I was annoyed after first hearing the Monty Hall problem. It wasn’t clear that the host must always open the door, which fundamentally changes the problem. Glad to see that it’s a recognized problem.
“The problem is not well-formed,” Mr. Gardner said, “unless it makes clear that the host must always open an empty door and offer the switch. Otherwise, if the host is malevolent, he may open another door only when it’s to his advantage to let the player switch, and the probability of being right by switching could be as low as zero.” Mr. Gardner said the ambiguity could be eliminated if the host promised ahead of time to open another door and then offer a switch. - http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=5&src=pm
I was annoyed after first hearing the Monty Hall problem. It wasn’t clear that the host must always open the door, which fundamentally changes the problem. Glad to see that it’s a recognized problem.
More discussion on the previous page of that article: http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=4&src=pm