In the case where he just opens random doors, it doesn't matter that you switch, your door and the other unopened have the same chance. After all, it'd be the

In the case where he just opens random doors, it doesn't matter that you switch, your door and the other unopened have the same chance. After all, it'd be the same if you chose the door to be opened. If that mattered, you should always mentally choose a door, choose another to randomly open, switch and make that your choice. That's absurd. The whole thing is that be cause the host has to open a door with a goat, switching means you basically get to choose both other doors.