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The way I've always thought about it is: - you pick one door. The chance of having picked the door with the prize behind it is 1/3. - you now have two choices: either open the door you picked, or open both of the doors you didn't. It should be obvious that it makes more sense to open both...

Not correct with the 50% bit. If there are 3 doors then you have a 1/3 chance of winning if you stick to your original choice and a 2/3 chance of winning if you switch your choice.