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The Monty Fall problem asks you about the case when the host has managed to reveal a goat. That only includes a subset of the total attempts that you would star

by EGPRC 4y ago

The Monty Fall problem asks you about the case when the host has managed to reveal a goat. That only includes a subset of the total attempts that you would start selecting a door, not all. Once a goat is revealed, you could only be in the 1/3 case of when the player's choice is correct, or in the 1/3 case of when the other door randomly left closed is correct, so each represents 1/2 of this subset, not one 1/3 and the other 2/3.

firstlink 4y ago
> That only includes a subset of the total attempts that you would start selecting a door, not all. In the trial invalidation version of the problem, but not in the problem as stated. The problem as stated provides, the host does not reveal a car (or your original door). Let me put it another way. If the question had asked, "Conditional on the host not revealing a car (or your original door), what is the probability of winning if you switch?", then that too would be 1/2. My problem is that this is not what is asked. We don't get to answer an easier or different version of the problem. And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. What matters, as you have demonstrated and I have tried to clarify (we aren't really disagreeing), is whether we are exploring the conditional probability in the uniform distribution over a sample space where the host might open another door (1/2), or the probability in the uniform distribution over a sample space where he cannot (2/3). If one denies the difference between these versions of the problem, one ends up in woo-space where the host's knowledge or intentions matter. They don't.
- mcv 4y ago
  > And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. Knowledge and intentions don't matter? They most certainly do. Imagine a third version of the problem (I'm afraid I don't have a good name for it) where the host actively tries to lure you away from the correct answer, and only opens an empty box if you've picked the correct box. Now, if you pick a box and the host opens an empty box, you should absolutely not switch, because the remaining box has 0% of being the right one. Knowledge and intentions matter. The real problem happens when you don't know what strategy the host is using.

by EGPRC 4y ago

firstlink 4y ago

> That only includes a subset of the total attempts that you would start selecting a door, not all. In the trial invalidation version of the problem, but not in the problem as stated. The problem as stated provides, the host does not reveal a car (or your original door). Let me put it another way. If the question had asked, "Conditional on the host not revealing a car (or your original door), what is the probability of winning if you switch?", then that too would be 1/2. My problem is that this is not what is asked. We don't get to answer an easier or different version of the problem. And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. What matters, as you have demonstrated and I have tried to clarify (we aren't really disagreeing), is whether we are exploring the conditional probability in the uniform distribution over a sample space where the host might open another door (1/2), or the probability in the uniform distribution over a sample space where he cannot (2/3). If one denies the difference between these versions of the problem, one ends up in woo-space where the host's knowledge or intentions matter. They don't.

mcv 4y ago
> And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. Knowledge and intentions don't matter? They most certainly do. Imagine a third version of the problem (I'm afraid I don't have a good name for it) where the host actively tries to lure you away from the correct answer, and only opens an empty box if you've picked the correct box. Now, if you pick a box and the host opens an empty box, you should absolutely not switch, because the remaining box has 0% of being the right one. Knowledge and intentions matter. The real problem happens when you don't know what strategy the host is using.