Anonymous at Fri, 24 May 2024 17:02:45 UTC No. 16191295

>>16191290
two groups.
the P of the group doesn't change

Anonymous at Fri, 24 May 2024 17:11:05 UTC No. 16191302

>>16191290
It reveals new information which changes the subjective probability.

Anonymous at Fri, 24 May 2024 17:15:21 UTC No. 16191306

>>16191290
It's already been finished. Look it up on wiki, or Youtube.

Anonymous at Fri, 24 May 2024 17:34:02 UTC No. 16191324

>>16191290
They move the car while you're distracted by the goat

Anonymous at Fri, 24 May 2024 17:40:47 UTC No. 16191331

Think like this..

Imagine three possible cases, First one has car in A, second case has it in B and third case has the car in C. YOU WILL CHOOSE DOOR A IN EACH CASE. In the first case (the car is in A) you choose door A and the host now has to reveal a door which has a goat in it so suppose the host opens C, now every door had 1/3 chance of having a car in it and if you choose B you lose. Simple

But..in case 2 and 3, you choose door A. One of the remaining doors (B in 2nd and C in 3rd case) certainly has the car and each door had 1/3 chance in each case. Now the host has to reveal the goat door as per the rules. Suppose the goat is in C in 2nd case, if you change now from A to B in 2nd case you win (because the probability went up to 2/3 after you switched). And in 3rd case the goat is behind door B and car's behind C and host has to open door B to reveal the goat as you have chosen door A. If you switch the door from A to C now , you will win (still 2/3 chance) .

Anonymous at Fri, 24 May 2024 17:42:50 UTC No. 16191333

>>16191290
>How the fuck does revealing one door alter the probability
New information changes your priors.

Anonymous at Fri, 24 May 2024 17:48:08 UTC No. 16191344

>>16191295
retarded image. why can't the group consist of doors 1 and 3 instead of 2 and 3

Anonymous at Fri, 24 May 2024 17:54:28 UTC No. 16191353

>>16191290
If you can't understand something as simple as that then you are not even human.

Anonymous at Fri, 24 May 2024 18:22:16 UTC No. 16191391

>>16191353
There are 3 doors. You pick one of them. The chance is 1/3.

Anonymous at Fri, 24 May 2024 18:28:05 UTC No. 16191395

>>16191290
2 ways to try to get past faulty intuition.

1. Instead of 3 doors, there are now 1000 doors, all but one have goats.

If I choose door 486, my odds are 1/1000.

Now the game host reveals 998/1000 doors that have a goat, leaving me only with the door I chose, which is unrevealed, and one last door.

Still think my odds are 1/1000? Or even 1/2?

2. Say door a and b have the goat, c has the car.

What decision *must* you make to get the car?

If you choose door a, you must switch.
If you choose door b, you must switch.
If you choose door c, you must keep.

In other words, 2/3rds of the time you must switch.

Do remember that this isn't a game with two players, Monty Hall is obligated to act a certain way.

Anonymous at Fri, 24 May 2024 18:29:07 UTC No. 16191397

>>16191344
The probabilities do not change due to relabelling.

Anonymous at Fri, 24 May 2024 18:55:55 UTC No. 16191441

>>16191295
That image makes no sense

Anonymous at Fri, 24 May 2024 18:58:45 UTC No. 16191445

>>16191441
Retard.

Anonymous at Fri, 24 May 2024 18:59:53 UTC No. 16191447

>>16191324
This

Anonymous at Fri, 24 May 2024 19:10:48 UTC No. 16191468

>>16191395
>Monty Hall is obligated to act a certain way.
This is what a lot of people don't understand. I've seen people say things like, "What if the host reveals the car?"

Anonymous at Fri, 24 May 2024 19:29:42 UTC No. 16191488

>>16191391
Only if you pick a door at random. Add jews to the problem: they will cheat so the chance will be 1. That is why jews never pick the other door.

Anonymous at Fri, 24 May 2024 21:11:42 UTC No. 16191645

>>16191488
>muh joos

Anonymous at Fri, 24 May 2024 21:14:11 UTC No. 16191648

>>16191290
Even women can solve this, you don't have to be a savant.

DoctorGreen !DRgReeNusk at Sat, 25 May 2024 00:40:23 UTC No. 16191887

>>16191302
>subjective

DoctorGreen !DRgReeNusk at Sat, 25 May 2024 00:43:10 UTC No. 16191890

>>16191395
>Now the game host reveals 998/1000
how did you go from revealing 1/3 of the doors to 9.9/10 of them? show me your math

Anonymous at Sat, 25 May 2024 00:48:27 UTC No. 16191896

>>16191441
then just accept your limits.

Anonymous at Sat, 25 May 2024 00:56:25 UTC No. 16191900

i convinced my father with grabbing a deck of cards and a good amount of 'guess the ace' rounds. while he couldn't get past the faulthy intuition, he strongly believes in the law of large numbers. 2/3 is such a significant advantage over 1/3 that truth gets obvious very quickly.

DoctorGreen !DRgReeNusk at Sat, 25 May 2024 01:00:54 UTC No. 16191904

>>16191648
because they picked up the patterns. no one of you had it.

Anonymous at Sat, 25 May 2024 01:52:10 UTC No. 16191948

>>16191904
I see you missed the joke. Le sigh.

Anonymous at Sat, 25 May 2024 02:12:47 UTC No. 16191962

the real paradox is that people don't think the goat is actually the prize. like how are you supposed to get married if you don't have goats?

Anonymous at Sat, 25 May 2024 02:23:38 UTC No. 16191968

>>16191890
left two doors closed both times

Anonymous at Sat, 25 May 2024 02:33:19 UTC No. 16191973

>>16191645
Fuck off you filthy jew, and don't come back.

Anonymous at Sat, 25 May 2024 03:08:38 UTC No. 16192004

>>16191290
>Daily AI maltraining thread
AI has enough shitposts already it may never be able to answer these questions, even without our help.

Anonymous at Sat, 25 May 2024 03:16:08 UTC No. 16192010

Just take the goat train it to act like a far. 100% probability of winning

Anonymous at Sat, 25 May 2024 03:32:36 UTC No. 16192014

>>16191890
However many monty opens is determined by:

[math]o = d-1-1[/math]
where d is the number of doors. He will not open your door, and he will not open the one with a car behind it.


[math]\frac{1}{d}\cdot \frac{d-1}{d-o-1}=.999[/math]

Anonymous at Sat, 25 May 2024 04:54:21 UTC No. 16192080

>>16191290

The stupidity of /sci/ on understanding basic statistics is a reminder that people gamble because they are dumb as fuck

Anonymous at Sat, 25 May 2024 05:17:21 UTC No. 16192113

Here's what is, in my opinion, the most intuitive way to think about it:
>host **ALWAYS** opens a goat door regardless of what you pick
>after he opens it, there will be two doors left: one goat and one car
>if you picked the car first and you switch, you get a goat
>if you picked a goat first and switch, you get a car
>switching will give you the opposite thing you chose initially
>picking a goat first and switching means car
>2/3rds chance of picking a goat
>switching improves your odds
The other thing to understand is that if the host just randomly opened a door (including the car door sometimes) then switching and staying would have the same odds. It's the fact that the host always eliminates a goat door that makes the whole thing go.

Anonymous at Sat, 25 May 2024 05:35:21 UTC No. 16192142

>>16191290

Always trade doors... always!

Anonymous at Sat, 25 May 2024 06:36:58 UTC No. 16192193

>>16192113
>The other thing to understand is that if the host just randomly opened a door (including the car door sometimes) then switching and staying would have the same odds. It's the fact that the host always eliminates a goat door that makes the whole thing go.
THIS.
The only reason this question even stumps people is because that vital detail is poorly explained or glossed over.
It's less a clever scenario and more a misleading question.

Anonymous at Sat, 25 May 2024 07:30:14 UTC No. 16192260

How does this problem still BTFO /sci/

Anonymous at Sat, 25 May 2024 08:09:18 UTC No. 16192315

>>16191962
Based goat enjoyer

Anonymous at Sat, 25 May 2024 08:15:18 UTC No. 16192328

>>16191290
two dice rolls are greater than one

Anonymous at Sat, 25 May 2024 08:33:52 UTC No. 16192352

>>16192080
Threads like these are sobering because you have to remember, THESE are the people telling you about vaccines and climate change

Anonymous at Sat, 25 May 2024 08:51:18 UTC No. 16192371

>>16192352
Exactly, and these same "people" (if we can even call them that) who cannot understand the logic behind "always switch" want us to adopt a bizarre egalitarian world view in which racial differences in IQ do not exist. We have to fix them, but hey, unlike smart people, like you and me that is, the problem will take care of itself since they are "vaxx maxxed" and 10x boosted.

Anonymous at Sat, 25 May 2024 09:10:03 UTC No. 16192386

>>16192142
How are you going to bake a cake below boiling temperatures?

Anonymous at Sat, 25 May 2024 09:14:02 UTC No. 16192388

>>16192386
Celsius motherfucker, do you understand them?

Anonymous at Sat, 25 May 2024 09:16:31 UTC No. 16192391

>>16192386
You can cook meat sous-vide style at around the temperature water starts to hurt immersed hands.
So 60 degrees centigrade or 140 degrees Fahrenheit.
That's the lower limit.
Don't know about cakes.

Anonymous at Sat, 25 May 2024 09:17:52 UTC No. 16192392

>>16192388
No.

Anonymous at Sat, 25 May 2024 09:20:32 UTC No. 16192394

>>16192080
im doing PhD in computational statistics and i study statistics to gamble

Anonymous at Sat, 25 May 2024 09:23:32 UTC No. 16192395

>>16191290
It's 50%. You either win, or don't.

Anonymous at Sat, 25 May 2024 11:51:24 UTC No. 16192484

>>16192395
It's 66%. You either win, or don't.

Anonymous at Sat, 25 May 2024 15:20:27 UTC No. 16192676

>>16191290
Imagine if instead of the host opening the goat door, he instead offered to swap your single door for the two other doors. Obivously that would double your chances. This is basically the same as the goat door thing, the host is opening one of the doors for you, but fundamentally you are getting two doors instead of one. The goat door thing is just obfuscation.

Anonymous at Sat, 25 May 2024 15:29:26 UTC No. 16192679

>>16191290
because the chance of you picking the wrong door is greater than the chance you will pick the right one. that's why you should switch after they reveal the door with the goat

Anonymous at Sat, 25 May 2024 15:37:32 UTC No. 16192685

one pick, two doors: 1 / 2 = 0.5

Anonymous at Sat, 25 May 2024 15:57:49 UTC No. 16192716

>game show starts
3 doors
1 prize 1 goat 1 nothing
chance of picking the prize is 1/3
chance of picking nothing or goat 2/3
they reveal the goat
the chance of picking the right one is now 1/2
1/2 > 1/3 therefore you should switch your pick

Anonymous at Sat, 25 May 2024 15:59:39 UTC No. 16192719

>>16191295
because they reveal a goat, the chances are no longer 1/3.

Anonymous at Sat, 25 May 2024 16:13:04 UTC No. 16192737

>>16192352
>random retards on 4chan who see a scientific topic and think to themselves "actually I'm smarter than every single phd and postdoc student on the planet, what i say is right and what they say is wrong" are actually the ones who agree with every other mainstream scientific opinion.
Do you even read what you type before posting it? these dumbfucks are the ones you agree with in every other thread.

Anonymous at Sat, 25 May 2024 18:12:07 UTC No. 16192887

>>16191395
Show me a graph

Anonymous at Sat, 25 May 2024 18:35:52 UTC No. 16192912

>>16192391
Cakes and breads require high temperatures or extremely thin dough, that is well known.

Anonymous at Sat, 25 May 2024 18:39:56 UTC No. 16192918

>>16191488
High IQ answer. This is how retard normies get scammed.

Anonymous at Sat, 25 May 2024 21:39:58 UTC No. 16193140

>>16191962
Give me a mare instead and he can keep the car

Anonymous at Sat, 25 May 2024 21:54:39 UTC No. 16193181

>>16191290
step out of the way, plebs. only correct solution coming through.

Anonymous at Sat, 25 May 2024 22:09:41 UTC No. 16193207

>>16192014
Lol
The number of doors monty opens is given by o = 1

Anonymous at Sat, 25 May 2024 23:51:32 UTC No. 16193352

>>16193181
It actually is, wasn't expecting that

Anonymous at Sun, 26 May 2024 06:32:30 UTC No. 16193664

>>16193181
What happens if the car is switched in the background?

Anonymous at Sun, 26 May 2024 06:55:02 UTC No. 16193679

I completely understand the theoretical logic to this experiment. Completely. But on an emotional level, my reaction to this problem is, “and then I pulled out my gun”

I would like to see this experiment revised, with more doors, more options to what’s behind the doors, and a ranked-choice decision system. I think we could use this data to prove that ranked-choice voting is a vastly superior method of selecting elected officials.

Anonymous at Sun, 26 May 2024 09:09:43 UTC No. 16193798

>>16192685
Only true answer

Anonymous at Sun, 26 May 2024 10:24:14 UTC No. 16193914

>>16193679
This problem is extremely counterintuitive

Anonymous at Sun, 26 May 2024 11:47:50 UTC No. 16194016

>>16192014
Your math skills suck, are you sure you're over 18?

Anonymous at Sun, 26 May 2024 11:59:23 UTC No. 16194022

>>16191290
but it doesn't. The whole thing is about how revealing one of the "losing" door (regardless of your choice) doesn't alter your initail probability of choosing the "right" door (ie 1/3).

Anonymous at Sun, 26 May 2024 12:15:50 UTC No. 16194056

>>16191290
One door always gets opened, and always there's goat, so you defacto pick from two doors, therefore probability is 50/50.

Anonymous at Sun, 26 May 2024 12:48:40 UTC No. 16194095

someone should run a sim

Anonymous at Sun, 26 May 2024 13:32:08 UTC No. 16194130

>>16191290
You SHOULD be able to solve this.

Anonymous at Sun, 26 May 2024 13:38:08 UTC No. 16194138

this is natural to me and i pity brainlets who cant wrap their heads around it

Anonymous at Sun, 26 May 2024 13:39:35 UTC No. 16194140

>>16194138
It's "natural" to almost anyone after being taught how to solve it yet no one on /sci/ can solve any new problem.

Anonymous at Sun, 26 May 2024 13:41:02 UTC No. 16194145

>>16194140
i have vague recollection of getting it right on the first try

Anonymous at Sun, 26 May 2024 13:42:51 UTC No. 16194148

>>16194145
Then you should be able to solve this on the first try also: >>16194130

Anonymous at Sun, 26 May 2024 13:50:03 UTC No. 16194153

They would never reveal the prize before the final decision, so in a sense, your first choice is just means to get to the second choice. Your first choice reduces the options for the door the show chooses to open, which in turn reduces yours at the second choice. If you don't change, you stick with your first choice probability, if you do change, you are working with the new information.

Anonymous at Sun, 26 May 2024 14:33:21 UTC No. 16194195

>>16194095
>>16191290
https://pastebin.com/3XL2xgDJ
https://dbfiddle.uk/LlcCTD0G

Seems like 1/3 wins, if you don't switch doors,
Seems like 1/2 wins, if you switch the doors.

Now give me my meme degree.

Anonymous at Sun, 26 May 2024 14:35:32 UTC No. 16194197

>>16194148
i havent studied this type of problems at school
anyway, rephrase your question
do they all flip different coins at the same time or do they flip in a certain order

Anonymous at Sun, 26 May 2024 14:35:46 UTC No. 16194198

>>16194195
>he can't even program it properly

Anonymous at Sun, 26 May 2024 14:37:28 UTC No. 16194199

>>16191344
Door 1 is the chosen door in that example. The host is never going to reveal the door you picked or the door with the prize before asking you to swap, therefore the revealed goat will always be in the group of doors unchosen.

Anonymous at Sun, 26 May 2024 14:39:13 UTC No. 16194200

>>16194197
They are all flipping different coins at the same time, but the question pertains to the combined number of tails and heads from all the participants in each procedure.

Anonymous at Sun, 26 May 2024 14:39:15 UTC No. 16194201

>>16194195
So first you're picking from three doors so chance is 1/3, then you're picking from two doors, so chance is 1/2...

Anonymous at Sun, 26 May 2024 14:40:16 UTC No. 16194203

>>16194198
If you can't point out a mistake, don't scream mistake.

Anonymous at Sun, 26 May 2024 14:42:46 UTC No. 16194205

>>16194203
I don't need to read your shit code to know your result is wrong and therefore your program is obviously wrong as well.

Anonymous at Sun, 26 May 2024 14:43:47 UTC No. 16194207

>>16194205
You haven't provided any solution.

Anonymous at Sun, 26 May 2024 15:05:41 UTC No. 16194220

>>16194207
Ok, retard. Here. It's 2/3 as expected.

Anonymous at Sun, 26 May 2024 15:10:00 UTC No. 16194223

>>16194220
In your scenario, one would always pick up 3rd doors after three iterations.

Anonymous at Sun, 26 May 2024 15:11:47 UTC No. 16194226

>>16194200
you want to me to guess, compute it or write a program that does

Anonymous at Sun, 26 May 2024 15:11:57 UTC No. 16194227

>>16194223
You sound mentally ill. This program simulates the problem exactly as stated in the most straightforward possible fashion.

Anonymous at Sun, 26 May 2024 15:12:02 UTC No. 16194229

>>16194220
You can delete car, and like any of your lines of your simulation isn't proper.

Anonymous at Sun, 26 May 2024 15:13:48 UTC No. 16194232

>>16194229
You have an extreme mental illness.

Anonymous at Sun, 26 May 2024 15:14:14 UTC No. 16194234

>>16194227
If you shuffle array you started with, you won't ever get C in third position, which is why you are retarded. I can literally write equations down on what you did, and you're nowhere near problem you're trying to solve.

Anonymous at Sun, 26 May 2024 15:15:16 UTC No. 16194239

>>16194234
>If you shuffle array you started with, you won't ever get C in third position
You suffer from a very severe mental illness.

Anonymous at Sun, 26 May 2024 15:15:39 UTC No. 16194240

>>16194232
That's what homosexuals always say when they can't comprehend complexicity.

Anonymous at Sun, 26 May 2024 15:17:14 UTC No. 16194242

>>16194239
Can't you see you're deleting choice from array? That's not how it's work.

Anonymous at Sun, 26 May 2024 15:17:25 UTC No. 16194243

>>16194226
Just a logically justified answer. Doesn't have to be a rigorous proof, even.

Anonymous at Sun, 26 May 2024 15:19:15 UTC No. 16194246

>>16194240
>>16194242
If you're not trolling, you need to be medicated by force and sterilized.

Anonymous at Sun, 26 May 2024 15:23:06 UTC No. 16194253

>>16194243
i've just realized i think i saw a video about that idea yesterday and it was fucking insane to me how people can get that wrong
P(A) >= P(A|B)
but before i realized that my answer was "yes" because there can be more than 3 tails but there can't be more than 3 heads and tyrone isn't relevant i think?

Anonymous at Sun, 26 May 2024 15:25:47 UTC No. 16194256

>>16194253
The answer is "yes" but your reasoning isn't quite right.

Anonymous at Sun, 26 May 2024 15:26:25 UTC No. 16194257

>>16194246
Funny fact:
You are stating to be correct, despite answer is win chance is always 50%. You are another take your meds Pokemon, who cannot say anything else.

Anonymous at Sun, 26 May 2024 15:28:20 UTC No. 16194260

>>16194257
You have no human rights until you are properly medicated. The state has a right to force you to take your meds and you have no right to say 'no'.

Anonymous at Sun, 26 May 2024 15:28:51 UTC No. 16194261

>>16194256
i'm pretty sure it is but my explanation isn't exactly convincing

Anonymous at Sun, 26 May 2024 15:29:55 UTC No. 16194262

>>16194260
That doesn't change the fact, you are not correct. And you are against human rights and never reading that shit obviously.

Anonymous at Sun, 26 May 2024 15:33:43 UTC No. 16194268

>>16194262
>you are not correct
And yet you can't show anything in my little code snippet that's incorrect. Curious.

Anonymous at Sun, 26 May 2024 15:36:07 UTC No. 16194273

>>16194130
Yes because the only deviation from a 50% heads rate from fair coin flips is the three heads in a row which ends the game for each player besides Tyrone.
Since each player flips coins and finishes individually, two players ending with 50%+3 heads and one player ending with 50% should have a higher percentage of heads than one player ending with 50%+3 heads and the other player ending with 50%

Anonymous at Sun, 26 May 2024 15:38:05 UTC No. 16194275

>>16194273
>two players ending with 50%+3 heads and one player ending with 50%
What?

Anonymous at Sun, 26 May 2024 15:43:13 UTC No. 16194280

>>16194268
I don't even know what programming language it is. Seems like you couldn't even screenshot output, because it's fake.

Anonymous at Sun, 26 May 2024 15:45:40 UTC No. 16194281

>>16194280
>I don't even know what programming language it is
So what? It's completely straightforward to read. It's Nim.

>Seems like you couldn't even screenshot output,
The output is literally in the screenshot, retard.

Anonymous at Sun, 26 May 2024 15:48:54 UTC No. 16194283

>>16194281
You can get deleted car in choice.
You can reveal the car.

Like you should literally KYS.

Anonymous at Sun, 26 May 2024 15:49:31 UTC No. 16194284

>>16194283
>You can get deleted car in choice.
>You can reveal the car.
Neither one can happen. You are literally too retarded to understand even the most basic program.

Anonymous at Sun, 26 May 2024 15:50:45 UTC No. 16194286

>>16192388
>Celsius motherfucker, do you understand them

ONE country on the planet earth does NOT use the metric system... ONE

Anonymous at Sun, 26 May 2024 15:52:38 UTC No. 16194290

>>16192371
>want us to adopt a bizarre egalitarian world view in which racial differences in IQ do not exist

Anonymous at Sun, 26 May 2024 15:53:33 UTC No. 16194292

>>16194275
The game ends for Bob and Jane when they flip three heads in a row. Therefore no matter their luck or how long they were playing for, we know the last three coins they flipped came up heads. Since they flip the coins at the same time and individually stop flipping once getting three heads, Bob & Jane playing is effectively the same as if Bob's flips just counted twice.
The higher the ratio of players leaving when scoring three consecutive heads to players leaving whenever the other players do, the higher the expected percentage of heads.

Anonymous at Sun, 26 May 2024 15:53:37 UTC No. 16194293

>>16194284
You should literally stop gaslighting people.

Anonymous at Sun, 26 May 2024 15:54:54 UTC No. 16194294

>>16194293
I'm not gaslighting anyone. I'm just bullying someone who is clearly mentally ill and intellectually disabled. Maybe I should stop.

Anonymous at Sun, 26 May 2024 15:55:54 UTC No. 16194296

>>16194292
>The game ends for Bob and Jane when they flip three heads in a row.
That's not what the problem statement says.

Anonymous at Sun, 26 May 2024 15:56:19 UTC No. 16194297

>>16194294
You should explain lines 10 and 11 and start being polite.

Anonymous at Sun, 26 May 2024 15:57:50 UTC No. 16194302

>>16194220
Your door switching makes no sense

Anonymous at Sun, 26 May 2024 15:59:22 UTC No. 16194305

>>16194297
Player picks a random door. His choice is then removed from the game.

Anonymous at Sun, 26 May 2024 16:05:53 UTC No. 16194309

>>16194305
We simulated different games, no wonder probability is different.

Anonymous at Sun, 26 May 2024 16:07:02 UTC No. 16194310

>>16194309
You have an extreme mental illness. You are no longer human until you take antipsychotics.

Anonymous at Sun, 26 May 2024 16:10:08 UTC No. 16194313

>>16194310
Bully who repeats same sentence all over again, having his precious mistake simulated. Screaming people need antipsychotics...

You should get them yourself.

You're dumbfuck, and your rethorics consist mainly of gaslighting people.

Anonymous at Sun, 26 May 2024 16:12:06 UTC No. 16194317

>>16194313
I'm just trying to help you. You have a very severe psychotic episode and you need to be taken care of by professionals.

Anonymous at Sun, 26 May 2024 16:13:41 UTC No. 16194319

>>16194317
No, I don't have very severe psychotic episode.

Anonymous at Sun, 26 May 2024 16:15:06 UTC No. 16194321

>>16194317
Now get back to ball "take meds" pokemon.

Anonymous at Sun, 26 May 2024 16:15:23 UTC No. 16194322

>>16194317
>>16194319
You're both stupid, one for getting it wrong, the other for thinking "meds" is a convincing argument

Anonymous at Sun, 26 May 2024 16:16:10 UTC No. 16194324

>>16194322
I'm not trying to convince anyone. I seriously don't consider this thing to be fully human.

Anonymous at Sun, 26 May 2024 16:18:00 UTC No. 16194326

>>16194322
Well, non commutative bayes inverse,

You switched doors before revealing, therefore you are not correct.

That's it.

Anonymous at Sun, 26 May 2024 16:23:27 UTC No. 16194331

>>16194326
Ok. I see what's going on. You're not even a person, you're a spambot.

Anonymous at Sun, 26 May 2024 16:25:27 UTC No. 16194333

>>16194331
What an argument, your majesty! You truthfully understand the rhetorics!

Anonymous at Sun, 26 May 2024 16:26:35 UTC No. 16194336

>>16194333
It's programmed to keep replying no matter what. You can come back to this thread 9 hours later, (You) it and it will immediately reply because it's not a person.

Anonymous at Sun, 26 May 2024 16:27:31 UTC No. 16194339

>>16194336
Why are you mirroring it then? You also always reply...

Anonymous at Sun, 26 May 2024 16:28:24 UTC No. 16194340

>>16194339
>You also always reply...
Wrong.

Anonymous at Sun, 26 May 2024 16:30:51 UTC No. 16194342

>>16194296
Oh it says Jane quits when she lands tails three times in a row I thought it said three heads for both players. I still stand that the number of heads is different between the two games, since it would be a 50%+3, a 50%, and a 50%-3

Anonymous at Sun, 26 May 2024 16:33:42 UTC No. 16194345

>>16194342
>50%+3
>50%-3
I understand what you're vaguely alluding to, but what does this even mean mathematically?

Anonymous at Sun, 26 May 2024 16:42:45 UTC No. 16194353

>>16194345
Not that anon but if you look back at the sequence of HT prior to the three flips that ended the game you'd have an expectation that they'd be half heads and half tails.

Anonymous at Sun, 26 May 2024 16:46:13 UTC No. 16194359

>>16194345
What I'm trying to get at is that, being a fair coin with an indeterminate amount of flips, the only thing that would influence the ratio of heads to tails would be those last three flips that Bob and Jane has to get in order to end the game. Even with the coin being random, the three heads have to happen for the game to end, and no further flips happening after that result of triple heads should influence the ratio of heads to tails slightly.

Anonymous at Sun, 26 May 2024 16:49:23 UTC No. 16194362

>>16194359
That's an acceptable intuitive answer but I expected more from "/sci/ - Science & Math".

Anonymous at Sun, 26 May 2024 16:52:43 UTC No. 16194364

>>16194353
>>16194359
Shouldn't the sequence of 3 be included in the overall 50% probability?

I think the + and -3 are negligible anyway. Any specific three-flip sequence of heads and tails is equally likely as any other. Obviously the flipping will continue for longer if you have to wait for two people to get a specific sequence rather than one, but the distribution should average out to 50%

Anonymous at Sun, 26 May 2024 16:53:50 UTC No. 16194366

>>16194220
This doesn't simulate the problem at all.

Anonymous at Sun, 26 May 2024 16:56:50 UTC No. 16194369

>>16194366
Name one thing wrong with it. You can't.

Anonymous at Sun, 26 May 2024 16:56:58 UTC No. 16194370

>>16192113
you don't understand the question
>there are two doors
>one has a car, the other a goat
>you pick one
>the host shows you the picture of a goat
which way, western man?

Anonymous at Sun, 26 May 2024 16:57:28 UTC No. 16194371

>>16194362
Maybe, but I'm stupid, and I only come to the monty hall threads to laugh at people stupider than me. I'm terrible at the actually difficult statistics problems.
>>16194364
Oh yeah the three flips are negligible, but the question asks if the expected percentage of heads changes, not if it changes by a significant amount.

Anonymous at Sun, 26 May 2024 16:58:20 UTC No. 16194373

>>16194364
>I think the + and -3 are negligible anyway
They're not.

> the distribution should average out to 50%
It can't because selecting only sequences ending with 3 heads introduces a bias in favor of heads.

Anonymous at Sun, 26 May 2024 17:03:28 UTC No. 16194378

>>16194373
>It can't because selecting only sequences ending with 3 heads introduces a bias in favor of heads.
There would be a TTT sequence to balance it out

Anonymous at Sun, 26 May 2024 17:04:50 UTC No. 16194381

>>16194369
Your code deletes the goat

Anonymous at Sun, 26 May 2024 17:05:47 UTC No. 16194382

>>16194378
In the first but not in the second run.

Anonymous at Sun, 26 May 2024 17:08:16 UTC No. 16194384

>>16194381
All it does is to first remove the player's choice from the doors the host can open to reveal the goat, then the goat from the doors the player can choose to switch to, leaving only one door that the player can switch to at the end. You people are legitimately retarded.

Anonymous at Sun, 26 May 2024 17:08:17 UTC No. 16194385

>>16194382
Yes there would. You're only counting the TTT sequence that ended Jane's run, but statistically, Bob is just as likely to get TTT - it just won't end his run. And Jane can also get HHH in her run to balance out her ending sequence.

Anonymous at Sun, 26 May 2024 17:09:46 UTC No. 16194387

>>16194384
But you also delete the car

Anonymous at Sun, 26 May 2024 17:11:13 UTC No. 16194389

>>16194385
Your "logic" barely makes sense and you're wrong 100%.

Anonymous at Sun, 26 May 2024 17:12:15 UTC No. 16194390

>>16194387
>it's the broken spambot again
What a useless board. lol

Anonymous at Sun, 26 May 2024 17:15:03 UTC No. 16194397

>>16194390
I literally posted some observations about your shitty code and yuo call me a spambot. Learn to take some criticism

Anonymous at Sun, 26 May 2024 17:15:34 UTC No. 16194398

>>16194389
What part is unclear?
Any three-coin sequence is as likely as any other
TTT is therefore as likely as HHH
Any sequence of coin flips is going to average to 50% heads
The three-coin sequence that ends it is arbitrary and a red herring because its opposite is equally likely to appear in the larger sequence.

Anonymous at Sun, 26 May 2024 17:15:44 UTC No. 16194399

>>16194397
>the spambot keeps going
It probably doesn't remember the last time it posted the exact same nonsensical spam.

Anonymous at Sun, 26 May 2024 17:17:11 UTC No. 16194401

>>16194398
>TTT is therefore as likely as HHH
For whom? TTT is impossible for bob.

>Any sequence of coin flips is going to average to 50% heads
Not for the set of sequences ending in TTT.

Anonymous at Sun, 26 May 2024 17:18:02 UTC No. 16194403

>>16194399
You clearly have no idea hiw Monty Hall works and you post your shit code for everyone to see. You embarrass everyone here

Anonymous at Sun, 26 May 2024 17:18:32 UTC No. 16194404

>>16194403
>the spam bot just keeps going

Anonymous at Sun, 26 May 2024 17:20:48 UTC No. 16194406

>>16194389
>>16194398
might even argue it's biased *against* heads because TTT can appear infinite times

It's like that paradox of the king who wishes to redress the gender balance in his kingdom in favour of women, and so decrees that every couple must keep trying to have children until they give birth to a daughter, after which they stop. Counter-intuitively, it leads to more boys being born.

Anonymous at Sun, 26 May 2024 17:21:25 UTC No. 16194410

>>16194406
>might even argue it's biased *against* heads because TTT can appear infinite times
Yeah, this board is absolutely done. lol

Anonymous at Sun, 26 May 2024 17:21:50 UTC No. 16194411

>>16194401
>TTT is impossible for bob.
lol why?
>Not for the set of sequences ending in TTT.
The ending sequence is arbitrary and doesn't matter. The ending is not more important than the rest.

Anonymous at Sun, 26 May 2024 17:22:36 UTC No. 16194412

>>16194411
Statistics problems filter LLM spambots.

Anonymous at Sun, 26 May 2024 17:22:51 UTC No. 16194413

>>16194410
I'm right tho

Anonymous at Sun, 26 May 2024 17:24:42 UTC No. 16194414

>>16194413
I like how this bot also hallucinated a "paradox of the king" and a wrong answer to that problem.

Anonymous at Sun, 26 May 2024 17:24:54 UTC No. 16194415

>>16194410
Not an argument

Anonymous at Sun, 26 May 2024 17:25:55 UTC No. 16194416

>>16194415
>argue with bots
No. Just filter them using trivial statistics problems.

Anonymous at Sun, 26 May 2024 17:27:49 UTC No. 16194418

>>16194414
Your unawareness of a famous probabilty problem does not reflect poorly on me. But I had misremembered the answer.

The ratio ends up being 50-50. Just like with the coin flips.

Anonymous at Sun, 26 May 2024 17:30:20 UTC No. 16194423

>>16194418
>the broken bot contradicts itself

Anonymous at Sun, 26 May 2024 17:33:03 UTC No. 16194425

>>16194423
Point out the contradiction. You can't. Unless you think correcting myself is a contradiction.

Just so we're clear, are you the person who thinks TTT is a forbidden sequence unattainable through random chance unless you're required to end a sequence on it? Because that's ironically exactly the sort of nonsenical drivel some poorly trained chatbot might produce.

Anonymous at Sun, 26 May 2024 17:33:40 UTC No. 16194428

>>16194423
>anyone who disagrees with me is a bot
kys

Anonymous at Sun, 26 May 2024 17:35:00 UTC No. 16194433

>>16194425
Dumb, hallucinating bot.

Anonymous at Sun, 26 May 2024 17:41:13 UTC No. 16194446

>>16194433
Is anyone who's brain wasn't irretrievably fried by a glimpse of the depressing future willing to point out any flaws in my reasoning, or confirm that I'm correct? I shouldn't put too much stock in the opinion of a mentally ill person who is clearly not rational but I'm still wondering if I made some mistake which triggered him to go into a semi-catatonic state like this, and I'm not going to get it from him.

Anonymous at Sun, 26 May 2024 17:46:42 UTC No. 16194453

>>16194446
It's /sci/, the summer camping site of /pol/ tourists. Don't expect too much from these people

Anonymous at Sun, 26 May 2024 17:48:48 UTC No. 16194456

>>16194446
i can confirm that you're wrong and the expected value does change if you remove jane

Anonymous at Sun, 26 May 2024 17:56:52 UTC No. 16194464

>>16194456
Then please confirm it.

Anonymous at Sun, 26 May 2024 18:01:56 UTC No. 16194469

>>16194464
consider all possible sequences for bob, of length 3. is the percentage of heads 50%?
what about length 4? 5? etc.

Anonymous at Sun, 26 May 2024 18:18:56 UTC No. 16194485

>>16194469
>consider all possible sequences for bob, of length 3. is the percentage of heads 50%?
On average, yes.
If Bob gets HHH, he's done.
But in his first three coin flips, he is just as likely to get:
TTT
TTH
THT
HTT
HHT
HTH
THH
and after each of these he would have to keep going. The average of every possible three-coin sequence combined is 50% heads. And his next coin flip is also 50% likely to be heads. And the next. How many three-coin sequences will he get before HHH? He might even get a massive streak of T. But on average, a sequence of coin flips will be 50% heads.

Anonymous at Sun, 26 May 2024 18:22:09 UTC No. 16194489

>>16194485
>On average, yes.
what are you talking about? list all of bob's possible sequences of length 4.

Anonymous at Sun, 26 May 2024 18:28:59 UTC No. 16194500

>>16194489
If his sequence is exactly four coin flips long then obviously it is THHH. However, if Bob does not get that after four coin flips, he necessarily has to continue, and any longer sequence will include a sequence of four that is not THHH. If we look at every possible combination of four coins with the exclusion of THHH, then T is more likely. This balances out the possibility of ending the streak at four with THHH.

Anonymous at Sun, 26 May 2024 18:30:24 UTC No. 16194503

>>16194500
>it is THHH
so what's the expected heads percentage for bob's sequences with length 4? what about 5? what about 6?

Anonymous at Sun, 26 May 2024 18:31:16 UTC No. 16194504

the first time you open the door you are sampling from a 1/3 uniform distribution. after they reveal one door you get another chance to sample from another 1/2 uniform distribution which gives you better winning chance. however, you have to explicit choose to do so aka choose to switch the door otherwise you still get the "stale" sample from the old 1/3 distribution.
I hope that helped.

Anonymous at Sun, 26 May 2024 18:32:10 UTC No. 16194505

>>16194504
>. after they reveal one door you get another chance to sample from another 1/2 uniform distribution
No, you don't. You don't get to sample from anything at that point.

Anonymous at Sun, 26 May 2024 18:34:33 UTC No. 16194511

>>16194505
by your retard logic you don't get to sample anything at any time either, even your choice at the beginning. it's all deterministic.

Anonymous at Sun, 26 May 2024 18:36:34 UTC No. 16194514

>>16194511
No, it's just that the outcome of your choice to switch completely determined by the first random sample. It's not random. There is no second distribution.

Anonymous at Sun, 26 May 2024 18:38:25 UTC No. 16194518

>>16194503
Consider that THHH is no more likely than any other combination of four, and that any other combination would force him to continue.
>what about 6?
If it ends at six then even within that six coin streak, there is the possibility of 50% heads, namely TTTHHH. Of course, that specific sequence is relatively unlikely. But it is just as likely as any other sequence of six. There are a good amount of six-coin streaks that allow Bob to stop, beyond just this one. But more that would force him to continue; and a lot of them include the sequence TTT, or even TTTT and TTTTT and TTTTTT.
You should weigh the expected HT-ratio in a game-ending three (or four, or five, or six) coin streak against all the possible sequences that don't end the game there, and the relative probability of getting each of them.

Anonymous at Sun, 26 May 2024 18:40:33 UTC No. 16194523

Year of the Lord 2024
/sci/ is still baffled by the Monty Hall problem

Anonymous at Sun, 26 May 2024 18:40:43 UTC No. 16194524

>>16194518
ngl i can see why angry-kun called you a bot...

Anonymous at Sun, 26 May 2024 18:43:32 UTC No. 16194526

>>16194524
If we consider a simplified scenario where you flip a coin until you get heads, you can get:
H
or
TH
or
TTH
or
TTTH
etc. but never more than one H.
What's the expected ratio of heads to tails?

Anonymous at Sun, 26 May 2024 18:45:20 UTC No. 16194532

>>16194526
how about instead we consider the simplified scenario of all bob's possible sequences of length 5. can you list them?

Anonymous at Sun, 26 May 2024 18:47:41 UTC No. 16194540

>>16194514
think harder.

Anonymous at Sun, 26 May 2024 18:48:54 UTC No. 16194542

>>16194540
There's nothing for me to think about here. I already understand this properly. I was trying to help you reach some understanding, but you're a complete moron. Good luck with your life.

Anonymous at Sun, 26 May 2024 18:55:10 UTC No. 16194547

>>16194532
I already told you there is precisely one sequence of length five that enables Bob to stop after five coin flips. Now, how likely is Bob to get exactly that sequence of length five?

Consider it with HH as the win condition.
There is a 1/4 chance that you get to stop after two coin clips. But there is a 3/4 chance you will have to continue from either TT, TH, or HT. Of these, only TH (1/4) offers the opportunity of ending the game at three coin flips (50% likely at this point). The others require AT LEAST two more coin flips, and those two are also 1/4 likely to end it. If not, you will have to keep going till five, or more likely six.
The possibility of ending the game early is always offset by the greater likelihood of getting one of the non-winning combinations, which on average contain more T.

Anonymous at Sun, 26 May 2024 18:58:06 UTC No. 16194548

>>16194547
>I already told you there is precisely one sequence of length five that enables Bob to stop after five coin flips
ok, so what's the expected percentage of tails for bob's sequences of length 5? now do length 6

Anonymous at Sun, 26 May 2024 19:04:11 UTC No. 16194559

>>16194548
Anon, you're not getting it. How many possible sequences of five do NOT allow Bob to stop at five? If Bob gets to five coin flips, it is more likely that he will have to continue.

Anonymous at Sun, 26 May 2024 19:05:03 UTC No. 16194561

>>16194559
>How many possible sequences of five do NOT allow Bob to stop at five?
however many. now do 6 lol. keep going until you figure out the pattern

Anonymous at Sun, 26 May 2024 19:23:18 UTC No. 16194581

>>16194561
Let's stick to your initial example of three, yeah?
There are eight possible sequences of three coin flips. One of them is HHH.
The others are
TTT
TTH
THT
HTT
HHT
HTH
THH
That is twelve T and only nine H altogether, because we are excluding HHH from the non-winning sequences. So, in the likely scenario that your three-coin sequence did NOT end the game, you will get more T on average. And again, only ONE of these allows you even the CHANCE of finishing it with the next coin flip and only two let you finish it in the next two and four will require you to flip at least three more coins.
But all that is balanced out by the possibility of getting HHH in your first three coin flips. The HHH balances it out to exactly 50%. If you have an arbitrarily long sequence that ends with HHH, those last three coins just bring it to 50%. On average.

So, in other words, the overwhelming heads-to-tails ratio of the one winning three coin sequence is balanced out by the seven non-winning three coin sequences, which skew towards tails.
In fact, if we look at every sequence ending in T, we see:
TTT
THT
HTT
HHT
We see TWICE as many T as H, and each and every one of these sequences requires at least three more coin flips with equal odds as the first three. Which is again offset by TTH and HTH allowing you to end it in two, and THH allowing you to end it in one.

Anonymous at Sun, 26 May 2024 19:25:27 UTC No. 16194584

>>16194581
i'm not reading this shit lol. do what i said and you'll see why you're wrong

Anonymous at Sun, 26 May 2024 19:32:24 UTC No. 16194593

>>16194584
I am doing what you told me to do. I'm looking at the the one possible sequence of three coin flips that allows Bob to stop. And it is all heads.
But then I make the extra step of looking at the likelihood of this sequence vs. all other possible sequences of three.

Anonymous at Sun, 26 May 2024 19:34:37 UTC No. 16194596

>>16194593
>I am doing what you told me to do.
then why aren't all your sequences ending in HHH?

Anonymous at Sun, 26 May 2024 19:45:56 UTC No. 16194612

>>16194596
Only 1/8 three-coin sequences is going to be HHH.

Anonymous at Sun, 26 May 2024 19:49:47 UTC No. 16194617

>>16194612
yeah, ok, i can see why he called you a bot

Anonymous at Sun, 26 May 2024 19:53:14 UTC No. 16194620

>>16194612
kek, good troll

Anonymous at Sun, 26 May 2024 19:55:08 UTC No. 16194622

>>16194620
good trolling works the other way around: you get the victim to shit out paragraphs and reply with one-liners to keep them going

Anonymous at Sun, 26 May 2024 19:57:03 UTC No. 16194626

>>16194584
In fact, let's make this interesting. Let's look at ALL possible four-coin sequences:

TTTT
TTTH
TTHT
THTT
HTTT
TTHH
THHT
HHTT
THHH
*HHHT

You see, the average of all these sequences is 50%. But one of them is excluded. HHHT is impossible, because the game would have ended already at HHH. So the average of all allowed four-coin combinations skews in favour of tails.

Anonymous at Sun, 26 May 2024 19:57:34 UTC No. 16194627

>>16194626
still not seeing all those HHHs

Anonymous at Sun, 26 May 2024 20:00:14 UTC No. 16194634

>>16194627
You asked me about four-coin sequences as well.

Anonymous at Sun, 26 May 2024 20:01:34 UTC No. 16194637

>>16194634
ok, but all of bob's sequences end with HHH. lol

Anonymous at Sun, 26 May 2024 20:02:43 UTC No. 16194639

>>16194626
For the love of god, write some python code and run a simulation

Anonymous at Sun, 26 May 2024 20:03:56 UTC No. 16194641

>>16194637
I think I can see where you're going with this - you're committing the same mistake people make with the boy-girl paradox or with Bertrand's Box. You're forcing the outcome of a random event. You're saying, for a winning sequence of N coin flips, N-3 coin flips were 50-50, and the final three are heads, so added to the 50-50 ratio. But this ignores the fact that the final HHH sequence had to be randomly obtained and the sequence continues until it is. HHH is no more likely than any other three-coin sequence, and that's why the ratio will be exactly 50-50 regardless.

Anonymous at Sun, 26 May 2024 20:05:06 UTC No. 16194643

>>16194641
do you understand that all of bob's sequences end with HHH?

Anonymous at Sun, 26 May 2024 20:06:23 UTC No. 16194645

>>16194639
that would require him to understand the problem and i don't think he does. lol

Anonymous at Sun, 26 May 2024 20:08:19 UTC No. 16194647

>>16194643
Do you understand that HHH has to be randomly obtained?

You know Bertrand's Box, right? And the common error people make saying "well the first is guaranteed gold so it doesn't affect anything"? But actually the fact that it's randomly obtained leads to a different probability? This is like that.

Anonymous at Sun, 26 May 2024 20:10:05 UTC No. 16194648

>>16194643
>>16194647
Now, if you had a different point to make with your three-four-five coin sequences, spell it out for me, because the only one I can see is this one that's wrong.

Anonymous at Sun, 26 May 2024 20:11:28 UTC No. 16194651

>>16194647
>Do you understand that HHH has to be randomly obtained?
sure, but do you understand that all of bob's sequences end with HHH? yes/no

Anonymous at Sun, 26 May 2024 20:15:45 UTC No. 16194656

>>16194651
Yes, obviously.

Anonymous at Sun, 26 May 2024 20:17:22 UTC No. 16194658

>>16194656
write down all of bob's possible sequences of length 5, then

Anonymous at Sun, 26 May 2024 20:19:52 UTC No. 16194661

>>16194658
TTHHH
HTHHH
Your point?

Anonymous at Sun, 26 May 2024 20:23:29 UTC No. 16194663

>>16194661
based on this, can you figure out the expected heads percentage for bob's sequences of length 5?

Anonymous at Sun, 26 May 2024 20:24:23 UTC No. 16194665

>>16191290
>Let's finish this once and for all
End result: /sci/ doesn't know anything related to probability and statistics

Anonymous at Sun, 26 May 2024 20:28:49 UTC No. 16194669

>>16194663
70%
Have you noticed that getting to five coins means that HHH and THHH could not have happened? That among all sequences of three coin flips that lead to Bob winning in five coin flips, T and H are equally represented? What is the likelihood we can assign to ending the game in five coin flips?

Anonymous at Sun, 26 May 2024 20:29:26 UTC No. 16194670

>>16194669
>70%
ok, what about length 6?

Anonymous at Sun, 26 May 2024 20:29:58 UTC No. 16194671

>>16194670
Stop beating around the bush and make your point if you have one.

Anonymous at Sun, 26 May 2024 20:34:26 UTC No. 16194677

>>16194671
point is that it'll obviously be >50% for any length

Anonymous at Sun, 26 May 2024 20:40:36 UTC No. 16194682

>>16194677
No, it won't.
Three coins was 100%. Four is 75%. Then 70%. 66%. Eventually, the ratio starts to flip, as any HHH sequence is precluded from appearing earlier in the sequence. But this is counterbalanced by the likelihood of getting a sequence of a given length.

Anonymous at Sun, 26 May 2024 20:42:42 UTC No. 16194685

>>16194682
>Eventually, the ratio starts to flip
no, it doesn't

Anonymous at Sun, 26 May 2024 20:42:44 UTC No. 16194686

>>16194682
Your math is flawed

Anonymous at Sun, 26 May 2024 20:50:14 UTC No. 16194702

>>16194685
>>16194686
Consider, when you get to a nine-coin sequence.
The first six coin flips can contain six tails and five tails, but at most four heads, and also, none of the heads can be at the end of the six-coin sequence, excluding a number of sequences. By this point, the beginning of the sequence is statistically likely to contain more tails.

Anonymous at Sun, 26 May 2024 20:54:12 UTC No. 16194706

>>16194702
Coin flip results in the end do not depend on the coin flip results in the beginning

Anonymous at Sun, 26 May 2024 20:54:20 UTC No. 16194707

>>16194702
prove it lol. you're wrong and i'm not doing the legwork to show you that

Anonymous at Sun, 26 May 2024 21:07:43 UTC No. 16194724

>>16194706
They do if a certain coin flip result would have prevented the later coin flip result

>>16194707
All possible combinations of six coins:
HHHHHH HHTHHH HTHHHH HTTHHH THHHHH THTHHH TTHHHH TTTHHH
HHHHHT HHTHHT HTHHHT HTTHHT THHHHT THTHHT TTHHHT TTTHHT
HHHHTH HHTHTH HTHHTH HTTHTH THHHTH THTHTH TTHHTH TTTHTH
HHHHTT HHTHTT HTHHTT HTTHTT THHHTT THTHTT TTHHTT TTTHTT
HHHTHH HHTTHH HTHTHH HTTTHH THHTHH THTTHH TTHTHH TTTTHH
HHHTHT HHTTHT HTHTHT HTTTHT THHTHT THTTHT TTHTHT TTTTHT
HHHTTH HHTTTH HTHTTH HTTTTH THHTTH THTTTH TTHTTH TTTTTH
HHHTTT HHTTTT HTHTTT HTTTTT THHTTT THTTTT TTHTTT TTTTTT

Now we eliminate the ones which aren't allowed and we are left with:
HHTHHT HTTHHT THTHHT TTTHHT
HHTHTT HTHHTT HTTHTT THTHTT TTHHTT TTTHTT
HHTTHT HTHTHT HTTTHT THHTHT THTTHT TTHTHT TTTTHT
HHTTTT HTHTTT HTTTTT THHTTT THTTTT TTHTTT TTTTTT
See how most of the ones that skewed towards heads aren't possible in a nine-coin sequence?

Anonymous at Sun, 26 May 2024 21:09:12 UTC No. 16194727

>>16194724
i don't see them ending in HHH. try again?

Anonymous at Sun, 26 May 2024 21:10:14 UTC No. 16194730

>>16194727
These are the six-coin sequences that are allowed to precede HHH in a winning nine-coin sequence. That none of these end in HHH is part of my point.

Anonymous at Sun, 26 May 2024 21:11:16 UTC No. 16194732

>The bot is still going
The absolute state of this board.

Anonymous at Sun, 26 May 2024 21:14:50 UTC No. 16194742

>>16194730
but this is wrong. do it properly

Anonymous at Sun, 26 May 2024 21:19:39 UTC No. 16194750

>>16194742
It is not wrong, Anon. Why do you think it is wrong?
Every possible combination of HHH in the first six coin flips of a nine flip sequence has to be eliminated as a possibility, as the game would have ended before getting to nine coin flips in each of those cases. If you disagree, you do it. I've done the work of providing you all the possible combinations.

Anonymous at Sun, 26 May 2024 21:23:26 UTC No. 16194755

>>16194750
>Why do you think it is wrong?
because there should be 32 sequences and you only have 24. lol

Anonymous at Sun, 26 May 2024 21:28:17 UTC No. 16194767

>>16194755
>because there should be 32 sequences
Why? Show me which ones you're missing. Show me just ONE.

Anonymous at Sun, 26 May 2024 21:29:54 UTC No. 16194771

>>16194767
>Why?
exercise left for the reader. if you can't even figure that one out, you shouldn't be on this board

Anonymous at Sun, 26 May 2024 21:32:35 UTC No. 16194778

>>16194771
I accept your concession.

I've exhaustively shown all the possibilities. There is nothing left. I've even explained to you why. You're just shitposting at this point. It is clear that you do not understand my point and that's causing you to make unmathematical claims.

Anonymous at Sun, 26 May 2024 21:33:23 UTC No. 16194779

>>16194778
i accept your circumcision. there should be 32 sequences. you provided 24. therefore you're wrong

Anonymous at Sun, 26 May 2024 21:36:34 UTC No. 16194784

>>16194779
These are all the allowed sequences. Therefore, you are wrong.

Again, I challenge you to provide me just one sequence that I missed.

Anonymous at Sun, 26 May 2024 21:37:53 UTC No. 16194786

>>16194784
>I challenge you to provide me just one sequence that I missed.
nah. i'll just rub your nose in the fact that the number of possible sequences doubles for each subsequent length

Anonymous at Sun, 26 May 2024 21:41:47 UTC No. 16194789

>>16194786
Anon, if you would but attempt to do as I ask, you would see your folly. You are, presumably, overlooking the fact that no sequence of HHH is allowed with the first six, nor can the sixth be heads. If you eliminate all those sequences, but 24 remain.

Anonymous at Sun, 26 May 2024 21:45:19 UTC No. 16194792

>>16194789
i'm not overlooking anything, just rubbing your nose again in the fact that the number of sequences doubles every time the length grows by 1

Anonymous at Sun, 26 May 2024 21:49:13 UTC No. 16194797

>>16194792
>i'm not overlooking anything
lol
Only because you are blind.

Anonymous at Sun, 26 May 2024 21:51:32 UTC No. 16194802

>>16194797
start with THHH. how can you construct all 5-length sequences from this? and then: how can you construct all 6-length sequences from 5-length sequences?

Anonymous at Sun, 26 May 2024 21:56:53 UTC No. 16194811

>>16194802
>start with THHH. how can you construct all 5-length sequences from this?
You mean, working backwards from the final four coin flips to include all possible first coin flips?

Yes, you do that, keep going till nine, as I've said, and now, realise the snag: more and more combinations become disallowed because they contain the forbidden sequence that would have ended the game before that point. But I've explained all this already. So could you stop being an allusive twat and plainly address what you have a problem with?

Anonymous at Sun, 26 May 2024 21:59:57 UTC No. 16194814

>>16194811
>You mean, working backwards from the final four coin flips to include all possible first coin flips?
dunno what you mean. just do as i say. i'm trying to help you

Anonymous at Sun, 26 May 2024 22:00:46 UTC No. 16194816

>>16194814
No you're not. If you're trying to help, then you do as you say.

Anonymous at Sun, 26 May 2024 22:04:17 UTC No. 16194822

>>16194816
lol ok. it's only hard if you're a moron

THHH

HTHHH
TTHHH

HHTHHH
HTTHHH
THTHHH
TTTHHH

the magic of copy-paste. notice anything?

Anonymous at Sun, 26 May 2024 22:14:50 UTC No. 16194841

>>16194822
I notice that if you keep doing this you're going to fall right into my trap, because in your arrogance you've never even deigned to read any of my points that would've clearly warned you.

In fact, let's see what happens if we do it once more, with the magic of copy-paste.

HHHTHHH*
HHTTHHH
HTHTHHH
HTTTHHH
THHTHHH
THTTHHH
TTHTHHH
TTTTHHH

Uh-oh, what's that? We were expecting it to double, but... that first one isn't allowed! When we get to seven coin flips there are only seven allowed sequences.

Now let's do it once more:
HHHTTHHH*
HHTHTHHH
HHTTTHHH
HTHHTHHH
HTHTTHHH
HTTHTHHH
HTTTTHHH
THHTTHHH
THTHTHHH
THTTTHHH
TTHHTHHH
TTHTTHHH
TTTHTHHH
TTTTTHHH

Whoops, that's another! And, remember, the one we eliminated would have produced another two sequences. So that's already three fewer than you were expecting. Thirteen rather than sixteen. I can keep going but I think even you would get it by now. You can see we'll have two eliminate not one but two next, if we continue.

Anonymous at Sun, 26 May 2024 22:22:13 UTC No. 16194863

>>16194841
yeah, you got me there. my bad. you're still wrong overall, though

Anonymous at Sun, 26 May 2024 22:26:18 UTC No. 16194869

>>16194863
No, because after this tipping point you see sequences of tails predominate.

Anonymous at Sun, 26 May 2024 22:36:20 UTC No. 16194884

>>16194869
yeah, you're right about that, but you're still wrong overall because their likelihood diminishes much, much faster than the skew in favor of heads

Anonymous at Sun, 26 May 2024 22:39:22 UTC No. 16194887

>>16191290
> Let's finish this once and for all.
same thread will probably pop up in the next 2 weeks

Anonymous at Sun, 26 May 2024 22:40:31 UTC No. 16194889

>>16194884
I'm sure someone could calculate the exact probability of each sequence but I won't be the one to do it.

Anonymous at Sun, 26 May 2024 22:47:53 UTC No. 16194893

>>16194889
on average it would take 14 flips to get 3 heads in a row. you're not offsetting that bias

Anonymous at Sun, 26 May 2024 22:53:22 UTC No. 16194898

>>16194893
That's a lotta tails tho

Anonymous at Sun, 26 May 2024 23:00:53 UTC No. 16194906

>>16194898
doesn't matter. the likelihood of those sequences diminishes way faster than the bias in favor of heads

Anonymous at Sun, 26 May 2024 23:02:45 UTC No. 16194909

>>16194906
Did you do the maths on that?

Anonymous at Sun, 26 May 2024 23:07:48 UTC No. 16194917

>>16194909
no, i'm drawing a logical conclusion based on the fact that there's a significant bias in favor of short sequences, a significant bias in favor of heads in short sequences, and there is no symmetry whatsoever between the rapid decay of the likelihood of longer sequences and the slow drift towards a pro-tails bias

Anonymous at Sun, 26 May 2024 23:14:43 UTC No. 16194931

>>16194909
>>16194917
here, i simulated it and i was right

🗑️ Anonymous at Sun, 26 May 2024 23:58:37 UTC No. 16195007

The problem obviously has ambiguity regarding to the rules which doesn't give it a unigue solution. For example, if the "jugde" of the game show, or whatever he is called, always opens the door which has the goat no matter what you chose, then the probability of 1/3 that you had originally on the door that you first chose drops down to 50% because you have two doors which are strategically arranged so that the car is always in either one of them.

Anonymous at Mon, 27 May 2024 00:18:15 UTC No. 16195025

Think about it this way. Let's say that you do something today that is perfectly legal. Then the next month, the government decides that the thing you did is now illegal. Can you be put to prison because you did the illegal thing in the past when it still was legal? Of course not. At the moment of doing it, it was legal and there was nothing wrong about doing it.

How does this relate to the Monty Hall problem. Well think of the following. At the moment when you first choose the door out of three doors, the probability of winning the car was 1/3. Now the goat is revealed and there are two unknown doors remaining. The question is: can the probability of the door that you originally chose change just because the judge revealed a goat? No. At the moment of choosing the door the probability was 1/3 and that's what it will always be no matter what happens in the future.

So, with the two doors remaining, the probability is 100% that one of them has the car. YOUR door was 1/3. So what do we need to add to 1/3 to have 100%? 1/3 + x = 100%. The other door has a 2/3 chance. 2/3 > 1/3 so you should change the door.

🗑️ Anonymous at Mon, 27 May 2024 04:22:54 UTC No. 16195254

>>16191344
Who said that it can't? It certainly can, but then the probability of the group does not stay constant. If the group is doors one and three and three is the revealed goat, the P of the group drops from 2/3 to only 1/3 which means that the outsides of the group has now greater P than the inside, so in this case you should change to a door outside the group even if you first chose it inside. If door number two is the revealed goat, then the P of the group increases to 100% which is divided into 1/3 and 2/3 so you should then change the door within the group.

So it doesn't matter how you slice it.

Anonymous at Mon, 27 May 2024 04:50:13 UTC No. 16195282

>>16191344
Who said that it can't? It certainly can but then the probability of the group does not stay constant. Whether the goat is revealed inside or outside of the group you should still change the door.

Anonymous at Mon, 27 May 2024 05:55:22 UTC No. 16195328

there is no third door
there are only two to choose from
white man realizes this

Anonymous at Mon, 27 May 2024 06:13:14 UTC No. 16195342

>>16195282
I think it is a function dependent on the size and dimension of the nose on the game show host.

Anonymous at Mon, 27 May 2024 16:55:14 UTC No. 16196117

>>16194931
Go through your code line by line and notice the error you made

Anonymous at Mon, 27 May 2024 16:59:15 UTC No. 16196122

>>16196117
I am also curious to see what error he made but I am exceedingly tired of this allusive style of argumentation, so could you just tell us?

Anonymous at Mon, 27 May 2024 17:15:02 UTC No. 16196140

>>16195328
There is only one, but it's a question of how you enter it.

Anonymous at Mon, 27 May 2024 17:17:57 UTC No. 16196141

>>16195328
The interesting thing is that if you're convinced your odds are 50-50, and accordingly decide at random whether to stay or switch, your odds really will be 50-50. Mind over matter, Anon.

Anonymous at Tue, 28 May 2024 06:00:56 UTC No. 16197159

>>16196141
Schizo logic to think that reality will bend your will

Anonymous at Tue, 28 May 2024 08:50:14 UTC No. 16197410

>>16194273
lel, bad math is bad

Anonymous at Tue, 28 May 2024 09:02:58 UTC No. 16197422

The thing that pisses me off about the Monty Hall problem is the endless parade of brainlets that memorize the solution without understanding the underlying logic and then either repeat the problem incorrectly or rabidly defend the position that no matter how or why a goat door is opened, switching is advantageous

Anonymous at Tue, 28 May 2024 09:14:50 UTC No. 16197424

>>16191290
Chances of you picking the right door on your first try will always be 1/3, even if a different failure is revealed. Chances of your first choice being a goat is always 2/3. Extend the problem in your mind, if you had a million doors and chose one, then 999998 doors were opened to reveal goats, do you think its logical to stick to your original choice?

Anonymous at Tue, 28 May 2024 09:15:24 UTC No. 16197425

>>16195025
>The question is: can the probability of the door that you originally chose change just because the judge revealed a goat?
Yes. This is trivial to prove with the 2 doors case. The host's bias towards opening unchosen goat doors is what keeps it from changing. Ordinarily eliminating wrong options WOULD increase your odds of having chosen correctly initially.

Anonymous at Tue, 28 May 2024 09:24:08 UTC No. 16197428

>>16191295
>the P of the group doesn't change
That *happens* to be the case, but there's actually no reason why the probability couldn't change if the goat reveal gave you information. This is is why virtually every explanation of the problem is terrible for midwits, they actually end up thinking that probability estimations are 'stuck' and that learning things doesn't change them, when this is only the case for certain circumstances.

Anonymous at Tue, 28 May 2024 09:27:44 UTC No. 16197431

>>16197428
I'd assume the midwits you're talking about haven't taken a basic stats course because conditioning is heavily needed to pass said course

Anonymous at Tue, 28 May 2024 09:30:15 UTC No. 16197436

>>16197422
I know.

>>16192113
>>16192193
These people actually *get* it, but there are so many people who do not comprehend that the answer absolutely depends on Monty being limited in his freedom and that he could otherwise freely open a door in ways that match the scenario given, but just fucks you over.

Anonymous at Tue, 28 May 2024 09:36:26 UTC No. 16197439

>>16192193
>The only reason this question even stumps people is because that vital detail is poorly explained or glossed over.
Hard disagree. Explained correctly, the problem confuses halfwits. Explained incorrectly, the problem confuses midwits.

Anonymous at Tue, 28 May 2024 09:50:14 UTC No. 16197447

>>16191290
When you first picked it was a 1/3
When you pick again after a door was opened it is a 1/2.
Think of it this way, say you pick door 2 and he opens door 3 and door 2 and shows 2 goats. Would you switch?

Anonymous at Tue, 28 May 2024 09:54:53 UTC No. 16197450

>>16194290
Yes, IQ is a crackpot theory by some sociologist (not even science). How can you show that an IQ test measures intelligence and that IQ is a measure of intelligence, without even defining intelligence. It's all bullshit.

Anonymous at Tue, 28 May 2024 09:56:41 UTC No. 16197452

>>16197447
That assumes an unbiased host, the host is biased and will always only reveal a goat

Anonymous at Tue, 28 May 2024 10:58:07 UTC No. 16197504

>>16197424
Yes

Anonymous at Tue, 28 May 2024 12:25:07 UTC No. 16197595

This problem is always explained very poorly. It helps if the brain thinks there are stakes involved.

Consider that one of the goats is friendly, and the other will kill you if you look at it. You pick your door. If you chose the car, you will have a 50% chance of being killed when he reveals one of the goats. If you are not killed, that means you face a new scenario where the car is behind one door, and the killer goat behind the other. 50% car, 50% killer goat.

Also consider that you would have a 100% chance see the friendly goat if you had initially chosen the killer goat. The host of course would not reveal the car.

So if the host shows you a friendly goat, you have either chosen 50% car/50% killer goat, or 100% killer goat. By swapping, you are at the very least mitigating some probability that you will 100% see the killer goat to a mere 50% and maybe win your car.

The problem is less about "winning" and more about "not losing"

Anonymous at Tue, 28 May 2024 12:38:23 UTC No. 16197613

>>16191295
That's not what happens.
As soon as new information is introduced, the odds of getting the right door increase to 50% instead of 33%.
Imagine two scenarios:
1. Host asks you to pick a door. TWO doors have a donkey and ONE has a car. Simple, each has a 33% chance of being the winner.

2. In the second scenario, you pick a door, and THEN the host opens up a door that has a donkey in it. NOW, you have the choice to pick a different door. And because the host can't pick the "car door", that tells you that the door you have might have a donkey in it. Switching improves your odds from 33% chance of winning to a 50% chance of winning.

Even in the "switching" scenario, you will still lose 1/3 of the time, but the overall odds of winning have improved to 2/3 of the time.

https://www.youtube.com/watch?v=C4vRTzsv4os

Anonymous at Tue, 28 May 2024 14:26:25 UTC No. 16197731

>>16197159
Try it. You flip a coin to decide whether to stay or switch.
1/3 of the time switching would lose. So you win the car this way 1/6 of the time.
2/3 of the time switching would win. You win the car 1/3 of the time this way.
1/6+1/3 = ?

Anonymous at Tue, 28 May 2024 15:46:11 UTC No. 16197804

So, can I see it like this:

Say I have two choices instead of one. I am my own host. I start by choosing a door of the three say A. I open it, see a goat,SWITCH to B or C. So here statistically I've got better odds by switching (i.e, the action of switching itself, 2/3 or 66%), then holding onto the door (1/3 or 33%).

When the game in question begins and I choose one of the three doors, chances are the car is in the OTHER one as SWITCHING itself gives me higher odds as aided by the host when a door with a goat is opened, as now switching has only one door left.

The problem statistically analizes the outcome by weighing between the choice to either switch (right 2/3 of the time) or hold (right 1/3 of the time). The car can be in the originally selected door then, just lower odds?

Anonymous at Tue, 28 May 2024 15:50:56 UTC No. 16197806

>>16191290
Because you are allowed to change door after that.

Anonymous at Tue, 28 May 2024 16:12:16 UTC No. 16197828

>>16197804
The way the problem should be thought of is
>Does the host *deliberately* removing a goat door tell you anything relative the probability you chose correctly initially?
And the answer is no because they can always do that. It's a foregone conclusion when there's 2 goat doors and you can only keep them from choosing at most 1. So you being right stays at a 1/3 chance.

Trying to get too deep in the weeds risks coming to the wrong conclusion that your odds of having chosen correctly initially *can't* increase. They can. Most people's first instinct of it being a 50:50 is what happens if the host is just acting randomly. In that scenario, eliminating a door just spreads the odds between the other choices.

Fundamentally what complicates the problem is the uselessness of the deliberate opening of a goat door.

Anonymous at Tue, 28 May 2024 18:06:01 UTC No. 16197976

>>16196122
Not him but the obvious mistake is averaging the ratios of each run without weighting each run according to the number of coinflips.

Anonymous at Tue, 28 May 2024 18:11:52 UTC No. 16197985

>>16191290
Can you retards include "Monty Hall" in your thread title so I can filter it out? Thanks

Anonymous at Wed, 29 May 2024 09:54:31 UTC No. 16198933

>>16197985
Kek, not doing that with my next thread

Anonymous at Wed, 29 May 2024 10:42:47 UTC No. 16198969

>>16197828
That's explicitly not useless. You have two options: stay or switch. 2/3 odds with only two choices is better than random chance, and it is entirely due to the knowledge that the host will never reveal a car.

Anonymous at Wed, 29 May 2024 10:48:13 UTC No. 16198974

>>16194130
When they are all playing, expected percent heads is 0.5. When Jane isn't playing, expected percent heads is 0.55.

Anonymous at Wed, 29 May 2024 10:56:20 UTC No. 16198977

>>16198974
Proof?

Anonymous at Wed, 29 May 2024 10:57:50 UTC No. 16198978

>>16197976
The purpose of that code is to determine if the ratio of a single sequence is biased towards heads, weighting each run in that way would just give you the ratio of total heads to the total number of coin flips regardless of the sequence length, which would be the same as the probability any flip of the coin lands on heads, which is 50% for a fair coin.
The original question >>16194130 only removes a single sequence, the one ending on a tails run, and asks if removing that sequence that would change the expected percentage of heads.
That's equivalent to asking if the expected percentage of heads for the heads run terminated sequence is biased away from 50%.
The expected value of the ratio of heads can be estimated by the arithmetic mean of the simulated value over many runs. The values are already weighted by frequency of occurence, since a value that will occur twice as often as another will, on average, be added twice as often to the sum.
Therefore that code is correct.
Here's an attempt at calculating the expected ratios:

https://pastebin.com/5pPq2kJP

Average density of end tokens for sequences by terminating run length (simulated, approximated):
1: 0.69011081 0.69314718
2: 0.63555280 0.63490181
3: 0.60307957 0.60223363
4: 0.57914600 0.57783067
5: 0.55784174 0.55815776

https://pastebin.com/4LD0rq02

Average density of end tokens in prefixes before terminating run (approximate, empty prefixes are 50%):
1: 0.2498 0.25
2: 0.28098427 0.28195910
3: 0.34480386 0.34580731
4: 0.40011863 0.39949682
5: 0.43733850 0.43747325

So while the prefixes have a less than 50% percentage, the total sequence has more than 50%
This implies that the sequences are biased towards being shorter and short sequences have more end tokens because they all end with a run of them.
If sequences were longer, they would instead be biased the other way.

>>16191290
Simulation code for the goat problem:

https://pastebin.com/MXXvpGpH

stay 0.3369
switch 0.6656

Anonymous at Wed, 29 May 2024 11:05:59 UTC No. 16198984

guys i need ur help rn. what if n = 209 in this algorithm?

Anonymous at Wed, 29 May 2024 11:06:52 UTC No. 16198985

>>16198978
All right, I'm convinced. Thanks for taking the time to explain, Anon!

Anonymous at Wed, 29 May 2024 11:52:45 UTC No. 16199007

you must switch because if the car is behind one of the two doors that you haven't chosen first, you will know which one, because the host will show or has shown you which one of them holds a goat. so you're choosing between one of the three doors to be correct or one of tje other two to be correct. it's 1/3 v 2/3.

it's as if the host offered you to bet whether or not the car is in the firstly chosen door or in one of the other two, but with same odds. it makes sense to switch.

Anonymous at Wed, 29 May 2024 11:58:17 UTC No. 16199011

>>16191295
i've always viewed it this way and even posted >>16199007 before seeing your post. i owe you my upmost recognition for your image anon, as well as the recognition that the other replies on this post are retarded. very well depicted.

Anonymous at Wed, 29 May 2024 14:27:03 UTC No. 16199136

>>16194130
this anon
>>16194273
>>16194292
>>16194342
read it wrong at first but his thought process was exactly the same as mine. it's 50% + last three of the same. the percentage changes in favor of heads. is this the solution?

Anonymous at Wed, 29 May 2024 15:46:34 UTC No. 16199215

>>16198969
Uselessness with regards to increasing the odds of your initial choice being correct, ffs.

The odds of other doors having the car increase regardless. They just increase more because your initial choice doesn't have its odds improve.

Probability has to sum to 1. Eliminating outcomes with probability >0 ALWAYS increases odds somewhere.

Anonymous at Wed, 29 May 2024 17:26:13 UTC No. 16199320

>>16192328
What if they removed the 6 from the other roll and took the average

Anonymous at Thu, 30 May 2024 03:50:20 UTC No. 16200198

>>16198977
I just simulated it because I'm a nigger. Turns out the expected number of flips before getting HHH is 14, if anyone's interested.

https://pastebin.com/WqVsNS4K

🗑️ Anonymous at Thu, 30 May 2024 04:56:17 UTC No. 16200234

>>16192113
It's a lot more intuitive if you just expand the amount of possibilities.

Imagine there's twenty doors, and 19 goats. After you pick a door, I'm going to open 18 of the doors, leaving the one you picked closed, and one that you didn't pick closed, and all 18 of the doors I open have the goats.

Would you swap your choice then? Most people obviously would, because the odds they picked the goat the first time is unlikely. It's the same concept.

Anonymous at Thu, 30 May 2024 05:16:32 UTC No. 16200253

>>16191290
It's choosing two doors instead of just one.

Anonymous at Thu, 30 May 2024 05:54:34 UTC No. 16200297

>>16191290
Forget the word games about "altering the probability". Here's why switching doors is the best strategy. Suppose the car is behind door 3. There are 3 cases:
>You pick door 1, door 2 will be opened, switching doors means you win
>You pick door 2, door 1 will be opened, switching doors means you win
>You pick door 3, door 1 or 2 is opened, switching doors means you lose
So in 2/3 cases, switching your door is correct. The same applies if the car is behind door 1 or 2. Since you don't know if you selected a car or a goat, switching doors will on average lead to a win 2/3 of the time.

Anonymous at Thu, 30 May 2024 10:18:35 UTC No. 16200550

>>16191290
>most of the time you will pick a door with a goat
>that also means that most of the time, when they reveal the other goat, that the car is the only one left

Anonymous at Thu, 30 May 2024 11:40:12 UTC No. 16200625

>>16199011
the P for different amounts of doors, goats, reveals

Anonymous at Thu, 30 May 2024 12:55:02 UTC No. 16200709

>>16200625
Based excel man