🧵 Untitled Thread
Anonymous at Mon, 31 Mar 2025 14:02:51 UTC No. 16633764
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who *DOES NOT* know what's behind the doors either, flips a coin and, according to the result, opens another door, say No. 3, which happens to be a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Anonymous at Mon, 31 Mar 2025 14:04:40 UTC No. 16633766
Yes, and the fact you're asking shows you don't understand the mathematics behind the original problem
Anonymous at Mon, 31 Mar 2025 14:09:56 UTC No. 16633771
>>16633766
Oh, why's that?
Anonymous at Mon, 31 Mar 2025 14:12:39 UTC No. 16633775
>>16633764
1990 called, Marilyn.
It's been 35 years.
Anonymous at Mon, 31 Mar 2025 14:12:49 UTC No. 16633776
>>16633771
The odds of having picked the door correctly on first guess is unrelated to the hosts knowledge, since you specified he opens a goat door it doesn't matter HOW you got to the final state only that you are now there.
Anonymous at Mon, 31 Mar 2025 14:14:46 UTC No. 16633778
>>16633776
>since you specified he opens a goat door it doesn't matter HOW you got to the final state
It's explicitly random.
Anonymous at Mon, 31 Mar 2025 14:16:12 UTC No. 16633780
>>16633778
my point: proven
Anonymous at Mon, 31 Mar 2025 14:17:47 UTC No. 16633781
>>16633780
All right, then you must believe that picrel is 50-50, right? Since it specifies you got a gold ball it doesn't matter HOW you got to the final state only that you are now there.
Anonymous at Mon, 31 Mar 2025 14:19:01 UTC No. 16633783
>>16633778
>It's explicitly random.
And implicitly too. You still can't define "random".
Anonymous at Mon, 31 Mar 2025 14:19:29 UTC No. 16633785
>>16633764
I've did simulations on this problem and the result was suprising:
If you picked first door at random, your chance to find car was 1/3.
If you repicked in 2 doors remaining it was 1/2.
Sorry I didn't read the post, but I have to say this once I see a goat.
Anonymous at Mon, 31 Mar 2025 14:20:19 UTC No. 16633787
>>16633781
>waaaaaah
Retard
Anonymous at Mon, 31 Mar 2025 14:20:27 UTC No. 16633788
>>16633783
>You still can't define "random".
Already seeking refuge in semantics?
Anonymous at Mon, 31 Mar 2025 14:23:49 UTC No. 16633790
>>16633788
Told you so. You might not understand this, ever, but definitions matter in mathematics and probability.
Now go look up the answer, post it, and explain how the definition if random affects the result.
Anonymous at Mon, 31 Mar 2025 14:29:20 UTC No. 16633798
>>16633787
Anon, consider the following.
If the host picks which door to open at random, what are the odds of him opening a goat door?
If you picked the car, then it's 100%. However, if you picked a goat, then it's only 50%. Half as likely. He'd have revealed the car half the time. If you see a goat, it therefore becomes twice as likely that you have the car. On the other hand, you were initially twice as likely to pick a goat.
Your odds are therefore 1/3 * 1 vs. 2/3 * 1/2, in other words, identical.
Compare to the original problem, where it was 1/3 * 1 vs. 2/3 * 1, entirely due to the fact that the host is forced to pick a goat every single time. You're making the exact same mistake people make with Bertrand's Box: they assume that because a certain random outcome is stated to be the case, that it was therefore a given, and that leads them to discard the information.
Anonymous at Mon, 31 Mar 2025 14:31:07 UTC No. 16633799
>>16633764
>go on game show
>offered beautiful goats
>did not study math in college
>fuck fuck fuck
>choose wrong
>now i have to pay car insurance and my family will have no cheese this winter
The monty hall problem is a false problem in my opinion. Bound by temporal imagination.
There are two doors that were not going to be opened. Behind one is the good prize, the other the dud. You had a 50% chance to have chosen the correct one before the door that was going to be opened (which we know with hindsight you didn't choose and wasn't in play) was opened, and after. The third door is entirely smoke and mirrors.
Anonymous at Mon, 31 Mar 2025 14:32:09 UTC No. 16633800
>>16633798
You have 100 doors. You pick door number one.
The host generates a random number, 2-100. He gets a 2
He opens 98 doors, leaving only door 2 closed.
Do you switch?
Anonymous at Mon, 31 Mar 2025 14:34:54 UTC No. 16633802
>>16633798
Since I know you're 100% going to try to worm out of >>16633800
>The setup is the same otherwise
>The host doesn't know which door it is
>It just happened to be that all 98 doors contained goats
>The car is either behind door 1 or door 2
Anonymous at Mon, 31 Mar 2025 14:35:07 UTC No. 16633803
>>16633800
Obviously not, you said only door number two is closed so I know that my pick (door 1) contains a goat. I only wish the studio would let me take the other 97.
Anonymous at Mon, 31 Mar 2025 14:35:56 UTC No. 16633804
>>16633803
Called it.
100 - 98 = 2 btw, so 2 doors are closed, retard.
Learn to count.
Anonymous at Mon, 31 Mar 2025 14:36:03 UTC No. 16633805
>>16633800
If you're both picking at random, what makes his choice better than yours? You just witnessed an incredibly statistically unlikely event: either you picked the right door at random, or he did.
The fact that the host's knowledge of where the car is constrains his options is, in fact, crucial to the original problem, and the only reason that revealing a goat gives you information.
Anonymous at Mon, 31 Mar 2025 14:37:16 UTC No. 16633807
>>16633800
>>16633802
These are the same scenario?
Anonymous at Mon, 31 Mar 2025 14:37:42 UTC No. 16633808
>>16633804
Well okay mister no fun.
Then per my original post it doesn't matter regardless. There is always a 50/50 chance unless the host opens a car door which then nullifies the entire game anyway so the problem only exists when that does not happen, rendering it always either a 50/50 or a 0.
Anonymous at Mon, 31 Mar 2025 14:39:26 UTC No. 16633809
>>16633805
The fact that after his choice you know with near certainty that the car is behind door #2, as you only had a 1/100 chance to pick correctly on no guess.
Your odds of having picked right the first time do not go up, and having done simulations to prove it you only get 50/50 if you pick the resulting door randomly, and 2/3 if you switch. This scales up to n doors.
>>16633807
Yes.
>>16633808
Retard
Anonymous at Mon, 31 Mar 2025 14:43:26 UTC No. 16633812
>>16633809
It's just not a math problem. It's a logic problem designed to present two different mathematical solutions around a game that in reality always resolves to a 50/50 coin flip.
That's why people argue endlessly over it. It's designed to incur that outcome. The third door is not real.
If I'm a retard it's for pointing out the obvious instead of playing along with the invitation to math about it I guess.
Anonymous at Mon, 31 Mar 2025 14:44:24 UTC No. 16633814
>>16633809
>The fact that after his choice you know with near certainty that the car is behind door #2
No, you don't. In 1/100 cases, he wouldn't be able to reveal the car. In 99/100 cases, he has a 1/99 chance of not revealing the car. 99/100*1/99 = 1/100. Your odds are, again, identical. The symmetry is rather beautiful, isn't it?
>>16633812
You're incidentally right for all the wrong reasons.
Anonymous at Mon, 31 Mar 2025 14:47:47 UTC No. 16633817
>>16633812
Lets look at the past, shall we?>>16633798
>B-but you are in le Bertrand BOX!!!
And now what are you saying?
>IGNORE THE MATH, ONLY LOOK AT THE PROBLEM AS PRESENTED
>>16633814
You picked a door randomly out of 100. Only 1 has a car, so you have a 1/100 of having the right guess.
After opening 98 other doors, none of which were cars, there are 2 doors closed: your choice and the hosts secret door.
It does not matter if the host knows who's right, you only know you're almost certain to have been wrong.
The worst you could say here is that you now have a 50/50 from picking randomly, but any logical person would realize that their odds of having picked right blindly haven't gone up from 1/100.
Anonymous at Mon, 31 Mar 2025 14:54:22 UTC No. 16633828
>>16633814
>both doors are 1/100
I was also thinking this lol.
>You're incidentally right for all the wrong reasons
What do you mean by that? There are only two outcomes from square one: monty opens a car door or he doesn't. If true, your probability of having made the correct choice is 0 and was from the instant you made it. If false, your probability is and was 50%. Monty was always going to open a door, and you were always going to have chosen one he won't open, and in the only relevant outcome of his choice to the game your choice was 50/50. Before you even make your choice, the game is either locked into a 50/50 or a 0 by the fact that Monty will make a choice. It's an answer set of 2 with one discardable answer.
>>16633817
That post wasn't me. I came here mainly to post about how a goat is a superior prize to a car but I decided to give my input on monty hall also. >>16633799 is me.
Anonymous at Mon, 31 Mar 2025 14:57:14 UTC No. 16633830
>>16633828
>>16633814
>>both doors are 1/100
So, to be clear, when you retards are presented with 2 closed doors, 1 of which contains a car, even ignoring the aspect of previous choice, there is a 98% chance the car is behind neither door, when you know from the setup that there is a 100% chance the car is behind one of them?
Proof by contradiction, I'm right and you're wrong. Even if you still won't admit I'm right, you have to admit that you're now wrong claiming there's only a 2% chance of a car being behind one of the closed doors.
Anonymous at Mon, 31 Mar 2025 14:57:34 UTC No. 16633831
>>16633817
Would it surprise you to learn that there appear to be at least two others in this thread besides you and me? I never said to ignore the maths. Why do you think I'm arguing with "myself"?
Your mistake is that you fail to take into account how incredibly unlikely it is for the host not to reveal the car among 99 doors if it's there. Yes, it's 99 times more likely to be among those doors, initially - but with each door that is opened, it becomes less likely. Because the host is choosen at random.
>>16633828
>What do you mean by that?
It matters whether or not the door is opened randomly. It's 50-50 now, but not if the host knows how to avoid the car.
Anonymous at Mon, 31 Mar 2025 15:02:08 UTC No. 16633834
>>16633830
>there is a 98% chance the car is behind neither door
No, not when there are two left. There was, however, a 98% chance that the car was behind neither door. There was only a 2% chance of getting to the point where there are two doors left and no car is revealed. And, of those 2%, 1% accounts for you picking the car initially (in which case Monty couldn't have revealed it), and the other 1% accounts for the car being among the other 99 doors (which is 99% more likely) *and* Monty then also not revealing it after opening 98 of them (which is, conversely, very unlikely again).
Anonymous at Mon, 31 Mar 2025 15:03:15 UTC No. 16633838
>>16633771
He opens the goat door which gives you more information about the system. How he got about to opening the goat door is irrelevant. Your newfound knowledge about goat door is what affects probability.
Anonymous at Mon, 31 Mar 2025 15:06:07 UTC No. 16633841
I get being caught off guard by the problem and unwilling to accept the result 40 years ago but if you still have a problem with it in current day it's either stupidity or willful ignorance.
Anonymous at Mon, 31 Mar 2025 15:06:10 UTC No. 16633842
>>16633838
See >>16633798
Here's the information that seeing a randomly revealed goat gives you: it is now less likely than before that you didn't pick the car.
Anonymous at Mon, 31 Mar 2025 15:08:57 UTC No. 16633845
>>16633841
I think you got caught off guard, but I don't blame you. I did sneakily alter the problem a little to catch those who don't read carefully.
Anonymous at Mon, 31 Mar 2025 15:09:57 UTC No. 16633846
>>16633830
>monty presents me 100 doors
>i pick one door not to open
>1/100 to be right
>monty picks one door not to open
>if his choice was independent of mine, 1/100 chance to be right
>if his choice was changed by my choice removing an option, 1/50 chance to be right
>monty's choice is either twice as likely to be right as mine or half as likely to be right as mine depending on an unknowable variable, presenting two entirely separate mathematically correct answers
>a shell past this, is the separate logic problem of whether monty opening a car door is even a relevant part of the solution set at all or if his choice is just a 1/3 roll on simply ending the game, in which case it would be correct to treat it as a foregone conclusion that either monty was never going to open the car door or the question never mattered
See what I mean? Designed to make people argue. The correct answer is give me my goat.
>>16633831
Ah I see what you mean. My contention sort of poorly explained above would be that even the random choice scenario should be treated the same as a scenario where the host always avoids the car, because we are really only considering the scenario where he randomly did not choose the car to open. If he opens the car door your second choice didn't matter, it won't get made. So in situations where the choice to switch is relevant the car door was always going to be opened.
Anonymous at Mon, 31 Mar 2025 15:11:31 UTC No. 16633847
>>16633831
Oops lol completely reversed my statement with a single word. Meant:
>In situations where the choice to switch is relevant the car door was NEVER going to be opened
Anonymous at Mon, 31 Mar 2025 15:11:49 UTC No. 16633849
>>16633781
Back to Bertrand's Box:
You all acknowledge that it matters whether or not the first ball is chosen at random, right? If you get a gold ball at random, it is twice as likely to have come from the ball that always gives you gold than from the one that only gives you gold half the time. But if you are guaranteed to get gold every time, it's a 50-50 choice between two possible boxes.
If you can see why randomness matters here, you should be able to see why it matters to Monty Hall.
Anonymous at Mon, 31 Mar 2025 15:14:16 UTC No. 16633850
>>16633846
>if his choice was independent of mine, 1/100 chance to be right
>if his choice was changed by my choice removing an option, 1/50 chance to be right
That doesn't sound right
Anonymous at Mon, 31 Mar 2025 15:17:06 UTC No. 16633854
>>16633831
>>16633834
>>16633846
Retards, proven experimentally. Picrel.
How do you dumbasses literally not get the most basic logical thinking? You have to be at least 18, right, so you should get this.
Anonymous at Mon, 31 Mar 2025 15:21:10 UTC No. 16633859
>>16633764
If you switch the door the probability is 66% to get it correct the 2nd time. It's pretty good explained in the movie "21" (great movie btw)
https://youtu.be/CYyUuIXzGgI
Quote of one of the YT commends:
"While many people explain to those who do not understand it, they often fail to explain why the probability of 33.3% is added on top of the other probability. Let's consider a simplified scenario for those who think the chances should be 50/50:
Let's say there are three doors, and behind them are like the following:
Goat - Car - Goat
Let's look at all the possibilities.
If you choose Door 1, the host must open Door 3, and if you change your choice to Door 2, you win.
If you choose Door 2 and decide to change your door, you lose.
If you choose Door 3, the host must open Door 1, and if you change your choice to Door 2, you win.
As we can see, in all three possibilities where you change your door, you win twice out of the three possibilities.
Similarly, let's consider the possibilities where you stick with your initial choice:
If you choose Door 1, you lose.
If you choose Door 2, you win.
If you choose Door 3, you lose.
We can clearly see that the strategy of changing your door gives you a higher chance of winning the prize. It's not a 50/50 scenario, but rather a 2/3 probability of winning if you switch doors. When host opens one of the remaining doors, he provides you with a new information. This information is not changin the initial probabilites but rather telling you that:
"The probability of the car being in one of the 2 doors you did not choose is 66.7% and I am opening one of these doors for you. In the beginning there was a 66.7% probability that the car was in one of these two doors, and I showed you which of these doors had a goat."
The 33.3% probability was added because of the information the host gave us. Thus, when we change our door, we have a 66.7% probability of winning."
Anonymous at Mon, 31 Mar 2025 15:22:14 UTC No. 16633861
>>16633854
>If the car door is anything but 0, host will open all doors except it
You are forcing the host to act as if he knows where the car is, you dope. You've just recreated the original Monty Hall again. The host revealing the car does end the game, but that doesn't mean you can just ignore the probability of that happening.
Here's how you properly simulate it: just have the host open the other doors besides yours at random, and then stay or switch to the remaining closed door. Both will have a ~1% win rate. Yeah, it's an unfair game. The house always wins, baby.
Anonymous at Mon, 31 Mar 2025 15:23:13 UTC No. 16633863
>>16633861
The game ends.
In my situation, the game is restated and rerolled over and over until it works out.
Do you think a game end should count as a win?
Anonymous at Mon, 31 Mar 2025 15:26:12 UTC No. 16633867
>>16633863
No, it counts as a loss. We can assume that the host either doesn't offer a switch if the car is revealed, or just offers to switch to the remaining closed door. Staying and switching therefore both have a 99% loss rate if the host doesn't know where the car is.
Anonymous at Mon, 31 Mar 2025 15:29:14 UTC No. 16633870
>>16633867
In what world would that count as a loss?
Anyway, you're changing the game from the original, you said explicitly that he DOES NOT OPEN the car door in yours.
The simulation shows that you are wrong, period.
If you want to pose a different scenario, feel free to try again, but first tell me with your hands typing words to my screen that you were WRONG.
Anonymous at Mon, 31 Mar 2025 15:34:53 UTC No. 16633875
>>16633870
>In what world would that count as a loss?
You don't get the car.
>you said explicitly that he DOES NOT OPEN the car door in yours.
I said he happens not to reveal the car, randomly.
Let's go back to three doors.
You pick A.
If the car is behind A (odds 1/3):
>the host reveals a goat, every time
If the car is behind B (odds 1/3):
>Host reveals a goat half the time (1/6)
>Host reveals the car half the time (1/6)
If the car is behind C:
>Host reveals a goat half the time (1/6)
>Host reveals the car half the time (1/6)
If we restrict ourselves to only the times that the host reveals a goat, how likely is it then that the car is behind either B or C? 1/6 + 1/6. Which is the same as the odds that it's behind A.
Anonymous at Mon, 31 Mar 2025 15:36:01 UTC No. 16633876
>>16633875
Hey fucking retard
Read the OP again
Once you get into that situation, it is ALWAYS RIGHT TO SWITCH.
I proved this emperically.
Tell me with your words you were wrong, and that it IS right to switch once you get into the situation that you laid out in OP
Anonymous at Mon, 31 Mar 2025 15:36:06 UTC No. 16633877
>>16633870
>you said explicitly that he DOES NOT OPEN the car door in yours.
Incidentally, this is why I brought up Bertrand's Box.
>But you said the first ball is always gold!
Anonymous at Mon, 31 Mar 2025 15:41:11 UTC No. 16633883
>>16633877
I like the deflecting. Say with your mouth that you were wrong.
Anonymous at Mon, 31 Mar 2025 15:42:31 UTC No. 16633885
>>16633876
>Once you get into that situation, it is ALWAYS RIGHT TO SWITCH.
I mean, it's not *wrong* - it offers no advantage or disadvantage compared to the alternative.
>I proved this emperically.
No, you accidentally wrote a simulation of the original Monty Hall problem, because you don't understand randomness, or how the Monty Hall problem hinges upon the host's knowledge. When the host chooses at random, you have to weigh the probability of picking the car initially against the equally unlikely probability of the host not revealing it if you don't. This in contrast with the original, where the probability of the host revealing the car is 0. Surely you don't think that wouldn't make a difference?
>>16633883
>The first ball is always gold! That's why it's 50-50!
Explain to me why Bertrand's Box is not 50-50. I mean, I know why. But using your method, it should be 50-50. You see that, right?
Anonymous at Mon, 31 Mar 2025 15:43:26 UTC No. 16633888
>>16633850
Yeah I fucked that up trying to condense an already too verbose greentext lmao. 1/99, so about 1/100 of a percent more likely than player choice to be correct. But then, by the time he's opened 97 doors it becomes the original problem again, and if he opens a car in the interim we were in the 0 outcome all along. So it's still always 50/50 or 0, the fraction there is a meaningless step. Still dumb of me though lol. Must be too starved of goat cheese.
Anonymous at Mon, 31 Mar 2025 15:45:57 UTC No. 16633892
>>16633885
You picked a box that contains a gold ball, which could either be
LL LR CL
CR RL and RR are all eliminated as possibilities
Any one of these is equally likely, 33%
In 2 cases, the other ball is gold. in 1 case it is silver
2/3 = 66%
Anonymous at Mon, 31 Mar 2025 15:46:37 UTC No. 16633893
>>16633861
>The host revealing the car does end the game, but that doesn't mean you can just ignore the probability of that happening.
NTA, goatanon, you can though! Your first choice is functionally meaningless because it's followed by a binary state of the game either ends if it doesn't. All that matters are scenarios where you are at the second choice already, and in every case that is a 50/50 choice, because a car door was never going to be opened before the final 2 in those scenarios. So in reality there was always a 100% chance of the car being in one of the two final doors, no matter how many doors you add.
Anonymous at Mon, 31 Mar 2025 15:46:57 UTC No. 16633895
>>16633885
If the game ends with you losing the moment he reveals a car, then the only game states in which you get to play are those where the car is hidden
In all gamestates where the car is hidden, you are better off switching.
How are you so dense?
Anonymous at Mon, 31 Mar 2025 15:47:56 UTC No. 16633897
>>16633892
>LL LR CL
wot
>CR RL and RR are all eliminated as possibilities
???
Anonymous at Mon, 31 Mar 2025 15:49:46 UTC No. 16633901
>>16633897
<box> <ball>
[L]eft [C]enter [R]ight
I don't know why I expected a retard as dense as you to be able to use context clues and common shortenings to understand a post, though. Next time I'll be sure to spell it out.
Anonymous at Mon, 31 Mar 2025 15:52:07 UTC No. 16633906
>>16633893
>Your first choice is functionally meaningless because it's followed by a binary state of the game either ends if it doesn't.
So is Russian Roulette. The first pull of the trigger is still relevant.
>So in reality there was always a 100% chance of the car being in one of the two final doors
That's wrong, though. If the host can never reveal the car, then yes, there was always a 100% chance that the car was going to be among the final two. But you are mistaking the outcome for a guarantee.
>>16633895
No, see >>16633875
If the host chooses at random, then in all gamestates where the car is hidden, you know precisely nothing.
Anonymous at Mon, 31 Mar 2025 15:52:18 UTC No. 16633908
>>16633895
>In all gamestates where the car is hidden, you are better off switching
False. In all game states where the car is hidden your choice to switch or not to switch is rendered irrelevant. If you were always going to land at 2 doors and an open dud the third door was never a part of the equation.
Anonymous at Mon, 31 Mar 2025 15:54:51 UTC No. 16633910
>>16633908
>>16633906
How do people not understand Monty Hall after 50 years.
People figured this shit out before you were even born
You can run a simulation and prove it to yourself, you can run billions of simulations in a single minute to boil it down to the pure chance
Anonymous at Mon, 31 Mar 2025 15:55:48 UTC No. 16633914
>>16633901
Fuck's sake why are you using the same letter to denote balls and boxes? Use the colours like a normal person.
The point is GG and GS are the options and the order doesn't matter. GG is twice as likely as GS.
Anonymous at Mon, 31 Mar 2025 15:56:31 UTC No. 16633915
>>16633906
It's not comparable to russian roulette though, because your initial pull doesn't remove an option. It's like playing russian roulette with the safety on for the first trigger, then unloading all but two of the chambers, then (assuming the live round didn't just fire into a wall) asking whether you want to pull with the safety off on the final chamber, or the one you skipped initially.
In other words, it always resolves down to either an incomplete game or a 50/50 between one guaranteed bullet and one randomly chosen empty chamber, with no way to gauge whether your initial choice or Monty's final unopened door is the one that shoots you in the head with a goat.
Anonymous at Mon, 31 Mar 2025 15:57:09 UTC No. 16633916
>>16633914
Thanks for repeating my point back to me retard.
>i can't read
>i didn't understand
>let me tell you what i think
Anonymous at Mon, 31 Mar 2025 15:57:35 UTC No. 16633918
>>16633910
Anon, we're talking about randomness here, it's not the classic Monty Hall problem.
I knew this would be a great thread topic because a lot of people who are convinced they get it in fact don't. They've memorised the answers but they can't deal with a curve ball like this.
Anonymous at Mon, 31 Mar 2025 15:58:48 UTC No. 16633920
>>16633771
>Oh, why's that?
Sorry, I don't speak Jig Latin.
Anonymous at Mon, 31 Mar 2025 15:59:44 UTC No. 16633924
>>16633918
In the case where you get to 2 doors, it's standard monty hall.
In the case where you lose on car being revealed, the game is over, you never can switch.
I know it's hard to undestand, but adding an extra losing gamestate that you DONT REACH as per the OP is like saying
>but you're ignoring the silver balls
in the box thing.
Yes, I am ignoring the silver balls and the instant loss game, because that's what you asked me to do
You're literally stuck in the box
Anonymous at Mon, 31 Mar 2025 16:03:24 UTC No. 16633930
>>16633910
>People figured this shit out before you were even born
Well yeah the guy who wrote the problem in the first place "solved" it. But it's a trick based on a false premise that the first choice matters. Whether or not your door contains the car alters Monty's choices, which makes both random. If you pick the car, Monty opens a completely random door.
The question may as well be
>There are two unopened doors. Behind one of them is a car. One of them has your name on it. You have no additional information. Which do you open?
Anonymous at Mon, 31 Mar 2025 16:04:35 UTC No. 16633932
>>16633916
Not my fault you've written down Bertrand's Box in the most unintuitive way possible.
But at least you understand that getting gold tells you that the gold box is twice as likely. Why's that, when your first pick is guaranteed to be gold? The game ends if you don't get gold, right? So we dismiss those probabilities? Is that not how it works?
Anonymous at Mon, 31 Mar 2025 16:06:26 UTC No. 16633934
>>16633924
>I know it's hard to undestand, but adding an extra losing gamestate that you DONT REACH as per the OP is like saying
>but you're ignoring the silver balls
>in the box thing.
Exactly my point - if you ignore all the times you get silver on your first pick, the problem becomes identical to
>you have a box which is guaranteed to have at least one gold ball, here it is, now which one contains the other gold ball?
Which is, in fact, the wrong way to model it.
Anonymous at Mon, 31 Mar 2025 16:16:31 UTC No. 16633947
Actually kinda funny that the same people who go
>It's really intuitive if you imagine 100 doors, how unlikely is it that you picked the car?
do not grasp how unlikely it is for Random Monty to pick the car
Anonymous at Mon, 31 Mar 2025 16:20:11 UTC No. 16633949
>>16633947
>Be random Monty
>Cannot rig the game to never pick the car
>The game however dictates you not pick the car
>Simply roll a perfect 99 every time
Anonymous at Mon, 31 Mar 2025 16:20:25 UTC No. 16633950
>>16633920
Pardon me, good sir, but why do you believe that to be the case?
Anonymous at Mon, 31 Mar 2025 16:22:09 UTC No. 16633952
>>16633949
Can't tell if you're arguing with me or agreeing with me lol
Because yeah it would be ridiculous if the Fates conspired to prevent Monty from revealing the car, try as he might. That's some Greek tragedy shit.
Anonymous at Mon, 31 Mar 2025 16:33:27 UTC No. 16633964
>>16633952
I'm the goatmilk anon who was arguing that the entire Monty Hall question is a deliberate farce made to make people argue (and to sell magazines). You just put the image of rngesus blessed random Monty in my head and it was too funny not to greentext.
>it would be ridiculous if the Fates conspired to prevent Monty from revealing the car, try as he might. That's some Greek tragedy shit
LMAO
Anonymous at Mon, 31 Mar 2025 16:35:20 UTC No. 16633967
>>16633947
Monty hall problem falls apart when you make your pick knowing the host isn't going to reveal the fucking car first because that makes for bad TV.
Anonymous at Mon, 31 Mar 2025 16:36:29 UTC No. 16633969
>>16633967
Wasn't meant to be a reply my bad
Anonymous at Mon, 31 Mar 2025 17:14:09 UTC No. 16634001
All right, 100 doors - but Monty opens them randomly, one by one. So, you pick one, then he picks one of the remaining 99, and reveals a goat. Picks another of the 98 remaining doors, and reveals a goat. Picks one of the 97 doors, and reveals a goat. Etc. etc. until he has done this 98 TIMES and you are left with just two doors.
You see just how unlikely it is to get that outcome randomly? Unless! Unless Monty wasn't able to select the car at all. But that is only the case if you happened to have it. What was initially quite unlikely (you selecting the car at random from among 100 doors) becomes more and more likely with each door that is opened - as it becomes less likely that the car is among the doors you didn't pick, in an inverse relationship. Until finally it's just as likely as the car being behind the one you did pick.
If you think this is no different from regular Monty Hall then you're saying that Monty's odds are the same whether or not he knows where the car is.
Anonymous at Mon, 31 Mar 2025 17:28:37 UTC No. 16634019
>>16634001
Or, here's another elegant solution:
You select one door from among 100, and Monty, ever the showman, begins to open the rest one by one, until one of the following conditions is met:
>He reveals the car
>Your door is the only one left, confirming you've won
1% of the time, he'll reveal the car on the first try. 1% of the time he'll reveal it on the second. 1% on the third, etc. and 1% of the time you win.
The cumulative odds are: 1% of the time the car was in the first door he picked, 2% of the time it's in the first two, 3% it's among the first three, etc. until finally, 98% of the time it'll be among the first 98 doors that he picks. Getting to the point where there are only two doors represents 2% of all cases. Of those, 1% of the time it's door 99. 1% of the time it's yours. He may as well flip a coin at this point.
Anonymous at Mon, 31 Mar 2025 17:32:21 UTC No. 16634021
>>16634001
Ah good but this still doesn't change the odds on the switch. Again, try to think atemporally. Every time Monty lands a goat, the odds for a car increase for his next roll, if we stop and compound there. But with a precondition that Monty will never open more than N-2 doors, the game is still always built around a string of disconnected dice rolls culminating to a 100% chance in any Lucky Monty timeline that the car will be equally likely to be behind either of the two remaining doors at the moment of your second choice. No matter what the variations, in an endgame Monty Hall timeline, Monty is shuffling cups around and then handing you a coin flip at the end.
Anonymous at Mon, 31 Mar 2025 17:37:27 UTC No. 16634026
>>16634019
Correct answer, based!!
>goatanon
Anonymous at Mon, 31 Mar 2025 17:51:24 UTC No. 16634034
>>16634021
>No matter what the variations
Ah, but that's the thing, if his choice is constrained, you have the advantage - and, in fact, it should be easy to see why, if we consider the times when it really is 50-50.
Anonymous at Mon, 31 Mar 2025 18:07:18 UTC No. 16634048
>>16634034
It's a collapse of a sort of informational superposition. Even without a random element, when Monty narrows it down to two doors he's altering the conditions you thought were true when making your initial choice. The second choice in a Chained Monty timeline is always predestined to tell you the car is behind either the door you picked or one other. An arbitrary third door will always have been going to disappear from consideration, as Caged Monties pull the curtain away and reveal there was actually a 1 in 2 chance that your initial choice was correct. There were never any doors in play but the car door and one arbitrary wrong door which you or Monty would always select. That's why a Lucky Monty with an arbitrary number of doors N, and a Caged Monty are functionally identical. The contestant has always picked one of the two doors present in the final choice, both of which have a 1/N chance to contain a car.
Anonymous at Mon, 31 Mar 2025 18:22:17 UTC No. 16634068
>>16634048
Consider >>16634019 again, but this time Monty knows where the car is. 99% of the time, the car is among the doors you didn't pick, as before,
but 100% of the time, the car will be among the last two doors, as opposed to the 2% from before. You're still 1% likely to get it right on the first try. But Monty doesn't reduce the odds of the car being among the remaining doors by opening them, because he was always saving it for last. Meaning there always was a 99% chance that the car is in the last remaining door, and that remains that way.
It is funny though that there are two people who think Random Monty and Regular Monty are identical problems with the same solution yet they disagree on what that solution is.
Anonymous at Mon, 31 Mar 2025 19:23:02 UTC No. 16634121
>>16634068
Actually no yeah you're right. In rigged Monty Hall you should always switch, in random it doesn't matter but the game is also completely broken by random. Dumb of me.
>It is funny though that there are two people who think Random Monty and Regular Monty are identical problems with the same solution yet they disagree on what that solution is
Honestly I think I just got lost in the 4D Monty Hall with multiversal time travel meme.
Anonymous at Mon, 31 Mar 2025 19:35:49 UTC No. 16634132
>>16634121
>Actually no yeah you're right. In rigged Monty Hall you should always switch, in random it doesn't matter but the game is also completely broken by random. Dumb of me.
I gotta say, it's rare to read this on 4chan. You're uncommonly intellectually honest for this place, perhaps even in general, and for what it's worth, I enjoyed our back and forth.
>Honestly I think I just got lost in the 4D Monty Hall with multiversal time travel meme.
kek, happens to the best of us (I actually have no idea what you're talking about)
Anonymous at Mon, 31 Mar 2025 19:47:15 UTC No. 16634146
>>16633764
The details of the host's knowledge and strategy are crucial to this problem. For the usual version, the host is assumed to know what is behind the doors, and to deliberately show a goat. In that case, you are better off switching (2/3 vs 1/3 of winning).
In the version you have described, the host doesn't see what's where, and happens to choose a goat. In that case changing door doesn't affect your odds (50 50 either way).
The actual Monte Hall said that his actions depended on his mood, and how he thought the contestant would react, which is beyond modelling. You could have a trickster Monte who tried to trip you up, in which case you'd be better sticking (100 to 0) or a helpful Monte, in which case you'd be better switching (0 to 100).
Eyedol at Mon, 31 Mar 2025 22:46:39 UTC No. 16634274
>>16633849
>>16633781
So it's 2/3? If you ran this experiment 100 times 66% of the gold balls will be from the first box?
Anonymous at Mon, 31 Mar 2025 22:53:40 UTC No. 16634280
>>16634274
Yeah but they're not exactly the same problem. Bertrand's Box is 2/3 when it's random and 1/2 when it's not. Monty Hall is 1/2 when it's random and 2/3 when it's not. Point is just that it's wrong to say that randomness doesn't matter.
Anonymous at Mon, 31 Mar 2025 23:46:23 UTC No. 16634331
>>16633781
Gambler's fallacy, it's 2.05/6
Anonymous at Mon, 31 Mar 2025 23:57:25 UTC No. 16634340
>>16633764
https://tinkerdeck.com/projects/mon
Anonymous at Tue, 1 Apr 2025 00:09:56 UTC No. 16634349
A distressing amount of people either do not read the OP or think it doesn't matter if Monty opens doors at random
Anonymous at Tue, 1 Apr 2025 00:46:28 UTC No. 16634377
>>16633766
>Yes
ok, I guess again and still pick door 1, now my odds are 50/50
Anonymous at Tue, 1 Apr 2025 00:51:54 UTC No. 16634383
>>16633764
>Suppose you're on a game show, and you're given the choice of 100 doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who *DOES NOT* know what's behind the doors either, rolls a d100 and, according to the result, opens every other door except what show on the d100, which all happens to be goats. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Yes, I would switch my choice
Anonymous at Tue, 1 Apr 2025 01:25:27 UTC No. 16634439
>>16634246
This isn't the Monty Hall problem. It's the Monty Fall problem. Different problem with a different solution.
>>16633764
No.
Anonymous at Wed, 2 Apr 2025 08:36:51 UTC No. 16634830
>>16634383
You're going to be disappointed about half the time. So what, exactly, makes you think your 1/100 odds of getting the car are so much worse than Monty's 1/100 odds of getting the car? To the tune of 99 times? If you've both rolled a d100, why is his one virtually guaranteed to win? Do you think that if I wrote down a random number between 1-100, that you are guaranteed to get it if you roll a d100 twice?
What if you have a pile of 100 coins, 99 of them fair, one of them double-headed? You take one coin at random, flip it ten times, and get ten heads. Are you still 99% sure it's a fair coin?
Years of Monty Hall threads and all you've learnt is to reflexively switch when you see a goat but no car, rather than actually applying conditional probability.
Anonymous at Wed, 2 Apr 2025 10:01:09 UTC No. 16634866
>>16633764
>Is it to your advantage to switch your choice?
Yes since your initial choice still only has 1/3 chance of being right.
Barkon at Wed, 2 Apr 2025 10:15:49 UTC No. 16634874
This thread exemplifies the need for intervention into some of sci posters minds, perhaps with more severe medication than antipsychotics.
Anonymous at Wed, 2 Apr 2025 10:28:35 UTC No. 16634882
>>16634866
And so does the other choice.
The remaining 1/3 you don't even get to this point because the host will have revealed the car. So if he happens to reveal a goat, it's a choice between two options with identical odds.
>>16634874
They don't have medication for hubris, unfortunately.
Anonymous at Wed, 2 Apr 2025 12:01:15 UTC No. 16634951
>>16633854
If you think this is an accurate simulation of the problem presented in this thread, then how would you modify it to model the regular Monty Hall problem? It has to be different, right?
Anonymous at Wed, 2 Apr 2025 13:11:51 UTC No. 16634994
>>16634830
unlikely =/= impossible
Anonymous at Wed, 2 Apr 2025 13:16:40 UTC No. 16634997
>>16634994
No, of course not. It is absolutely possible that Monty did, in fact, get the car. In fact, I told you exactly how possible it is. It is equally as possible, however, that you have the car instead.
Anonymous at Wed, 2 Apr 2025 13:22:22 UTC No. 16635002
>>16634997
Your basic appeal was that fair coin can't turn up the same time 10x in a row. This is not true. Whatever part of your conclusion that stems from this is also invalid.
We are actually in the multiverse where Monty is just born to pick goat doors.
Anonymous at Wed, 2 Apr 2025 13:27:10 UTC No. 16635006
>>16635002
>Your basic appeal was that fair coin can't turn up the same time 10x in a row.
No, Anon. The appeal is that it's unlikely. You know how unlikely it is to get ten heads in a row? Far more than picking a specific random coin from a pile of 100.
>We are actually in the multiverse where Monty is just born to pick goat doors.
You are just denying the premise now. The question is, what if we aren't?
Anonymous at Wed, 2 Apr 2025 13:32:14 UTC No. 16635011
>>16635002
>>16635006
>You know how unlikely it is to get ten heads in a row? Far more than picking a specific random coin from a pile of 100.
In fact, we can calculate exactly how many times you would have to flip the coin before it becomes more reasonable to assume that you got the double-headed one.
One flip: 1/2
Two flips: 1/4
Three flips: 1/8
Four flips: 1/16
Five flips: 1/32
Six flips: 1/64
Seven flips: 1/128
After six heads, you're still more likely to have a fair coin. After the seventh, the balance tips.
>Ah but actually er clearly this is the multiverse where I get heads no matter what
Anonymous at Wed, 2 Apr 2025 13:46:15 UTC No. 16635029
>>16633764
Not this shit again, i refuse to believe that simply changing your mind can change the probability of something, it just doesn't make any sense.
Anonymous at Wed, 2 Apr 2025 13:56:50 UTC No. 16635039
>>16635029
It's not changing your mind that does it, as the present variant of the usual Monty Hall problem shows. It's the host's behaviour. If he is guaranteed not to reveal the car, his odds of getting the car are naturally higher than your random chance.
Anonymous at Wed, 2 Apr 2025 13:57:27 UTC No. 16635041
the host will never reveal the car, that is what boosts your chances by switching
Anonymous at Wed, 2 Apr 2025 13:58:01 UTC No. 16635043
>>16635011
Incorrect. There is no point where it is more likely. DIdn't you learn nothing from the 2020 elections? Joe Biden got 110k+ votes all for him after being shuffled through a mailing system. What you call rigged, I call freedom.
Anonymous at Wed, 2 Apr 2025 14:00:27 UTC No. 16635048
>>16635039
I will tell you precisely why i cannot accept such delusions, if the monty hall scam were true, it would require that, once you changed your mind, the object behind the doors also physically switches places, OTHERWISE, the odds would be exactly the same, since no object changed places, it is an obviously ridiculous notion.
Anonymous at Wed, 2 Apr 2025 14:08:47 UTC No. 16635062
>>16635043
Jumped the shark there, bud
>>16635048
This is the wrong way to conceive of it. Monty does not have to move the car - after all, he already knows where it is, and can avoid it that way. Usually. Again, not in the variant described in the OP, where his choice is instead fully random, and as a consequence it doesn't matter whether or not you stay or switch.
Anonymous at Wed, 2 Apr 2025 14:14:27 UTC No. 16635069
>>16635062
i simply disagree with the fundamental notion that you can change a probability by doing literally nothing in reality, it doesn't make any sense and i'd give you a gold coin if you could come up with any reasonable justification for it.
Anonymous at Wed, 2 Apr 2025 14:31:58 UTC No. 16635080
>>16635069
Probability is only an expression of certainty. Technically, you're not changing it. If anyone can be said to be affecting it, it's the host. But really what he's doing is avoiding changing the probability.
You get the car on your first guess one out of three times.
Two out of three times, therefore, the car is among the other two doors.
One of out three times, the host may open a door at random to reveal a goat.
Two out of three times, the host is forced to open a specific door, because the car is behind the last one.
Therefore, when he reveals a goat, two times out of three, that means the car is behind the one remaining door you didn't pick.
You see how nothing changes? You are only updating your knowledge of the situation.
Anonymous at Wed, 2 Apr 2025 14:41:23 UTC No. 16635088
>>16635080
>If anyone can be said to be affecting it, it's the host.
The host is doing literally nothing in reality either, the best i can grant you is that by some mathematical manipulation you can make it look as though something changed whereas in reality literally nothing changed which noone disputes which means the chances are all the same.
Anonymous at Wed, 2 Apr 2025 14:49:11 UTC No. 16635092
>>16635088
The one thing you are doing that affects the outcome is selecting a door, which has the potential of determining the host's choice. The one thing the host is doing is avoiding the car.
You initially had a 1/3 chance of getting the car, and that remains unchanged. The car had a 2/3 chance of being behind one of the other two doors, and that remains unchanged. The car was always going to be among the last two options, and that remains unchanged. In the 2/3 likelihood that the car is not behind the door you chose, Monty forces it to be behind the remaining door. That's what he does. He's not moving the car for this, he's simply moving his pick of door to the one that doesn 't have the car.
It is because nothing really changes in the original Monty Hall that your odds are better if you switch.
Anonymous at Wed, 2 Apr 2025 14:51:52 UTC No. 16635095
>>16635092
And I'd like to add to that that if Monty determines his door randomly, that actually does change the odds and that is what makes it 50-50, which it wasn't before
Anonymous at Wed, 2 Apr 2025 15:10:05 UTC No. 16635106
>>16635092
>The one thing you are doing that affects the outcome is selecting a door
Literal schizophrenia, selecting a door does nothing to change the outcome, there is nothing magic about either door that changes the probability.
Anonymous at Wed, 2 Apr 2025 15:17:00 UTC No. 16635119
>>16635106
A door contains either a car or a goat. If you select a car, then the car isn't anywhere else. If you don't, then it is. That is how selecting the door affects whether or not switching wins. You don't know where the car is, however, so you don't have enough information to put this ability to any use.
Anonymous at Wed, 2 Apr 2025 15:19:29 UTC No. 16635121
>>16635106
>>16635119
That is, you can't consciously adapt your choice of door to a specific strategy, because you cannot distinguish them. Of course your knowledge of the relative probability of picking the car vs. a goat does factor into your strategy with regard to staying or switching. But that is a choice made later that does not affect the probabilty.
Anonymous at Wed, 2 Apr 2025 15:21:26 UTC No. 16635122
>>16635119
>A door contains either a car or a goat. If you select a car, then the car isn't anywhere else. If you don't, then it is.
Proof for any of this made up schizo shit? You have zero idea whats behind any door at any point in time and you cant magically change it by quickly grabbing the other door thats just retarded.
Anonymous at Wed, 2 Apr 2025 15:29:22 UTC No. 16635128
Let’s just go through the problem real quick. We’ll say that the car is behind door 1.
These are all the possible options:
>you pick door 1
The host reveals a goat behind door 2 or 3.
You stay (win)
You change (lose)
>you pick door 2
The host reveals a goat behind door 3.
You stay (lose)
You change (win)
>you pick door 3
The host reveals a goat behind door 3
You stay (lose)
You change (win)
Notice that in 2/3 cases, changing doors wins.
Why is this so hard for people to understand?
Anonymous at Wed, 2 Apr 2025 15:30:20 UTC No. 16635131
>>16635122
>Proof for any of this made up schizo shit?
Well, I mean
There is one car, two goats, and three doors
No, you don't know where they are, that's why you assign them a probability
Anonymous at Wed, 2 Apr 2025 15:33:46 UTC No. 16635134
>>16635128
You did notice that the OP altered the problem so Monty is picking at random?
Anonymous at Wed, 2 Apr 2025 15:33:55 UTC No. 16635136
>>16635131
I mean, a car, is behind one door, a goat another, who gives a fuck it doesnt matter, you still havent proved that changing your decision somehow changes the outcome when you at no point know whats behind any of the doors, it's insane.
Anonymous at Wed, 2 Apr 2025 15:34:52 UTC No. 16635139
>>16635136
Of course it matters. Because if the car is behind YOUR door, switching loses. But if it isn't, then switching wins.
Anonymous at Wed, 2 Apr 2025 15:35:33 UTC No. 16635140
>>16635134
So it only works when you already know the outcome of one door? Well that makes much more sense if true. What a stupid thread.
Anonymous at Wed, 2 Apr 2025 15:36:34 UTC No. 16635141
>>16635139
>Because if the car is behind YOUR door, switching loses. But if it isn't, then switching wins.
BUT YOU DONT FUCKING KNOW THAT SO HOW COULD SWITCIHNG AFFECT THE OUTCOME??
Anonymous at Wed, 2 Apr 2025 15:36:38 UTC No. 16635142
>>16635140
>So it only works when you already know the outcome of one door?
Uh, yeah, welcome to the Monty Hall problem
Anonymous at Wed, 2 Apr 2025 15:37:35 UTC No. 16635143
>>16635142
Then why are a bunch of retards trying to argue with me that it works even when its random? Or are they not saying that and im just stupid
Anonymous at Wed, 2 Apr 2025 15:39:07 UTC No. 16635145
>>16635141
No, you don't know it. That's why you assign it a probability.
Anonymous at Wed, 2 Apr 2025 15:39:44 UTC No. 16635147
>>16635041
>the host will never reveal the car, that is what boosts your chances by switching
This variant doesn't say the host will never reveal the car. That's why your odds aren't boosted by switching.
Anonymous at Wed, 2 Apr 2025 15:40:12 UTC No. 16635148
>>16635134
>>16635140
>>16635142
>>16635143
Please reread my answer and try again.
Anonymous at Wed, 2 Apr 2025 15:40:55 UTC No. 16635149
>>16635145
So why does the probability change when literally nothing has happened apart from your hand moving to another door when you have no idea whats behind any of the doors. protip: it doesn't schizo.
Anonymous at Wed, 2 Apr 2025 15:41:55 UTC No. 16635152
>>16635148
What answer?
Anonymous at Wed, 2 Apr 2025 15:42:05 UTC No. 16635153
>>16635147
It does, retard. That is literally the entire point.
IF HE REVEALED THE FUCKING CAR, YOU WOULD SWITCH TO THE CAR
Anonymous at Wed, 2 Apr 2025 15:43:39 UTC No. 16635156
>>16635153
Yeah, what the fuck does that have to do with probability? If i see a free car i'll take it.
Anonymous at Wed, 2 Apr 2025 15:44:42 UTC No. 16635157
>>16635153
>IF HE REVEALED THE FUCKING CAR
He didn't reveal the car.
Anonymous at Wed, 2 Apr 2025 15:46:32 UTC No. 16635159
>>16635153
The host offers you the choice of switching to the remaining closed door. Not your choice of door. We can assume that if he reveals the car, you just lose.
Also this >>16635157
Anonymous at Wed, 2 Apr 2025 15:52:36 UTC No. 16635169
>>16635149
Probability isn't reality. In reality, the car is 100% behind one door and 0% behind another. Probability is only an indication of how likely the car is to be behind a door given our incomplete knowledge.
Anonymous at Wed, 2 Apr 2025 16:00:09 UTC No. 16635181
>>16635176
Prove that you shouldn't hate yourself then
Anonymous at Wed, 2 Apr 2025 16:01:53 UTC No. 16635186
>>16635169
>Probability isn't reality. In reality, the car is 100% behind one door and 0% behind another.
Finally, you admit it's all bullshit, enjoy your made up probabilites, as i said, mathematical manipulation, not reality.
Anonymous at Wed, 2 Apr 2025 16:04:58 UTC No. 16635192
>>16635186
Okay, but the absolute statistical reality is that if you're on this game show 100 times, and the host will always avoid revealing the car, then you'll win roughly 66 times if you switch every time. In that sense, probability can be said to describe reality.
Anonymous at Wed, 2 Apr 2025 16:14:31 UTC No. 16635202
>>16635192
>statistical reality
Alright we're just playing semantical games now, yes probability can be useful, no it isn't reality as you just agreed with me, we can debate all day on whether it describes reality or how accurate it is or whatever, for me it's not useful to differentiate between reality and a description of reality because it just becomes a basic philosophical discussion of "they're not the same thing but it is a descrpition", but i think we basically agree more or less.
Anonymous at Wed, 2 Apr 2025 16:16:41 UTC No. 16635206
>>16635202
Nah we do not agree at all lol
Anonymous at Wed, 2 Apr 2025 16:36:12 UTC No. 16635220
>>16635206
>We don't agree
>We just don't ok!
Ok lol
Anonymous at Wed, 2 Apr 2025 16:42:18 UTC No. 16635224
>>16635128
Please do the needful and read this again.
Thank you sirs.
Anonymous at Thu, 3 Apr 2025 11:27:54 UTC No. 16635934
>>16633764
You know, I figured I'd catch out a couple of cocksure psueds with this one, but I'm still absolutely astonished at how many people not only refuse to accept the answer despite having the maths explained to them, but even call upon their shallow "understanding" of Monty Hall to justify it. Ironically, years of exposure to one of the most famous problems of conditional probably has only worsened your actual understanding of conditional probability. The mistakes repeatedly on display here are really no less egregious than those made by people who think regular Monty Hall is 50-50. I'd have expected this from /v/, maybe, but I held /sci/ in a slightly higher esteem.
Anonymous at Thu, 3 Apr 2025 11:30:13 UTC No. 16635936
>>16633876
>Tell me with your words you were wrong
all right
you were wrong lol
Anonymous at Thu, 3 Apr 2025 11:46:39 UTC No. 16635947
>>16635934
Three coins are flipped, the host is covering up the results and tells you to pick a coin. He reveals one is heads. What are the odds the one you picked is tails?
Anonymous at Thu, 3 Apr 2025 12:00:34 UTC No. 16635960
>>16635947
Do you mean he reveals one coin that you didn't choose to show that it is heads, or does he divulge the information that one coin of the three is heads? And in the latter case, does he mean at least one or exactly one?
I don't think any of these is a proper analogy for what we're talking about but we can have a look anyway.
Anonymous at Thu, 3 Apr 2025 12:22:56 UTC No. 16635982
>>16635947
>>16635960
Let's just go over the options.
>He reveals one coin besides yours
Your odds are 1/2. You have a coin that is either heads or tails, and its probability is not affected by anything else.
>Host tells you exactly one coin is heads
Your odds are 2/3. One coin is heads, the other two necessarily aren't, you picked from among three of them. I suppose this is the one you're going for; Monty "tells" you something by opening a door. If this is what you meant, you're not taking into account that Monty has to know where the car is and actively avoid it in order to meaningfully "tell" you anything.
>Host tells you at least one coin is heads
Your odds are 1/3. We've ruled out all tails. Two, one, or zero tails are all equally likely. So you got a 1/3 shot at 2/3 odds, a 1/3 shot at 1/3 odds, and a 1/3 shot at 0/3 odds.
Like I said, none of these properly model "random" Monty. If Monty is truly acting at random, you don't even need him there; you can replace him with a random event, like the roll of a die or the flip of a coin. Here's a better analogy:
Suppose you have three coins, two of them fair, one of them double-headed. You take one coin at random and flip it. It comes up heads. What are the odds that you got a fair coin?
Anonymous at Thu, 3 Apr 2025 12:35:38 UTC No. 16635996
>>16635947
>>16635982
Or, if that's not convincing, let's try something else instead.
I write down a random number between 1-100. I hand you a d100 and ask you to roll and note the result. I then take the d100 and do the same, rerolling if I get your number. I look at the results and tell you "one of them is correct".
I hope you can agree that:
>This outcome was not guaranteed
>We had equal odds
>Given the information we have, it's a choice between two equally likely scenarios, namely that you had the right number or I did
I hope you can also agree that these odds change drastically in my favour if I'm allowed to place the d100 any face up however I like, excluding the number you rolled - which is the big difference between the random scenario, and Monty knowing where the car is.
Anonymous at Thu, 3 Apr 2025 13:36:28 UTC No. 16636048
>>16635934
>You know, I figured I'd catch out a couple of cocksure psueds with this one, but I'm still absolutely astonished at how many people not only refuse to accept the answer despite having the maths explained to them, but even call upon their shallow "understanding" of Monty Hall to justify it
Having seen this shit before, I'm not surprised at all.
It doesn't help that literally the most famous phrasing of the Monty Hall problem isn't properly structured to account for the principle of indifference so none of these idiots were taught right in the first place.
>Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
If people weren't taught in the first place that the host has to actually be selecting for a goat, which this phrasing doesn't specify, then of course they're not going to know that shit's important. They're just going to memorize and regurgitate the answer they were told is correct.
Anonymous at Thu, 3 Apr 2025 13:39:27 UTC No. 16636050
>>16633854
>You get one try
>Host gets infinite tries to get it right
lol'ing @ the mental image of Monty going
>All right, let's reveal the go- wait, that's not supposed to happen, can we try that again? What, again? Er, whoops, third time's the charm... darn... er... maybe the next one... no... cut to commercial please...
for 100 straight tries and then announces
>Finally! So, now that I've completely RANDOMLY revealed only goats...
Anonymous at Thu, 3 Apr 2025 14:05:01 UTC No. 16636062
>>16636048
>of course they're not going to know that shit's important
It's implicit or explicit in any explanation they've memorised, though.
Anonymous at Thu, 3 Apr 2025 15:04:13 UTC No. 16636098
>>16635159
>>16633967
>host isn't going to reveal the fucking car first because that makes for bad TV
It doesn't though, and I don't get why people argue this. Having Monty always reveal the goat in the same way would be what gets old, in the actual show he could do what he wanted and mix things up by making deals with the contestants, which is the point of the thing, he's making an off the cuff deal by deliberating revealing a goat, but if the show could reveal a car instead to indicate a loss that would just be a natural losing outcome that would add tension every time a reveal was made.
Anonymous at Thu, 3 Apr 2025 15:11:29 UTC No. 16636108
>>16636048
>the host, who knows what's behind the doors,
This is the crucial part. According to the principle of relevance, we have to assume that this bit of information is mentioned for a reason, and that can only be that the host's knowledge would affect his behaviour. We can reasonably assume that the host wants the car to remain hidden. I think Vos Savant also mentions these assumptions in her answer.
The original phrasing of the problem seems quite carefully formulated, and, given the leading question at the end, I suspect that the letter writer knew the answer and intended it as a test, because it doesn't seem like an innocent question.
Anonymous at Thu, 3 Apr 2025 15:12:08 UTC No. 16636109
>>16636062
>implying they memorize the explanation
Anonymous at Thu, 3 Apr 2025 15:14:12 UTC No. 16636111
>>16636108
>According to the principle of relevance
That's not a mathematic principle.
Anonymous at Thu, 3 Apr 2025 15:16:29 UTC No. 16636113
>>16636111
It's a communication principle.
Anonymous at Thu, 3 Apr 2025 15:18:02 UTC No. 16636116
>>16636109
Well yeah, look how many people respond with
>imagine there's 100 doors...
and then they plum forget that that only works if Monty guarantees the outcome
Anonymous at Thu, 3 Apr 2025 15:22:16 UTC No. 16636118
>>16636108
>The original phrasing of the problem seems quite carefully formulated
If it were carefully formulated, the behavior of the host or at the least whether the selection of the door was arbitrary or conditional beyond it being "another" door would have been explicitly specified.
To be clear the Monty Hall problem predated that formulation. The writer just fucked up.
>>16636113
Kay, and? Not assuming shit is also a communication principle. Have you ever heard assuming shit makes an ass out of u and me? The principle of indifference exists for that very reason.
Anonymous at Thu, 3 Apr 2025 15:28:52 UTC No. 16636121
>>16636116
In fairness, the 100 doors "explanation" is basically designed to fuck them over since it's just a well disguised appeal to intuition and not actually a grounded explanation of the math if they don't understand the behavior of the host is fundamentally what matters.
Once you change the problem such that the small case is intuitive and the 100 doors case is counterintuitive they can't correct as long as they don't realize the 100 doors are really just 2 doors.
Honestly that's one of the reasons why I hate the 100 doors bit. It sets people that don't actually get it up for failure.
Anonymous at Thu, 3 Apr 2025 15:38:24 UTC No. 16636127
>>16636118
>If it were carefully formulated, the behavior of the host or at the least whether the selection of the door was arbitrary or conditional beyond it being "another" door would have been explicitly specified.
I did say "carefully", not "precisely" - it's a concise piece of writing that conveys all the relevant information, but it doesn't go out of its way to spell it out for you. Like I said, it's probably intended as a test. But if you dismiss that bit of information as a red herring, you're assuming bad faith.
Anonymous at Thu, 3 Apr 2025 17:41:10 UTC No. 16636242
>>16636127
>But if you dismiss that bit of information as a red herring, you're assuming bad faith.
What if I dismiss it as being overly descriptive like the host being Monty Hall or the prizes being a goat and a car hidden behind doors?
>that conveys all the relevant information
Except how the door is chosen. Which determines the answer. Admittedly that information is only relevant if the choice is intended to not be arbitrary.
Oh wait.
As I said, the writer fucked up.
Anonymous at Thu, 3 Apr 2025 22:59:36 UTC No. 16636728
>>16636242
I guess you'd like the platonic ideal of a maths problem, but that's not what this is. It's accurte without being precise. Marylin Vos Savant was able to intuit the correct interpretation, and though I can't expect everyone to be Marylin Vos Savant, it does show that the description was sufficient.
Anonymous at Thu, 3 Apr 2025 23:06:58 UTC No. 16636742
>>16636728
>Marylin Vos Savant was able to intuit the correct interpretation
The mathematically correct interpretation is as written. If someone writes 2+2=?, it is not correct to say 5 even if the 2nd 2 was supposed to be a 3.
That's not to say you can't say 2+3=5 and you believe it was supposed to be 2+3=?, but that should not be taken as an excuse to say 2+2=5.
Anonymous at Thu, 3 Apr 2025 23:12:52 UTC No. 16636753
>>16636742
But it's not written mathematically. You first have to translate it to maths.
Anonymous at Thu, 3 Apr 2025 23:18:35 UTC No. 16636760
>>16633764
I will pick door 3.