Explanation of the paradox

Before the master of the game opens a door, when we guess A we have one chance out 3 to win.

If somehow, we had been able to guess "B and C", we would have had two chances out of 3 to win.

By opening one of the two doors, B or C, the master of the game, enables us to guess "B and C" while asking him to open only one door.

So we should change our guess from A to C, which has become equivalent to guessing "B and C".

Our new guess now has two chances out of 3 to win.

Notice that the master of the game should be careful to "randomize" the door he opens when he has the choice (that is when our initial guess was correct, but we don't know it yet). Indeed, if the master systematically chose for instance the left-most door when he had the choice, and if we played the game many times with him, we would eventually observe this. Then there would be a case when we know for sure where the prize is.