I’m pretty sure that ‘if presented with a Monty Hall Problem, switch’, is a bad heuristic: you’d need to know what Monty’s strategy for deciding whether or not to open any doors before you could make a sensible decision.
A better heuristic might be ‘If presented with a Monty Hall problem, ask Monty why he decided to open a door and show you a goat’.
I’m pretty sure that ‘if presented with a Monty Hall Problem, switch’, is a bad heuristic: you’d need to know what Monty’s strategy for deciding whether or not to open any doors before you could make a sensible decision.
A better heuristic might be ‘If presented with a Monty Hall problem, ask Monty why he decided to open a door and show you a goat’.
Why? Regardless of his strategy, you do no worse by switching.
What if he only makes the offer to people whose initial choice of door was the car?
I read somewhere that on the show itself, the odds were about 50-50.
Here’s an interview in which he doesn’t quite say that.