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## Posts

That's...kind of the point though. Instead of thinking of it as "do you want to swap" think of it as "do you really think you picked the right door, or now that we've given you another chance with fewer options do you want to pick again?"

If there are a hundred doors and you pick one at random, and then they open *every other door except one* to show you that the prize is behind none of them, the question becomes "do you

reallythink you picked the right door, or do you think the prize might actually be behind this one other remaining door?"when you first picked, you only had a 1/100 chance of picking the right door. now they've narrowed it down to two choices, and you have to decide if you think you actually picked the right door. you probably didn't, and now you have the chance to switch to the door that

almost definitelyhas the prize behind it.the exact same odds apply to 3 doors, it's just less of a guarantee.

the best odds you can get at that moment are only ever 50/50, yes, but that's

onlyif you switch every time you have the chance. if you don't switch, your odds are locked in at whatever point they were when you made your initial choice.Houk the Namebringeronthis coin toss has a 50% chance of success if you pick tails, but a much smaller chance of success if you pick heads, because this coin used to be a d6, until very recently

What even is this metaphor

what I hear when reading houk's post

TheySlashThemonIt's still wrong.

There's 100 doors. One of them has a prize behind it. You pick one. 1 in 100 chance of success.

The doors are reduced to 2. Your door and one other. The prize is guaranteed to be behind one of them. Ask yourself, out of 100 doors do you think you picked the winning door? Or is it more likely you picked the wrong door at the start and the other door has the prize?

that doesn't matter! there's only two doors now!

(Switch Friend Code)SW-4910-9735-6014(PSN)timspork(Steam)timsporkAnd you picked one of them out of 100 others.

So do you think you got it right the first time? That's the key point to understanding the whole thing.

these hands.But they weren’t opened randomly. The person opening them to show you they were empty knew which one had the car in it. So by opening 98 wrong options, the choices are now 99% if you switch, and 1% if you stay.

That said, the Monty hall problem is fascinating just for how much people cannot understand it. It’s like the plane on a treadmill thing.

Knight_onOk lets do a million. There is a prize behind one door in a million. You pick one of the million doors.

Now they keep the door you picked, and one other out of the million, and ask you to choose. Out of that first million do you think you got it right on the first pick?

Keep in mind the prize IS NOT randomized after you pick and they remove all the ones you didn't pick. It is still behind the same door as it was the first time. All they've done is removed the 999998 doors that are guaranteed losses.

Chances are you did not pick the one in a million door the first time, and in fact the prize is in the other one they are offering you, so you should swap.

webguy20onOrigin ID: Discgolfer27

Untappd ID: Discgolfer1981

But you can demonstrate that the answer is true, why are you dying on this hill?

It really is a simple question you keep refusing to answer: Did you pick the right door the first time? The numbers are meaningless, scaling higher just reinforces that singular question.

Okay, let's do a billion.

There's a billion goats behind those doors. They're out for blood. What do you do?

This post was sponsored by Goop.'Get your fucking finger on the wookie'

die, probably

I was hoping with the bigger number it would be easier to see. Its almost paradoxical that way.

I assumed that most folks would believe they would not pick correctly the one in a million doors with a prize behind it, and it would help it make sense.

Origin ID: Discgolfer27

Untappd ID: Discgolfer1981

No, you obviously get in the car. Sheesh!

Let's try it again:

There's 10 billion goats...This post was sponsored by Goop.'Get your fucking finger on the wookie'

It's super basic, and people here definitely already know it, but that's what did it for me

I've seen people use 1000 doors as an explanation but I think it's easier with 2.

There are 2 doors. Behind one of them is a prize.

What are the odds that you will pick the correct door? 50/50.

You pick door 1.

I am very helpful and this isn't a real game show, so I tell you look I'm gonna open the door that doesn't have a prize behind it, and you can pick again if you like.

I open door 1. There is no prize behind it.

What are the odds that you will win a prize if you stick with door 1?

you don't need it explained, run the simulation that was linked earlier. Run "keep the door" 100 times and "switch doors" 100 times.

My simulation had a 75% chance of winning when i switched, and a 30% chance of winning when I kept the door.

It's just how it works, it doesn't matter if you don't understand it, it is objectively true.

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

cursedkingonthey're separate simulations? The percentage is always going to be different because they're two different simulations.

Like I just ran both again out of 100 and I won 71% on switch and 41% on keep.

The point isn't that it's a fixed percent, it's that it is overwhelmingly better to switch. Odds are still odds. You could still lose, but you have a way better chance if you switch.

cursedkingonThere are 10,000,000 doors infinitely arrayed before you, behind one of them is a very cool goat you want.

You pick a door. Your odds of correctly guessing which door has a cool goat are 1/10,000,000

I am very nice so I say wow that was a ridiculous thing to do, I'll open all but two doors: the one you picked, and the one with a goat behind it.

This leaves 2 doors. You now have a 9,999,999/10,000,000 chance of getting an awesome goat only if you switch which door you picked, because this new decision that you're making between two doors is between one that's really unlikely to have it (1/10,000,000) and one that's almost guaranteed to have it (every other door opened was opened because it either did not have a cool prize or was the door you picked. What are the odds that the one you picked also was the one with a cool prize? 1/10,000,000. So the other door will have the cool prize 9,999,999/10,000,000 times).

Edit: Also I still like my two-door extremely silly version. It's a bad game show, but the point is that if you remove the ability to stick with a closed door you've picked you're forced to confront the fact that if you do not switch you are actively deciding to have no chance of winning. In the 1/10,000,000 version you're deciding to have a super-small chance of winning.

Edit again: I explained it wrong at first! Just goes to show why it's a classic brain-teaser.

durandal4532onokay but if I'm being conspired against then why is this being presented as a math problem

Librarian's ghoston(Switch Friend Code)SW-4910-9735-6014(PSN)timspork(Steam)timsporkthe hurdle is not thinking of the percent as a fixed state through both circumstances. it just absolutely does not work that way, even though it feels like it should.

edit: when inantp says that humans do not understand statistics, they're not joking. Our brains are not wired for understanding statistics at a fundamental level. They go against any rational instinct. It's what makes trusting a computer so hard because it

feelswrong.cursedkingonBut if offered to change my selection, I step back and in my head consider the two doors as a new problem, I got two doors, one has a prize that is 50/50.

(Switch Friend Code)SW-4910-9735-6014(PSN)timspork(Steam)timsporkMy thought process:

Then you choose one, it locks that door in at a 1/3 chance of having the prize.

The other two doors have a combined 2/3 chance of having the prize.

Then the host reveals one of the doors. The secret to this problem is: The door he opens is

neverthe one with the prize. If the door he opened was random, then the monty hall problem wouldn't exist.Now you have one door which inherited a 2/3 chance of having the prize, and the one you picked, which has a 1/3 chance of having the prize.

ifthe host opened one of the other two doors at random. He doesn't though, he wants to draw it out, and so he only ever reveals an empty door.PsykomaonThat’s the part I absolutely can’t wrap my head around.

(Switch Friend Code)SW-4910-9735-6014(PSN)timspork(Steam)timspork1/3 chance it's the door you picked (door 1, say)

1/3 chance it's door 2

1/3 chance it's door 3

So 1/3 chance it's the door you picked, 2/3 chance it's either of the other two doors.

The host opens door 3, it's not door 3. Now it's a 2/3 chance that it's door 2 because we know it isn't door 3 and we know it's a 2/3 chance that it's either door 3 or door 2.

I mean it's def a problem designed to spin you around on probability, which is incredibly unintuitive in the first place.

This actually makes me miss talking stats, it's fun playing around with these problems.

durandal4532on