4 ms·

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

by dghf 9y ago

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.]

dmurray 9y ago
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?"
- chrismcb 9y ago
  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.
  - FabHK 9y ago
    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.
    - dmurray 9y ago
      > 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.
- thomasahle 9y ago
  If you skip the comment "say No. 3", the formulation literally says "opens another door which has a goat."
  - justinpombrio 9y ago
    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-versus-that-0 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.

by dghf 9y ago

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.]

dmurray 9y ago

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?"

chrismcb 9y ago
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.
- FabHK 9y ago
  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.
  - dmurray 9y ago
    > 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.
thomasahle 9y ago
If you skip the comment "say No. 3", the formulation literally says "opens another door which has a goat."
- justinpombrio 9y ago
  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-versus-that-0 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.