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by ghusbands
4219 days ago
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On top of this, if you're at all unsure about the wording, you can apply the meta-solution that it's best to switch, because the chance of it giving you the car is always at least 1/2 and has a non-zero probability of being 2/3. That gives an expected cross-universe probability of more than 1/2. |
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If I was in a culture where gameshow hosts behaved differently the question would have different priors and a different answer.
What if all gameshow hosts shot contestants immediately after they won? Would you be better of switching? No, you'd be dead, so you didn't "win" the car. Completely silly example but it shows why this can't be taken seriously as a mathematical question with probabilities without injecting additional assumptions (unless of course it is stated clearly but then I bet few mathematicians would get tripped up).