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PaperclipPerfector  1mo ago (text post)   25702 thread views

Culture War Roundup for the week of November 10, 2025

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Your description of the Monty Hall problem is new to me,

(is it guaranteed that he would pick and open a door regardless of what you do? If yes: switch;

I've never heard of a version of the problem where it is not guaranteed that the host picks a door and opens after you have selected your door.

People were still confused by it.

From the wiki

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?

After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them calling Savant wrong.[4] Even when given explanations, simulations, and formal mathematical proofs, many people still did not accept that switching is the best strategy.[5] Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating Savant's predicted result.

The description that you quoted says nothing whatsoever about whether the host is guaranteed to pick a door. It talks about exactly one possible "run" of the system, namely the one where you started by picking door 1. Supposing the car is actually behind Door 2, it is perfectly consistent with this description that if you had picked Door 2, the host would not have done anything. There is nothing whatsoever about it suggesting that it talks about a set of rules, and in general, I will never read any text that is written as an account of events ("you do this, and then he does that, and (...)") as if it were an account of rules ("whenever you do this, he will do that (...)").

If you wanted to write a description to the effect that the host will always behave in the same fashion, you could write it as follows: "You are on a game show, and you're given the choice of three doors. (...) Per the rules, after you pick a door, the host, who knows what's behind the doors, will open one of the other doors that has a goat behind it. He will then say to you: (...) Is it to your advantage to switch?". The description was not written in this way.

I should have remembered where I was and refrained from commenting on anything approaching a 'logic puzzle' here. I am the stupid sort who just assumes things when interacting with this kind of puzzle, like that the rules are 'fair' or at least that the trick would not be, this. So I would never even consider the possibility of the puzzle formatted in such a way that the host only opens the second door conditionally on you having selected the correct door, as I would not even see the point in asking such a question.

In my defense, I have never once heard someone raise this objection(before now) when trying to solve the problem or discussing the answer, so it seemed totally out of left field for me. I take it your contention is that this is the primary area of confusion though, based on your comment. I guess it goes to filter bubbles, I associate with people who are stupid enough to be confused by the basic problem where as your circle could only ever be confused by the under-specificity in the description of the scenario.

I do think that my description captures the essence of the confusion, but that isn't to say that I think that the confused would necessarily describe their confusion like this, or be able to describe it at all. I'm following a fairly mechanistic analysis of "normies" here: their everyday experience, and perhaps their memetic heirloom (in the form of tropes, stories and catechisms), tells them that if they are in an asymmetric-information setting and a person who knows more than them and has interests misaligned with theirs tries to persuade them to act in a particular way, that person is probably trying to bait them into harming themselves.

The exact way in which this self-harm happens doesn't even matter: "they wouldn't be trying so hard to convince me if this were actually good for me" is a straight corollary of this life lesson, and if you analyse the corollary carefully you see that it all but says that the game show host's behaviour may depend on your choice of door (=whether switching would be good for you).

(By the way, I'm not terribly impressed by the invocation of Erdős. People who actually have to deal with his output may tell you that while he certainly had great flashes of intuition and a superhuman tolerance for grindy proof work, he was also hardly a precision machine in the vein of von Neumann, and had plenty of moments where he got sloppy or just didn't get something. A buggy lemma of his tanked a course paper I wrote once. I'm still salty.)

I am still not really seeing this, as far as I can tell you are simultaneously holding that most people are too stupid to interact with a hypothetical (but I did have breakfast) while also contending that the same people, if they could interact with a hypothetical, would understand how the host opening a second door changes the probability such that they would consistently get the Monty Hall Problem right.

You seem to leave little to no room for the, in my opinion far simpler explanation that people have a hard time intuitively understanding how the host opening the wrong door changes the probability of switching doors.

Elsewhere Skeletor describes his own experience, and it is more or less a perfect match for every person I have ever seen try and tackle this problem. Do you think that the secret real root of Skeletor's confusion was that he thought the host was trying to trick him?

I also did not intuitively understand the probability when first hearing the problem. My solution was to pull out paper and pencil and just simulated the problem 9 times, which quickly revealed that I would win by switching 6 out of the 9 times. My internal experience did not really feel like what you are describing, and my attempted solution is basically incoherent if I was concerned in the way that you describe.

I think this might not be a useful discussion to have without identifying a concrete example of a person who is confused about it (and is really convinced that the answer should be something else, rather than just being like "uh, I don't know, 50/50?"). For the 50/50 answer, I'm positing a theory that is more or less:

(1) people won't do particularly complex math;
(2) people have a strong intuition that a well-informed adversary enthusiastically doing something for you will not help you;
(3) this intuition is adaptive and justified by real-life experience;
(4) if you accept as an "axiom" that Monty's opening of the door did not help you, then you can conclude something like that the outcome of Monty's action can at most be as good for you as if the state it brought about (one door open, has goat) were naturally there from the start. In that scenario, though, the conditional probability of the car being behind each remaining door is indeed 1/2.

As for why people would think that "the bound is tight"/it's not even worse, there might be some other technically-incorrect-but-adaptive axioms in play.

It is true that I am implying a form of "peaky", and not very introspectively closed, intelligence here: I think that people are okay at basic probability, and have a set of very solid but not perfect intuitions about benefit, trade and competition in the sort of weakly iterated games that were played within and among tribes since times when they looked more like apes. These intuitions do in fact operate extensively on comparison, as evidenced by the fact that in all of recorded history they were conveyed by way of allegorical stories.

The Monty Hall one clicked pretty easy for me once I realized something like:

There's a 1/3 chance the prize is behind my door, and a 2/3 chance the prize is behind "Not My Door." That knowledge doesn't normally help for obvious reasons, but when Monty comes along and eliminates one of the remaining doors and asks me to reconsider, I'm functionally being given "Not My Door" as a valid choice.

But there was that initial period of assuming that it must be 50/50 and reading an explanation and having it click. By comparison I don't get the point of this one. It's a lot more convoluted yet also more obvious.

Like if every box of Froot Loops contains a free Blue Foozle, and 50% of Froot Loops boxes also contain an additional Red Foozle, then the chance of any given Foozle being blue is two-thirds. Okay done, what's the big deal? It's not even counterintuitive. The guy at the Froot Loops factory probably realized that he needed to order twice as many blues as reds without even thinking about it.

All the shit about drugs and memory erasure is just obfuscation. Why is this problem even a thing?

The mathematical probability is almost a distraction and doesn't help intuition; even people who know the "right" answer don't have great intuition to transfer it to other problems.

This is basically the same intuition building as what you did, but made much clearer. Suppose you have a thousand doors instead of just three, you choose one, and then 998 are eliminated. Do you switch?

Yeah for Monty Hall I had to kind of chew on it until I had a mental model that made sense to me. With Sleeping Beauty I feel like I'm just being asked hey what are the odds of something with 1/3 odds?

I'm reading the Wikipedia article on it linked in the OP, and I like to think I'm a passably intelligent person, but most of the "Solutions" section just reads as complete nonsense to me.

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