3 ms·

Ignorant Monty can't exist. Monty is the host of a game show, not a contestant. He's not trying to win a prize, and if he opens a prize door, it's a production

Ignorant Monty can't exist. Monty is the host of a game show, not a contestant. He's not trying to win a prize, and if he opens a prize door, it's a production failure. Whether he knows or not, somebody told him which door to open, and that door does not have the prize behind it. Malicious Monty, however, can exist. He only ever opens a second door when you've picked correctly, but when you haven't simply accepts your choice. The problem was stated correctly and clearly, though, as long as you assume that Monty is not a person, has no motivation at all, and as part of a math problem simply wants to reveal a goat after you've made a choice and has the means to do it. That's Savant's Monty: the Monty that doesn't add significant features to the question.

btilly 3y ago
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.