The results are very counterintuitive. For the three-door problem, if the contestant is correct on the first choice, then he or she will be incorrect after a switch. Or, if a contestant was incorrect on the first choice, he or she will be correct after a switch. Since the probability of being incorrect on the first choice is 0.667, then the probability of being correct after a switch is 0.6667.
Yes, I understand that if you make the assumptions that I laid out, then it is advantagous to switch. I'm not confused or bafffled by the problem. The simulation you linked to is predicated on those assupmtions.
But I don't think those assuptions are intuitive based on how the problem is usually presented. At least they are not intuitive for me. Here is the famous Ask Marylin column that popularize the Monty Hall problem;
Suppose you’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?
When I read this, I think that the host is potentially a trickster, or possibly he was waiting to see what I chose before he gave me the choice. I don't view him as a mechanical device that must always open a door that I did not open and that has a goat.
If you think that it is intuitive to say that he always opens a door that the contestant did not open and that the door he opens must contains a goat, then I suppose the result would seem really cool. I don't share that intuition, and so the result seems cheap and misleading.
We need data.
Try it our for yourself! http://onlinestatbook.com/2/probability/monty_hall_demo.html
This quote is what got me to understand it.
Yes, I understand that if you make the assumptions that I laid out, then it is advantagous to switch. I'm not confused or bafffled by the problem. The simulation you linked to is predicated on those assupmtions.
But I don't think those assuptions are intuitive based on how the problem is usually presented. At least they are not intuitive for me. Here is the famous Ask Marylin column that popularize the Monty Hall problem;
When I read this, I think that the host is potentially a trickster, or possibly he was waiting to see what I chose before he gave me the choice. I don't view him as a mechanical device that must always open a door that I did not open and that has a goat.
If you think that it is intuitive to say that he always opens a door that the contestant did not open and that the door he opens must contains a goat, then I suppose the result would seem really cool. I don't share that intuition, and so the result seems cheap and misleading.