Two doors remain closed, so switching feels like a coin toss. It isn’t—provided the host follows the rules.
At the start, your first choice has a 1-in-3 chance of hiding the prize. That leaves a 2-in-3 chance it is behind one of the other doors. The host, who knows what is where, then opens a losing door among those you did not pick.
That reveal does not erase your original odds. If your first pick was wrong—which happens 2 times out of 3—the only other unopened door must hold the prize. Switching wins in those cases. Staying wins only when your first pick was right: 1 time in 3.