5 ms·

It doesn't matter what he only does, or always does. It matters what he did in the problem as it is described. Because that is what you're solving.

jncfhnb 3y ago
The problem as described does not specify his behavior. Only what happened. If all you know is that he opened a goat door you have learned nothing. It could be that he always opens a goat door meaning you should switch. It could be that he only opens a goat door if you picked the car and you should not. It could be he only opens a goat door if you picked a goat and you should. Probability cannot determine which of these is any more likely than the other. You have learned nothing.
- bemusedthrow75 3y ago
  "If all you know is that he opened a goat door you have learned nothing." This is precisely where you are wrong.
  - jncfhnb 3y ago
    Ok let’s play! We play this game 1000 times. 33% of the time you pick the car and I show you a goat. You switch and lose 100% of the time. 66% of the time you pick a goat and I don’t show you a goat. Assuming you don’t switch because you believe this means you have an equal odd on your current door, you lose 100% of the time. Congrats. You have lost every single round.
    - bemusedthrow75 3y ago
      You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly argue the point, as you are doing, without resorting to misogynistic or patronising rudeness as so many did at the time! But you're still wrong. :-) And I'm going to leave it here.
      - jncfhnb 3y ago
        I have not restated the problem. You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car. There is nothing in the prompt that says we are not playing my variant of the game. Being told that you SAW a goat does not mean you would ALWAYS SEE a goat if the previous conditions had gone differently. And that is why you’re wrong :) Again > all you know is that he opened a goat door
        bemusedthrow75 3y ago
        > You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. Yes. It is. It is a fixed part of the scenario. Monty opens a door and shows you a goat. He knows it is going to be a goat (he is "well-aware of what is going on behind the scenes"). He's showing you a goat as part of the problem which is: should you switch? Again: think through what the problem actually SAYS: > Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats. > “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?” No matter what: the goat Monty shows you is not a matter of chance. It is a fixed part of the problem. It's there in writing: he shows you a goat. Full stop.
        jncfhnb 3y ago
        No! Read the prompt very carefully. > Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats. You know nothing except you picked door 1 and then he decided to show door 3. You do not know if he would have shown door 3 had you picked door 2! This is NOT in the prompt. You cannot assume that. The experience of this contestant is fully and equally possible within my version of the game too!

jncfhnb 3y ago

The problem as described does not specify his behavior. Only what happened. If all you know is that he opened a goat door you have learned nothing. It could be that he always opens a goat door meaning you should switch. It could be that he only opens a goat door if you picked the car and you should not. It could be he only opens a goat door if you picked a goat and you should. Probability cannot determine which of these is any more likely than the other. You have learned nothing.

bemusedthrow75 3y ago
"If all you know is that he opened a goat door you have learned nothing." This is precisely where you are wrong.
- jncfhnb 3y ago
  Ok let’s play! We play this game 1000 times. 33% of the time you pick the car and I show you a goat. You switch and lose 100% of the time. 66% of the time you pick a goat and I don’t show you a goat. Assuming you don’t switch because you believe this means you have an equal odd on your current door, you lose 100% of the time. Congrats. You have lost every single round.
  - bemusedthrow75 3y ago
    You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly argue the point, as you are doing, without resorting to misogynistic or patronising rudeness as so many did at the time! But you're still wrong. :-) And I'm going to leave it here.
    - jncfhnb 3y ago
      I have not restated the problem. You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car. There is nothing in the prompt that says we are not playing my variant of the game. Being told that you SAW a goat does not mean you would ALWAYS SEE a goat if the previous conditions had gone differently. And that is why you’re wrong :) Again > all you know is that he opened a goat door
      - bemusedthrow75 3y ago
        > You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. Yes. It is. It is a fixed part of the scenario. Monty opens a door and shows you a goat. He knows it is going to be a goat (he is "well-aware of what is going on behind the scenes"). He's showing you a goat as part of the problem which is: should you switch? Again: think through what the problem actually SAYS: > Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats. > “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?” No matter what: the goat Monty shows you is not a matter of chance. It is a fixed part of the problem. It's there in writing: he shows you a goat. Full stop.
        jncfhnb 3y ago
        No! Read the prompt very carefully. > Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats. You know nothing except you picked door 1 and then he decided to show door 3. You do not know if he would have shown door 3 had you picked door 2! This is NOT in the prompt. You cannot assume that. The experience of this contestant is fully and equally possible within my version of the game too!