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by Sandman 2279 days ago
then there is no point switching

Why not? Your chances of choosing the correct door were 1 in 3 from the start. That doesn't change with the fact that the host opens the doors at random.

3 comments

Sorry for the late reply, but if you look at the original article on GitHub I explore that scenario in the code. The answer is that if Monty randomly opens a door then the contestant automatically loses 1/3 of the time before given a chance to switch.
That's what the GP said. In reality, the host doesn't open the door at random. They know which door hides the car and avoid opening it. That's why switching the doors doubles your chances of finding it (because the host has already eliminated one of the goat doors).
Your chance was 1 in 3 yes, but if the host can randomly open the car door, there is a chance of 1 in 3 of that happening, leaving only 1 in 3 chwnce of switching being legal and useful.