Sorry for appearing to be perpetually stuck on the same problem, but my split personality brought it up - I didn't have a choice. Anyway, for the benefit of those new here, I am referring (again!) to the Monty Hall problem.

My friend argues that switching gives you fair odds if the host doesn't know what is behind the door. I have yet to wrap my brain around this slightly counter-intuitive claim; I do not claim that he is wrong, only that there is a fairly problematic hypothetical situation. Anyway, it is entirely probable that I may have left out something somewhere, so thoughts are appreciated.

Assume there is a host and three doors, one of which contains the prize, only that this time, he is behind drawn curtains. It is not known whether the host has prior knowledge of what lies behind the doors. The game is rigged such that if the host doesn't know, the instances where he opens the prize door are not revealed to the player. So, (assuming there is a case in which the host has knowledge, and one in which he doesn't) in both cases, the instances revealed to the player is when he makes his initial choice and the host opens an empty door.

Am unsure whether there would still be a difference in the outcomes of switching between the two cases. Would be very, very surprised if there is.