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Comment by dmurray | Hacker News Reader

This seems identical to the Monty Hall problem, except that the typical telling of the Monty Hall problem elides an important detail: that Monty knows which door conceals the car and intentionally always picks one that conceals a goat.

With that omitted (on Wikipedia [0], it's omitted in both the introduction to the page and the "canonical" reader's letter it quotes), people correctly conclude that their chance of winning doesn't go up by switching doors.

[0] https://en.m.wikipedia.org/wiki/Monty_Hall_problem

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From the letter quoted at your link:

> 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.

[Emphasis added.]

Right, but it doesn't say that he always picks one with a goat.

I think people would have a different response to the problem if before the host opened the door, the contestant said "Monty, can you please open one of the doors with a goat behind it?"

It is obvious. Why would he show the winning door? If he shows the winning door then the game is over and there is no reason to switch.

If one doesn't know the show, it's not obvious. Imagine an alternative universe in which the policy of the host is to open a random door (of the two remaining ones). Then, if it's a car, the show is over. If it's a goat, well, you can switch or not, doesn't matter.

The precise statement of the host's policy is fundamental to the whole problem, and it's these annoying vague formulations that lead to the endless discussions.

And that, in turn, is the nice thing about the Mosteller Hall Puzzle variation in the article: it makes the host/guard's policy very clear, and in fact so clear that one intuitively understands the damn problem.

> If one doesn't know the show, it's not obvious. Imagine an alternative universe in which the policy of the host is to open a random door (of the two remaining ones)

Yes, exactly. The wikipedia description is consistent with this alternative show. And if you say "that would make no sense as a game show", perhaps the contestant had to get through many other puzzles to get this far.

If you skip the comment "say No. 3", the formulation literally says "opens another door which has a goat."

That's still a little bit ambiguous. The problem statement mixes together the policy and the problem statement, and it's hard to tell which is which. Perhaps the policy is to pick a random door, but the problem statement specifies that it happens to contain a goat. In fact, I think the phrase "another door which contains a goat" technically means that the goat is coincidental, because of the difference between "which" and "that":

http://www.quickanddirtytips.com/education/grammar/which-ver...

So a better phrasing might be "opens a different door that has a goat".

That said, I suspect that most readers understand that the door was picked because it contained a goat.

I have shared the Monty Hall problem with people many times, and have always made explicit that the host knows which door the prize is behind and thus always intentionally choses a 'losing' door.

It has not yet stopped anyone I have tried it with from making the error that it doesn't matter whether they stick or twist.

It's not the same as the Monty Hall problem because the prisoner is not given a choice. If you are sure you know the answer to the Monty Hall problem and are a programmer then I suggest writing a little simulator to test your answer.

As far as I can see, it's identical to the Monty Hall problem, except slightly more precisely phrased in that the guard definitely does not reveal the name of the free prisoner, which is often a contentious point in these discussions (as it alters the probabilities).

It is structurally the same. With the wrong conclusion that A now has 1/2 chance of being pardoned, he'd be indifferent between remaining himself or rather being C.

With the (correct) conclusion that A still has 1/3 chance of being pardoned, and given that B has 0 chance of being pardoned, A would now rather "switch" with C, who has 2/3 chance of being pardoned. (That he doesn't have that choice doesn't matter.)

I didn't mean it was mathematically different, but the framing is sufficiently different to cause most people to miss the most interesting part. I was leaving out the correct conclusion so as not to spoil it for anyone.

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