Yeah, the trick with this one is the game show host knows where the prize is. In the case where you picked correctly first (1:3) the switching to the other doo

Yeah, the trick with this one is the game show host knows where the prize is. In the case where you picked correctly first (1:3) the switching to the other door will be a loss. But in the case where you picked wrong (2:3) the host will eliminate the non-prize door, so a win is guaranteed if you switch. So, 1/3 * 0 + 2/3 * 1 = 66% of winning for the always switch strategy. Shame on your teacher!