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A comment on Math Goblins. Parent comment
It does reveal new information, just not about the door you chose.
> lets say that he opened two doors with goats instead, then what is the probability of A, ie your first guess being correct?
But you can't guarantee that he can do that. If you do guarantee that he can do that then you are giving me more information.
It's always the way, if you change the problem you change the analysis.
> So the argument "your first pick is always 1/3, so you should always switch" is wrong. That doesn't normally apply.
Just because it doesn't normally apply, that doesn't mean it's wrong in this case. It does apply in this case (as you say) and therefore it's right.
Knowing when it's right is hard, I agree.
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It does reveal new information, just not about the door you chose.
> lets say that he opened two doors with goats instead, then what is the probability of A, ie your first guess being correct?
But you can't guarantee that he can do that. If you do guarantee that he can do that then you are giving me more information.
It's always the way, if you change the problem you change the analysis.
> So the argument "your first pick is always 1/3, so you should always switch" is wrong. That doesn't normally apply.
Just because it doesn't normally apply, that doesn't mean it's wrong in this case. It does apply in this case (as you say) and therefore it's right.
Knowing when it's right is hard, I agree.