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Comment by colinmhayes | Hacker News Reader

Well if the host opens a door and it never has a prize behind it they have to know which door has the prize right?

It depends on if that's the scenario explained, or you have just one example (not knowing if the host will always show a goat, or if the host will sometimes show you a car either intentionally or by accident).

The part about never having a prize behind it was not explained to me.

It was just "you pick a door, host opens a door without prize". That doesn't imply that there's never a prize behind the door that the host opens.

> That doesn't imply that there's never a prize behind the door that the host opens.

The entire activity is meaningless if the host opens the door with the prize—any questions about switching or not are pointless, since obviously both closed doors are worthless. So that can’t be the interpretation of the puzzle.

What else does "host opens a door without prize" mean?

The difference is "host opens a goat door because he knows which one has the car and chooses to not open it" versus "host opens a goat door by random chance".

For the purpose of the problem there's no difference between the two cases. The only thing that matters is that the host (whether by knowing or by chance) opens a door with a goat behind it.

There is a big difference, "Ignorant Monty"/"Monty Fall" makes switching 50/50 instead of 67/33. The main change is that the door could have had the car, but didn't by chance, and we get to ignore the (one third of the) times he would have revealed a car by mistake. The original Monty never shows you the car because he always picks right, so those possibilities could never happen.

That the host opens a door without prize.

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