3 ms·
The reason the scenario is kind of twisted is that in the iterated game of "you pick door, he shows goat, switch or no", vos Savant's answer is clearly correct.
by andrewla 3y ago
The reason the scenario is kind of twisted is that in the iterated game of "you pick door, he shows goat, switch or no", vos Savant's answer is clearly correct.
But in the iterated game of "you pick door, and host chooses whether to show a goat or to let you open the door you initially chose" I don't think you (or he) can get better than 50-50. If you chose the correct door initially, then he can try to trick you into switching by opening a goat-door. But if you chose a goat-door, then he can let you open your selected door (or offer some other deal -- $1,000 cash or the door you chose). If he only shows the goat-door when you have selected the car-door, then you should never switch, so his optimal strategy is to show a goat-door when you choose a goat-door 1/3 of the time, so you basically get no information from his actions.
The "always switch" solution imagines this as a one-player game rather than a two-player game, with Monty Hall actively trying to sabotage.
- flomo 3y agoThat's correct, the premise of the show was more Monty Hall doing something to challenge the contestant. That's probably why people missed the problem's premise where he always opens a goat door.
- grraaaaahhh 3y ago>I don't think you (or he) can get better than 50-50. Doesn't Monty reduce your win chances to 33% just by never opening a goat door?
- andrewla 3y agoThat's an excellent point.