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You might live in a world where the host doesn't want to give you the car, and only opens a door and offers you the option of switching if your first choice was

You might live in a world where the host doesn't want to give you the car, and only opens a door and offers you the option of switching if your first choice was the door with the car behind it. In that world, you shouldn't switch. I don't think this form of the problem statement gives you any reason to believe that you aren't in that world.

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ryao 2y ago
Here is what Marilyn vos Savant had to say: > So let’s look at it again, remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose. (There’s no way he can always open a losing door by chance!) Anything else is a different question. https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... What you are discussing is a different problem.
- penteract 2y ago
  Yes, I am discussing a different problem, and I don't think the original problem formulation gives enough information to distinguish between the 2 problems. The answer can add assumptions, which is fine. I'm not passing judgement on Marilyn vos Savant. I do object to claims that the problem statement is sufficient to have a single answer, and based on that, I'd object to claims that somebody in that situation would be wrong not to switch doors. I would object on exactly the same grounds to anyone who tells you "you're wrong, there's a 50% chance of getting a car" (I might object further, on the grounds that the most obvious interpretation which gives that answer is inconsistent with this form of the problem statement).
  - the_af 2y ago
    If you're discussing a different problem, then it's not the Monty Hall Problem, which we're discussing here. It's a probabilities logic puzzle, it's not about psychological tricks. Anything of that sort is an extraneous ad hoc hypothesis that you're introducing. The point is whether, upon the reveal of a goat, you should switch or stick to your original choice. Nothing else matters. What Monty had for breakfast doesn't matter. Whether he likes you or not doesn't matter.

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ryao 2y ago

Here is what Marilyn vos Savant had to say: > So let’s look at it again, remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose. (There’s no way he can always open a losing door by chance!) Anything else is a different question. https://web.archive.org/web/20130121183432/http://marilynvossavant.com/game-show-problem/ https://web.archive.org/web/20130121183432/http://marilynvos... What you are discussing is a different problem.

penteract 2y ago
Yes, I am discussing a different problem, and I don't think the original problem formulation gives enough information to distinguish between the 2 problems. The answer can add assumptions, which is fine. I'm not passing judgement on Marilyn vos Savant. I do object to claims that the problem statement is sufficient to have a single answer, and based on that, I'd object to claims that somebody in that situation would be wrong not to switch doors. I would object on exactly the same grounds to anyone who tells you "you're wrong, there's a 50% chance of getting a car" (I might object further, on the grounds that the most obvious interpretation which gives that answer is inconsistent with this form of the problem statement).
- the_af 2y ago
  If you're discussing a different problem, then it's not the Monty Hall Problem, which we're discussing here. It's a probabilities logic puzzle, it's not about psychological tricks. Anything of that sort is an extraneous ad hoc hypothesis that you're introducing. The point is whether, upon the reveal of a goat, you should switch or stick to your original choice. Nothing else matters. What Monty had for breakfast doesn't matter. Whether he likes you or not doesn't matter.