zero, then any pocketed cash must pay down the tab until it reaches $0. Once it reaches $0, then you get to pocket the pocketed cash. Your tab credit is unlimited, and I have unlimited amounts of cash to put in the jars. If you play this game over and over again are you expected to gain money, or lose money, by always KEEPING your selection?

suppose I play a game with you
there are 3 doors, with an empty jar behind a door, another empty jar behind another door, and a jar of money behind the remaining door. They are randomly assigned between game rounds, so you won't know anything about their positions at the beginning of each round. In order for you to play a round, you will need to pay $1. When the round starts, you will pick one of the three doors. In response, I will check behind the two doors that you didn't pick, and I will open whichever door has an empty jar behind it (or, if both doors have empty jars behind them, then I will just open one of them at random). Now there are only two closed doors remaining, the door you picked, and the door you didn't pick (and that I didn't open). One of these doors has the jar of cash behind it (worth $1.50), and the other has an empty jar behind it. If you KEEP your selection, then I will open your chosen door, and you will get to take any money that you find inside your chosen door's jar, but you will not pocket any cash from the two jars that you didn't pick (this round). If you want to SWITCH your selection, then you forfeit, and you don't pocket any money (this round). If you win the $1.50 jar, then, after you pocket your cash, the round will end, and I will put another $1.50 in the jar, and I will randomly assign the three jars behind the three doors. If you win the empty jar, the round will end, and I will randomly assign the three jars behind the three doors. If you don't have enough cash on you to play another round, then you can still play, but the $1 entry fee is charged to your tab. If your tab is non-zero, then any pocketed cash must pay down the tab until it reaches $0. Once it reaches $0, then you get to pocket the pocketed cash. Your tab credit is unlimited, and I have unlimited amounts of cash to put in the jars. If you play this game over and over again are you expected to gain money, or lose money, by always KEEPING your selection?

>>9837829
but muh uncertainty

>>9837848

The host will always open a goat door. P(B)=1

>>9838086
replace $1.50 with $2.50

>>9837694
One missing key piece of info is that the host always offers you to switch. He isn't playing a game of his own where he tries to fuck you over.

>>9837778
No you don't.

>>9837694
OP, you are right. The whole thing is fucking stupid.

>>9839804
I know, right?

>>9838086
>trying this hard

>>9837694
>It's no longer an option among three choices, which you got a 33% chance. It's now between two choices, which you got 50% chance regardless if you switch or not.
The two remaining doors aren't equal because the host is not able to open the door with the prize behind it when he does that "open a door and ask if you want to change your pick" thing.
If he could open the door with the prize behind it then that would make the game retarded since he'd be telling you for sure where the prize is. He would have no incentive to do that, and if he were also blind to which door was the right one for some reason that would also be retarded since it would mean 50% of the time he'd accidentally ruin the game and tell you the right answer.
So you can use this information to your advantage and map out the possibilities based on this known limitation the host is operating with:
A) You pick the first goat door and host is forced to reveal the second remaining goat door to you.
B) You pick the second goat door and host is forced to reveal the first remaining goat door to you.
C) You pick the car door and host can reveal either of the two remaining doors to you since they both have goats.
If A and you keep your answer, you lose.
If A and you change your answer, you win (+1 Win From Changing).
If B and you keep your answer, you lose.
If B and you change your answer, you win (+1 Win from Changing).
If C and you keep your answer, you win (+1 Win from Keeping).
If C and you keep your answer, you lose.
2 / 3 = Probability of Win from Changing.
1 / 3 = Probability of Win from Keeping.

>>9837750
The chance you picked the car on your first try is low. It actually increases once the doors are open if you switch.

>>9837694
>It's no longer an option among three choices, which you got a 33% chance. It's now between two choices, which you got 50% chance regardless if you switch or not.
The two remaining doors aren't equal because the host is not able to open the door with the prize behind it when he does that "open a door and ask if you want to change your pick" thing.
If he could open the door with the prize behind it then that would make the game retarded since he'd be telling you for sure where the prize is. He would have no incentive to do that, and if he were also blind to which door was the right one for some reason that would also be retarded since it would mean 50% of the time he'd accidentally ruin the game and tell you the right answer.
So you can use this information to your advantage and map out the possibilities based on this known limitation the host is operating with:
A) You pick the first goat door and host is forced to reveal the second remaining goat door to you.
B) You pick the second goat door and host is forced to reveal the first remaining goat door to you.
C) You pick the car door and host can reveal either of the two remaining doors to you since they both have goats.
If A and you keep your answer, you lose.
If A and you change your answer, you win (+1 Win From Changing).
If B and you keep your answer, you lose.
If B and you change your answer, you win (+1 Win from Changing).
If C and you keep your answer, you win (+1 Win from Keeping).
If C and you change your answer, you lose.
2 / 3 = Probability of Win from Changing.
1 / 3 = Probability of Win from Keeping.

>>9837694
Monte Carlo methods anyone? I'll make a python code for it in half an hour or so if anyone wants.

>>9841203
Already been done
https://en.wikipedia.org/wiki/Monty_Python

>>9837694
Because it was random to begin with

>>9837694
>This thread again for the ten billionth time.