Your simulation is not correct. Look at it this way: 1/3 of the time, you pick the right door up front. If you switch, you lose. 2/3 of the time, you didn't

Your simulation is not correct. Look at it this way: 1/3 of the time, you pick the right door up front. If you switch, you lose. 2/3 of the time, you didn't pick the right door. If you switch, you win. So switch.