Man the number of people suggesting it matters whether the host knows or not makes my head hurt. It doesn't. The problem is equivalent to "given that the host r

Man the number of people suggesting it matters whether the host knows or not makes my head hurt. It doesn't. The problem is equivalent to "given that the host reveals a goat and you swap doors, what is the probability you get the prize". This will be 2/3. Whether the host knows or not is irrelevant. There are only 2 possible paths in the problem: Path 1: you originally picked a goat (p = 2/3), now you swap and get the prize Path 2: you orinally picked the prize (p = 1/3), now you swap and get nothing This depends in no way on the host having knowledge.