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As stated, the answer is indeterminate. To demonstrate, consider these scenarios. - Savant's Monty: The host knows where the car is, and wants to prolong the g

by btilly 3y ago

As stated, the answer is indeterminate. To demonstrate, consider these scenarios. - Savant's Monty: The host knows where the car is, and wants to prolong the game. Switching wins 2/3 of the time. - Ignorant Monty: The host has no idea where the car is. Revealing the goat was luck and your odds remain 50-50. - Malicious Monty: The host knows where the car is, and wants you to lose. The fact that the host didn't reveal the car means that you have the right door. You'll have no chance of winning if you switch. Nowhere in the problem are Monty's knowledge and motivation stated. When explained, most go along with the assumptions that Savant's argument introduces. When the actual Monty was asked, it turned out that he was usually ignorant. And the malicious scenario demonstrates how different the answer can be. The fact that all three answers are consistent with the statement of the problem means that it is indeterminate.

saalweachter 3y ago
_Let's Make A Deal_ was on the air for twenty (thirty?) years at the time of this controversy. There was sufficient evidence for Savant's Monty -- the car was revealed 0% of the time, not 33 or 66% of the time.
- orblivion 3y ago
  I've never seen the show; I'm curious, did he always open one of the doors?
  - saalweachter 3y ago
    I mean, the original run ended and the first revival also went bankrupt before I was born, but my understanding of the show is that the host always presented the three doors [at the end, to the show's winner, similar to the prize puzzle at the end of Wheel of Fortune] and always eliminated one of the losers. Fun Facts which I think I'm remembering correctly: it wasn't always a goat, they would have other random animals behind the doors as well and because of the laws regulating game shows, the goats were actually a prize, for which you would receive "the cash equivalent" of the goat, if you picked that door. But because the goat was the prize, they couldn't force you to take the cash-equivalent of the goat, if you really wanted to keep the goat. Which was a big headache the handful of times it happened, because the goats were a rental.
    - btilly 3y ago
      So you made an assertion about what happened 100% of the time on the show, when you don't even remember it??? I went and re-read the interview with him that I'd read decades ago. It turns out that we're both wrong. The game was more complicated. He not only knew where the prize was, he was offering people money about whether or not to switch. He knew the answer, and was trying to manipulate the psychology of the person in front of him for the sake of entertainment. Whether he was on the side of the contestant depended on his mood. His quote about the actual game was: *My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."
  - mcv 3y ago
    And if there's actual show where this experiment was done dozens of times, surely there's tons of data to confirm the correct approach here. Did anyone ever document all of that?
orblivion 3y ago
So long as you describe a Malicious Monty that might not have shown you the door, you could also have a Benevolent Monty who won't show you the door if you've gotten it right. Though I'm not sure I've ever considered the Malicious Monty, only the other two.
KrazyButTrue 3y ago
> Nowhere in the problem are Monty's knowledge and motivation stated. "and the host, who knows what’s behind the doors, opens another door [..] which has a goat." The question is clear: The host (1) knows what is behind each door and (2) always shows a goat. It's clearly a determinate problem.
- jncfhnb 3y ago
  Doesn’t matter. If you don’t have a guarantee that he will always open a goat door, his opening of the goat door doesn’t give you information.
  - KrazyButTrue 3y ago
    > If you don’t have a guarantee that he will always open a goat door... Well you do have that guarantee -- as it is stated in the problem. It's clear that no matter what door you open, you will be shown a goat.
    - jncfhnb 3y ago
      Cite where it is stated then
      - zachm0 3y ago
        There is a link in the article to the first appearance of the Monte Hall problem. https://www.jstor.org/stable/2683689 https://www.jstor.org/stable/2683689 On the last line of the problem he opens an empty box.
        jncfhnb 3y ago
        It’s still wrong. He needs to declare (or at least he needs to consistently) open an empty box; not any random box or a box of his choosing at his whim. If he opens a random box; you have not learned anything about the keys GIVEN he opened an empty box This paper adds that in as an assumption after the prompt, which I’m pretty sure is not the original prompt
pessimizer 3y ago
Ignorant Monty can't exist. Monty is the host of a game show, not a contestant. He's not trying to win a prize, and if he opens a prize door, it's a production failure. Whether he knows or not, somebody told him which door to open, and that door does not have the prize behind it. Malicious Monty, however, can exist. He only ever opens a second door when you've picked correctly, but when you haven't simply accepts your choice. The problem was stated correctly and clearly, though, as long as you assume that Monty is not a person, has no motivation at all, and as part of a math problem simply wants to reveal a goat after you've made a choice and has the means to do it. That's Savant's Monty: the Monty that doesn't add significant features to the question.
- btilly 3y ago
  Ignorant Monty absolutely can exist. The person standing in front of the audience is not necessarily the person who arranged the prize. And if he's not, he knows nothing more than the audience. I was, however, wrong that Monty was ignorant. By his own statement, he always knew the answer. But whether or not he was on your side depended on his mood. And he applied various forms of pressure to get you to make the right, or wrong, decision. Therefore the problem was not stated correctly. A correct statement needs to not just state what you witness, but the counterfactuals about possibilities that you didn't witness.

by btilly 3y ago

saalweachter 3y ago

_Let's Make A Deal_ was on the air for twenty (thirty?) years at the time of this controversy. There was sufficient evidence for Savant's Monty -- the car was revealed 0% of the time, not 33 or 66% of the time.

orblivion 3y ago
I've never seen the show; I'm curious, did he always open one of the doors?
- saalweachter 3y ago
  I mean, the original run ended and the first revival also went bankrupt before I was born, but my understanding of the show is that the host always presented the three doors [at the end, to the show's winner, similar to the prize puzzle at the end of Wheel of Fortune] and always eliminated one of the losers. Fun Facts which I think I'm remembering correctly: it wasn't always a goat, they would have other random animals behind the doors as well and because of the laws regulating game shows, the goats were actually a prize, for which you would receive "the cash equivalent" of the goat, if you picked that door. But because the goat was the prize, they couldn't force you to take the cash-equivalent of the goat, if you really wanted to keep the goat. Which was a big headache the handful of times it happened, because the goats were a rental.
  - btilly 3y ago
    So you made an assertion about what happened 100% of the time on the show, when you don't even remember it??? I went and re-read the interview with him that I'd read decades ago. It turns out that we're both wrong. The game was more complicated. He not only knew where the prize was, he was offering people money about whether or not to switch. He knew the answer, and was trying to manipulate the psychology of the person in front of him for the sake of entertainment. Whether he was on the side of the contestant depended on his mood. His quote about the actual game was: *My only advice is, if you can get me to offer you $5,000 not to open the door, take the money and go home."
- mcv 3y ago
  And if there's actual show where this experiment was done dozens of times, surely there's tons of data to confirm the correct approach here. Did anyone ever document all of that?

orblivion 3y ago

So long as you describe a Malicious Monty that might not have shown you the door, you could also have a Benevolent Monty who won't show you the door if you've gotten it right. Though I'm not sure I've ever considered the Malicious Monty, only the other two.

KrazyButTrue 3y ago

> Nowhere in the problem are Monty's knowledge and motivation stated. "and the host, who knows what’s behind the doors, opens another door [..] which has a goat." The question is clear: The host (1) knows what is behind each door and (2) always shows a goat. It's clearly a determinate problem.

jncfhnb 3y ago
Doesn’t matter. If you don’t have a guarantee that he will always open a goat door, his opening of the goat door doesn’t give you information.
- KrazyButTrue 3y ago
  > If you don’t have a guarantee that he will always open a goat door... Well you do have that guarantee -- as it is stated in the problem. It's clear that no matter what door you open, you will be shown a goat.
  - jncfhnb 3y ago
    Cite where it is stated then
    - zachm0 3y ago
      There is a link in the article to the first appearance of the Monte Hall problem. https://www.jstor.org/stable/2683689 https://www.jstor.org/stable/2683689 On the last line of the problem he opens an empty box.
      - jncfhnb 3y ago
        It’s still wrong. He needs to declare (or at least he needs to consistently) open an empty box; not any random box or a box of his choosing at his whim. If he opens a random box; you have not learned anything about the keys GIVEN he opened an empty box This paper adds that in as an assumption after the prompt, which I’m pretty sure is not the original prompt

pessimizer 3y ago

Ignorant Monty can't exist. Monty is the host of a game show, not a contestant. He's not trying to win a prize, and if he opens a prize door, it's a production failure. Whether he knows or not, somebody told him which door to open, and that door does not have the prize behind it. Malicious Monty, however, can exist. He only ever opens a second door when you've picked correctly, but when you haven't simply accepts your choice. The problem was stated correctly and clearly, though, as long as you assume that Monty is not a person, has no motivation at all, and as part of a math problem simply wants to reveal a goat after you've made a choice and has the means to do it. That's Savant's Monty: the Monty that doesn't add significant features to the question.

btilly 3y ago
Ignorant Monty absolutely can exist. The person standing in front of the audience is not necessarily the person who arranged the prize. And if he's not, he knows nothing more than the audience. I was, however, wrong that Monty was ignorant. By his own statement, he always knew the answer. But whether or not he was on your side depended on his mood. And he applied various forms of pressure to get you to make the right, or wrong, decision. Therefore the problem was not stated correctly. A correct statement needs to not just state what you witness, but the counterfactuals about possibilities that you didn't witness.