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.

After the master of the game has opened a door and we've changed our guess, we have one chance out of 3 to lose.

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.