The Double Blind Monty Hall Problem

Last night as I was preparing today's lunch, I ran into an interesting real life scenario that is a variant of the Monty Hall problem. As I thought more about the subject I became more and more convinced that the probability of choosing the right door by switching was 0.5 instead of 0.6667. I even sketched out a Bayes theorem proof of why that is. Then I realized an assumption that the original Monty Hall problem had. And so in this post, I'll sketch out two variations of the Monty Hall problem. The picture above is of my lunch today: three muffins baked with MyProtein’s muffin mix. Two of them contain raisins, and one of them contains chocolate chips. I had forgotten which is which. I personally prefer raisins, as the chocolate chips had sunk to the bottom of the pan making a gooey mess that sticks to the muffin papers during the baking process. An initial thought that I had was concerning the probability of choosing a subsequent raisin muffin after I had eaten one. Naturally, in scenarios where there are 3 unknowns and one was revealed, my thoughts get pulled towards the Monty Hall problem.