3 ms·

> The problem is not always presented in a way that makes it clear that the game always progresses this way, and it's not just a description of the particular c

by baddox 11y ago

> The problem is not always presented in a way that makes it clear that the game always progresses this way, and it's not just a description of the particular circumstance you find yourself in one particular play. I'm not sure how that matters. The question is whether, in this scenario, you choose to switch after Monty Hall reveals the door. The terms of the thought experiment dictate that Monty Hall will reveal a losing door. Regardless of what force is actually causing the revealed door to be a losing door, you should switch, because you're essentially being given the option to take your original one door, or to take both of the other doors (at least one of which is a losing door).

dllthomas 11y ago
The terms of the thought experiment are intended to dictate that Monty will always reveal a losing door. However, they are often worded such that a reading that Monty merely has this time revealed a losing door is a valid interpretation. In that case, the problem is under-specified, as we don't know how Monty picks (randomly or always a losing door) and that changes the answer.
- 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 ago
    If 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 ago
      To 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.

by baddox 11y ago

dllthomas 11y ago

The terms of the thought experiment are intended to dictate that Monty will always reveal a losing door. However, they are often worded such that a reading that Monty merely has this time revealed a losing door is a valid interpretation. In that case, the problem is under-specified, as we don't know how Monty picks (randomly or always a losing door) and that changes the answer.

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 ago
  If 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 ago
    To 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.