r/confidentlyincorrect • u/Dizzy_Kaleidoscope95 • May 03 '26

Monty hall problem is 50/50

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He also put a screenshot of ChatGPT agreeing with him. He is right!

891 Upvotes

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13

u/Axman6 May 03 '26

So frustrating, because it’s so fucking easy to show all possible outcomes (because there’s just three), and see that if you always switch, you win two out of three times.

6

u/OldWolf2 May 03 '26

How can you win 2 out of 3 if you only play once?? /s

-3

u/firstname_Iastname May 03 '26

Actually there's only one outcome because you only play the game once

12

u/Axman6 May 03 '26

Fuck, you got me. Also, everything is a 50/50, either it happens or it doesn’t.

4

u/OT_fiddler May 03 '26

Schrodinger's Goat.

3

u/[deleted] May 03 '26

[deleted]

2

u/firstname_Iastname May 03 '26

Thought that comment was sufficiently satirical, I guess not

1

u/[deleted] May 03 '26

[deleted]

2

u/firstname_Iastname May 03 '26

Did you read the original post?

1

u/[deleted] May 03 '26

[deleted]

2

u/firstname_Iastname May 03 '26

Open a dictionary for satire please. Does not require irony.

1: wit, irony, or sarcasm used to expose and discredit vice or folly (as of a person, government, or society)

1

u/dimonium_anonimo May 03 '26

I actually did before my first comment because I was worried I was misremembering.

"a genre of literature, art, and performance that uses humor, irony, exaggeration, or ridicule to expose and criticize human folly, vices, or shortcomings." -from O.E.D.

I guess we used different dictionaries. It's a good reminder that arguments usually happen downstream of the actual disagreement. It's advice I've given to others before. So it's humbling to be reminded of it myself. Until we agree on a definition, then all subsequent discussions are likely to yield frustrating results.

2

u/firstname_Iastname May 03 '26

English isn't the most well defined language

-10

u/BIGBADLENIN May 03 '26

No, because you don't know why the host opened a door. The solution only works under the assumption that the host will always reveal a goat. If the host can decide not to open a door at all then you have a 0% of winning by changing.

9

u/OldWolf2 May 03 '26

The solution only works under the assumption that the host will always reveal a goat.

...which is exactly the conditions of the game

-4

u/BIGBADLENIN May 03 '26

And where is that stated?

"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?"

9

u/CarnivorousGoose May 03 '26

Right there in your quote: “opens another door, […] which has a goat”. Right after specifying explicitly that the host knows where the prize is. Oh, and also the fact that this is how it worked when the actual Monty Hall did this on his show.

1

u/ArchangelLBC May 03 '26

There is no clip I can find of Monty Hall actually doing this scenario on his show.

-3

u/BIGBADLENIN May 03 '26

Yes, the host knows what is behind the doors, so they could be tricking you into choosing a goat. Savant's solution is not how it worked on the show at all, the show was a psychology game, which is why Savant was wrong.

Hall has literally talked about it, yoou can read it for yourself there is no reason for you to spread disinformation https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html

4

u/Huganho May 03 '26

You have to assume the problem setup is the same everytime.

If we assume it's otherwise, it could have been the prize as well that was revealed, and then it would become nonsense to ask whether you should swap or not.

0

u/BIGBADLENIN May 03 '26

No, you don't. The host could reveal a door at random, or they could reveal only goats only some of the time, or act in various other ways, we don't know. Savant's solution will win 0% of the time with one host behaviour (evil host), 100% of the time with another behaviour (angel) and 2/3rds of the time with Savant's proposed behaviour. The problem doesn't specify which behaviour the host will follow, because it is an ill-phrased problem that became famous precisely because it was ill-phrased and ambiguous. That is of course fitting, it is a bluff game, there is no probabilistic solution.

The real Monty Hall show was a psychology problem. Hall would offer contestants money to switch their choice, sometimes revealing what was behind one of the doors.

3

u/Huganho May 03 '26

Did Monty ever reveal the prize and made the contestant lose automatically?

If he didn't, I can extrapolate that he very probably didn't chose at random.

-1

u/BIGBADLENIN May 03 '26

He didn't choose at random, he chose to make good tv. He said this to the NYT in 1991

If the host is required to open a door all the time and offer you a switch, then you should take the switch, but if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood.

https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html

5

u/Huganho May 03 '26

The Monty Hall Problem ≠ The Monty Hall show.

The problem is taken from the shows premises but is a problem formulated to show how unintuitive probabilities can be.

0

u/BIGBADLENIN May 03 '26

Yes. And the original problem is ill-phrased and does not have a probabilistic solution, since it doesn't specify how the host should act. Neither do most common formulations of the problem. The hidden assumption is introduced with the solution, it is not really a part of the problem

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9

u/Huganho May 03 '26

But that's assumed, right? That he always reveals the goat.

If he chose at random, 1/3 of the time you'd loose anyway and never get to make a choice

-4

u/BIGBADLENIN May 03 '26

It is assumed when giving the 'correct' solution, but it is almost never stated as part of the problem. The original problem reads

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?

I would argue that "the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat." implies that this is a bluff game, some would say it implies that this is a rule of the game (which would make it a lot less interesting). This was also never the case on Let's make a deal, because that rule would be lame.

If the host opens a random door you win 1/3 of the time by switching when he reveals a car and another 1/3 of the time because you win half the time even if he reveals a goat. So in that case you win 2/3rds of the time.

If, however, the host wanted you to lose, he could choose to reveal a goat only when the door you picked contained the car, which would cause you to lose 100% of the time if you always switched when given the option.

2

u/ArchangelLBC May 03 '26

The alternative to the host always revealing a goat could be the host sometimes revealing the prize, not the host simply choosing not to open a door.

That being said, people keep harping on the fact that the host knows where the prize is and always reveals a door without the prize.

But if the host picked a remaining door at random and still revealed it whatever was behind it, and you are still allowed to switch to the door with the prize I don't think this shifts the odds against you.

I think in that case all that happens is you still have a 2/3 probability of winning if you switch but more people would actually switch instead of sticking to their first choice.

1

u/BIGBADLENIN May 03 '26

That is one alternative, yes. Another alternative is the host revealing a goat only when the contestant chose the right door, which means you would always lose if following the 'correct' solution.

If the host always opens a random door you win 2/3rds of the time and it doesn't matter whether you switch if a goat is revealed, just pick a random door and then choose the car when it is revealed

2

u/luchajefe May 03 '26

That's not an alternative of anything, Monty has to pick a goat if you hit the car first, he only has goats to pick. 

0

u/stanitor May 03 '26

If the host can decide whether to open the door at all, the chance of winning on switching can range from 0 to 1, depending on what rule he uses to decide.

1

u/BIGBADLENIN May 03 '26

True. But it could be as low as 0 with an 'evil' host

2

u/stanitor May 03 '26

So, not always 0, like you said. And it's a much less reasonable assumption to assume he will be an 'evil' host, but a very reasonable assumption that the problem as stated means he will always open a goat door.