This seems overly complicated. Here's an answer on Quora which is a more straight forward deweirdification. https://www.quora.com/In-the-monty-hall-problem-how

This seems overly complicated. Here's an answer on Quora which is a more straight forward deweirdification. https://www.quora.com/In-the-monty-hall-problem-how-does-opening-the-second-door-skew-the-probability-in-favor-of-the-initially-unchosen-door https://www.quora.com/In-the-monty-hall-problem-how-does-ope... Reprinted: Q: In the monty hall problem, how does opening the second door skew the probability in favor of the initially unchosen door? A: The Monty Hall problem is generally poorly described, in order to make the conclusion seem more surprising then it is. The actual Monty Hall game — as imagined by the people who are asking the question— is set up like this: In front of you are 3 doors, there is a goat behind two of them, and a car behind the other one. In *round 1* of the game, you select a *pair* of doors, from which *one* “goat containing door” will be *automatically eliminated from*, leaving only *one* door of the selected pair of doors in play, (and only *two* of initial *three* doors in play). In round 2 of the game, you guess which of the two remaining doors in play has the car. The choice is this: should you choose the remaining door from the pair selected in round 1, or should you choose the door which was not part of the selected pair in round 1? When phrased like this, the answer is fairly obvious: the pair of doors contains a car 2/3 of the time, whereas the non-paired door contains a car 1/3 of the time. The Monty Hall problem— as normally described— messes this all up by introducing a game show host. This is an agent who— seemingly by their own whim— changes the game you thought you were playing, and introduces round 1 of the game once you have guessed the door you initially think the car is behind. The rules this game show host agent are following are almost never described to a sufficient degree to ensure the game is equivalent to the game laid out above. And yet, the people asking this problem pretend that it is exactly equivalent when they ask you for an answer. It’s generally a poorly described problem, whose answer depends entirely on what kind of agent the game show host is. Don’t worry if it doesn’t make sense to you as it’s usually described. If you can understand why— in the two round game I describe above— it’s better to pick the door from the pair of doors, rather than the single door, you understand probability just fine.