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That does sound underspecified, although I would think that it still makes sense to switch. If Monty reveals a winning door, it obviously doesn't matter whether
by baddox 11y ago
That does sound underspecified, although I would think that it still makes sense to switch. If Monty reveals a winning door, it obviously doesn't matter whether you switch (both other doors are losers), but if he reveals a losing door you're better off switching because you're still essentially getting 2 doors instead of the 1 door you originally selected.
- dllthomas 11y agoIf he might have opened a losing door, your odds are no longer 2:1 switching. This surprised me as well (in fact, I wrote a simulation for myself intending to reassure me that it was not the case, and learned better).
- qu4z-2 11y agoTo waffle on this point: He has a higher (double) chance of picking a goat if you've picked the car. So by unplannedly revealing a goat, he gives you more information about whether you're in a world where you've picked the car, or one where you've picked a goat. If you pick randomly between a fair coin and a double-headed coin, there's a 50/50 chance of picking either. If Monty then flips the coin and it comes up heads, that suggests you're more likely to be in a world where you've picked the biased coin. If, on the other hand, Monty deliberately takes your coin and places it so that it's heads (and he was gonna do that whatever coin you picked) then you have no new information.