[billforsternz]

The only reason people get confused about the Monty Hall problem is that the problem description rarely if ever makes it clear that the host knows where the car is and deliberately chooses a different door.

It's inconceivable (for example) that Paul Erdos, a world class mathematician, would fail to solve this problem if it were actually communicated clearly.

[yen223]

It is incredibly annoying that in the case where the host doesn't know where the car is but opens a goat door anyway, the probability goes back to 50-50

[dghf]

Eh, when you think about it, it makes sense.

Original rules (host knows where car is and always opens a door with a goat):

- 1/3 of the time your original choice is the car, and you should stick

- 2/3 of the time your original choice is a goat, and you should switch

Alternative rules (host doesn't know where car is, and may open either the door with the car or a door with a goat)

- 1/3 of the time your original choice is the car, the host opens a door with a goat, and you should stick

- 1/3 of the time your original choice is a goat, the host opens a door with a goat, and you should switch

- 1/3 of the time your original choice is a goat, the host opens the door with the car, and you're going to lose whether you stick or switch

So even under the new rules, you still only win 1/3 of the time by consistently sticking. You're just no longer guaranteed that you can win in any given game.

[zephyrfalcon]

But if he doesn't know where the car is, how can he be sure that the door he opens is going to have a goat?