[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.

[yen223]

We are conditioning out the case where the host picks the door with a car, so there's only two scenarios of equal probability left. Hence 50-50.

[dghf]

Well yes, if you throw out half of the instances where your original choice was wrong, then the chance your original choice was correct will inevitably go up.