Is the Monty Hall Problem based on a real game show game?
My question is not about math. My question is, what were the rules of the real game that that majority was thinking of instead of the carefully-defined puzzle that I read?
The puzzle is named for the host of Let's Make a Deal. In the puzzle, there is a prize behind one of three doors. The contestant chooses a door, the host opens a door with nothing behind it, and the contestant has an opportunity to switch her choice to the third door.
If this game really happened: did Monty Hall always open a door that contained nothing? Did he even know beforehand which door contained the prize?