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I'm sorry but you are incorrect

Think about it for a while.

If you pick a door, your odds of winning initially are 1 out of 3. Agreed.

Monty now flips a coin to pick a remaining door. There are 3 possibilities.

1: You have picked the 100K so the door he opens has junk. The game continues.
2: You have picked junk, he picks the remianing door with junk. The game continues.
3: You have picked junk, he picks the remaining door with 100K. The game is over. You have lost.

There are only TWO remaining possibilities if the game does not end at his pick. These are:

1. You are on the right door.
2. The one he did not open was the right door.

These are both equally possible.

Your odds are now 1 in 2 whether you switch or not.

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