If you only ever offered the players to switch if they picked the car, they'd soon realize this and never switch when they're offered this chance. Also, players that picked a goat at first would have no chance of winning the car.
That's assuming players knows about the other players, which is not specified in the problem description. It is not even specified if the same game is played several time with the same rules.
Given the description from the article:
> Suppose you're on a game show,
> and you're given the choice of
> three doors: Behind one door is
> a car; behind the others, goats. > You pick a door, say No. 1, and
> the host, who knows what's behind
> the doors, opens another door,
> say No. 3, which has a goat. He
> then says to you, "Do you want
> to pick door No. 2?" Is it to
> your advantage to switch your
> choice?
I'd say, no, it is not to my advantage because I'd think the host would only ask me to switch if I had taken the "right" choice and want to make me lose.
Unless I knew that the host always ask if one wants to change, in which case the paradox indeed apply.
Game show regulations would not allow that behavior. The problem assumes a typical game show in western media so the reader should assume the player knows all the rules governing the host’s behavior, which you can see in the other discussions.
