You need to know why the host did that though. The host might have an adversarial strategy where they only open the door when using vos Savant's logic would make the player lose.

Her logic was really interesting, it is easy to see why she gets to write a column. But at the end of the day the problem is technically ill-formed.

> There’s no way he can always open a losing door by chance!

Yes there is, he might have picked a remaining door at random with the plan of saying "You lose!" if he finds the car. An actor with perfect knowledge can still have a probabilistic strategy. That doesn't really change the decision to switch, but it does have a material impact on the analysis logic.

She's correct that is a necessary assumption to get the most interesting form of the problem. But that isn't what the questioner asked.

I doubt the person writing the question had the more nuanced version in mind. When the column was published, nearly everyone who wrote to Marilyn vos Savant had been in agreement that the host always opened a door with a goat as the problem was specified. This idea that the host did not was made after Marilyn vos Savant was shown to be correct and after she had already confirmed that it was part of the consensus.