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"You made a mistake, but look at the positive side. If all those Ph.D.’s were wrong, the country would be in some very serious trouble."

Best quote in the entire article.

And if I had to explain the problem in one sentence: Opening the first door obviously gives you a 1/3 chance, which remains unaffected by the host opening another door.

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> Opening the first door obviously gives you a 1/3 chance, which remains unaffected by the host opening another door.

You had a 1/3 chance if you opened the second door too. Why does the second door's chance change, but the first door's chance is somehow locked by you having chosen it?

First door as in the first door to be selected. When you select it, it has a 1 in 3 chance of being the correct door. The door presented to you obviously has a 0 in 3 chance, so the remaining one must be 2 in 3.

The chance is locked in because, by the rules of the game, the host can't open that one and show you anything -- regardless of what it contains. You know that there's at least one door that the host can open (of the two remaining doors), so them opening a door changes nothing about the door you've chosen.

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