As a lawyer, I don't like the Monty Hall problem as stated; the "solution" assumes facts not in evidence. Here is a lawyerly statement of the problem:

Suppose you're on a game show, and you're given the choice of three doors: You know that behind one door is a car and behind the others, goats. You pick a door, say №1, whereupon, under the rules of the game, which you also know, Monty, who knows what's behind each door, must open another door that has a goat behind it. He must then offer you the chance to switch. So he opens №3 and says to you, "Do you want to pick door №2?" Is it to your advantage to switch your choice?

Take away the details about what Monty knows and must do, and what the player knows, and the math becomes futile, because the player doesn't know under what circumstances Monty opens a door with a goat or even whether, when Monty opens a door, he knows that it hides a goat. All of these things affect the player's best choice.

Trouble is, if we state the details explicitly enough to establish that Monty's action contains no useful information, the goat's out of the bag, and the puzzle isn't so puzzling. Thus, given the stated version of the puzzle. the 50-50 "reasoning" is not driven so much by the probability of where the car is as by the 50-50 chance that the game is rigged to make switching the right solution.