I just watched 21 and there was brief mention of the Monty Hall problem.

Ben's answer to the reverse psychology question was inadequate - if the gameshow host is capable of trying to psyche contestants out of the right choice, it would appear that statistics do not 'back him up'. In fact, assuming that it is in the interest of the host to try prevent the contestant from winning, and if he does not have to open an empty door regardless of the contestant's choice (reverse psychology seems to be an irrelevant issue if he has to, since his choices would be effectively determined by the contestant's choice), then switching would always result in the wrong door.

It would be interesting to consider the possibility of the host accidentally opening an empty door, i.e, he has no prior knowledge of what is behind each door.At the moment, I am veering towards thinking that it is even chance before the host opens the door because the 1/3 probability that the host would open the door containing the prize would correct for the additional 33% but it would be essentially the same (i.e 66%) once the empty door is open, regardless of the host's knowledge.


The answer suggested is that, in this case, it does not matter if he switches because it is an even chance but that seems slightly counter-intuitive. I haven't gotten down to working in on paper yet. Thoughts, anyone?