Ignorant Monty absolutely can exist. The person standing in front of the audience is not necessarily the person who arranged the prize. And if he's not, he know

Ignorant Monty absolutely can exist. The person standing in front of the audience is not necessarily the person who arranged the prize. And if he's not, he knows nothing more than the audience. I was, however, wrong that Monty was ignorant. By his own statement, he always knew the answer. But whether or not he was on your side depended on his mood. And he applied various forms of pressure to get you to make the right, or wrong, decision. Therefore the problem was not stated correctly. A correct statement needs to not just state what you witness, but the counterfactuals about possibilities that you didn't witness.