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dghfyesterday at 10:43 AM1 replyview on HN

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.


Replies

yen223yesterday at 11:33 AM

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.

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