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what's confusing about it

is that an assumption is made on Monty Hall's behavior.

Indeed if Monty flips a coin to determine which remaining door to open, then he has given you no information (unless he reveals the 100K and then the game is over). If he does flip a coin, your odds of sticking or switching are the same- 1 out of 2.

But if he consciously decides to open the losing door that is left, he has revealed information to you. And this seems to be the traditional way that Let's Make a Deal worked.

Almost all the confusion comes from people who are assuming he has randomly selected. And given their assumption, they are right.

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