5 ms·

This is a famous problem and the solution is not contested.

by computerfriend 7y ago

brazzy 7y ago
I'd rather say that the solution is constantly contested by people who can't shake off their intuition.
- retsibsi 7y ago
  To be fair, the problem is often badly posed. The host always reveals a goat, and this is crucial information, but people often fail to make it clear. If the host chose randomly and just happened to reveal a goat, the solution would be the 'intuitive' one.
  - aardshark 7y ago
    No, I don't think that's accurate. In the scenario you pose, sticking and switching have an equal reward, so both are valid solutions.
    - retsibsi 7y ago
      > sticking and switching have an equal reward Right, and this is the intuitive solution. Nobody argues that switching reduces your chance of success; the split is over whether it increases it to 2/3 or leaves it at 1/3. (The problem statement ends with 'Is it to your advantage to switch your choice?' The right answer under the intended assumption about the host is 'yes', but the intuitive answer is 'no, it makes no difference'.)
      - retsibsi 7y ago
        Sorry, I shouldn't have said 'increases it to 2/3 or leaves it at 1/3'. If he picks randomly and reveals a goat, the probability that your original choice of door is a winner is now 1/2, as is the probability that the remaining door is a winner.
- andrewla 7y ago
  I think the reason that people can't shake off their intuition is that the intuition is based on the idea that the host (Monty Hall) has agency. The specific posing of the problem is that the game is you are presented with three doors, you choose one, and the host opens a door showing a goat, and you have to decide if you want to switch. The problem is that people imagine a game where you choose a door and the host decides whether to open a second door to convince you to switch OR they open the door you chose to show the goat. So given that they CHOSE to open a goat-door, is it the right move to switch? That problem is a game theory problem and requires that you understand the strategy that the host is employing; the intuition is that the host WANTS you to lose, so will only open the goat-door if you chose right (or has a significantly higher probability of doing so) so switching is "falling for" the trick. Re-imagining the problem as a different scenario, where you can ask to see which of two doors contains a goat, and then deciding which door to take avoids this trap. Then the solution is not obvious, but not counter-intuitive (maybe; depends on your intuition).

This is a famous problem and the solution is not contested.

brazzy 7y ago

I'd rather say that the solution is constantly contested by people who can't shake off their intuition.

retsibsi 7y ago
To be fair, the problem is often badly posed. The host always reveals a goat, and this is crucial information, but people often fail to make it clear. If the host chose randomly and just happened to reveal a goat, the solution would be the 'intuitive' one.
- aardshark 7y ago
  No, I don't think that's accurate. In the scenario you pose, sticking and switching have an equal reward, so both are valid solutions.
  - retsibsi 7y ago
    > sticking and switching have an equal reward Right, and this is the intuitive solution. Nobody argues that switching reduces your chance of success; the split is over whether it increases it to 2/3 or leaves it at 1/3. (The problem statement ends with 'Is it to your advantage to switch your choice?' The right answer under the intended assumption about the host is 'yes', but the intuitive answer is 'no, it makes no difference'.)
    - retsibsi 7y ago
      Sorry, I shouldn't have said 'increases it to 2/3 or leaves it at 1/3'. If he picks randomly and reveals a goat, the probability that your original choice of door is a winner is now 1/2, as is the probability that the remaining door is a winner.
andrewla 7y ago
I think the reason that people can't shake off their intuition is that the intuition is based on the idea that the host (Monty Hall) has agency. The specific posing of the problem is that the game is you are presented with three doors, you choose one, and the host opens a door showing a goat, and you have to decide if you want to switch. The problem is that people imagine a game where you choose a door and the host decides whether to open a second door to convince you to switch OR they open the door you chose to show the goat. So given that they CHOSE to open a goat-door, is it the right move to switch? That problem is a game theory problem and requires that you understand the strategy that the host is employing; the intuition is that the host WANTS you to lose, so will only open the goat-door if you chose right (or has a significantly higher probability of doing so) so switching is "falling for" the trick. Re-imagining the problem as a different scenario, where you can ask to see which of two doors contains a goat, and then deciding which door to take avoids this trap. Then the solution is not obvious, but not counter-intuitive (maybe; depends on your intuition).