[nmdeadhead]

I do not think that when it's explicitly stated it becomes intuitive for everyone and that adds a further wrinkle. Many people will still get it wrong, even when the problem is stated correctly.

However, if the rule is not explicitly stated, how can the player know that the rule exists? Perhaps "Monty" is evil and will not always open a door, "evil Monty" will only open a door when he knows you've chosen correctly.

IOW, without that rule explicitly stated, the answer "Switch" is simply incorrect. Without that rule, the answer is "I don't have enough information to know."

[em500]

Yup. Wikipedia contains a discussion on host behavior: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...

In fact, the Wikipedia Monty Hall article discusses pretty much any aspect of the problem that anyone has ever brought up in any Monty Hall forum thread or blog post.