TIL because he Monty Hall Problem is often worded ambiguous, leaving some loopholes, it is better do not switch doors when you play the game with the actual real Monty Hall.

TLDR: The statistics only work if the host has to reveal a goat and offer to let you switch.

In the show the question is based on, the host didn't always open an incorrect door after a guess. He didn't always allow them to switch. He also offered money instead of opening a door at all in some cases. He could use these tools to get the outcome he wanted most of the time.

tldr: The original problem statement does not say that the game host always has to open a losing door.