We do not currently know of any antonyms for Monty Hall problem.
The noun Monty Hall problem is defined as:
A brainteaser regarding probability, in which a game showcontestant picks a door to win a prize. One door conceals a car; the other two conceal goats. After the contestant picks a door, the host opens one of the two remaining doors which reveals a goat. Counterintuitively, it is then in the contestant's interests to switch to the remaining door.