I suspect that much of the contention around this famous problem is based on the original boundaries / rules of the problem being unclear. The problem as state

I suspect that much of the contention around this famous problem is based on the original boundaries / rules of the problem being unclear. The problem as stated sometimes leaves out crucial information that affects the outcome. Example: Game show, 3 doors. Contestant chooses one door. The host opens another door, which has a goat. Do you switch? In this situation, it is not explained whether the host randomly picked one of the two remaining doors to open, without knowledge that one of them would contain a goat. This is the key missing information. If the host ALWAYS reveals the goat, then it is beneficial to switch as 2 out of 3 times the contestant wins by switching. However, if the host is simply opening another door at random, and the door happens to contain a goat, then there is no advantage to switching, as the odds are 50/50. edit: it appears that from the original version of the problem stated in Parade magazine, the implication is that the host knowingly reveals a goat. "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?"