I don't know if I'd describe it as an advantage but being aware of stance allows you to look for openings in your opponent, noticing your opponents stance and then switching your stance to allow for you to attack an opening or maybe taking advantage of something your opponent has shown in his attack/defense. I think every fighter has a preferred side but a good opponent will constantly force you to change your stance, which is why we train both sides, so we have no weak side.
Congratulations. By allowing your opponent to determine your stance, you've come a long ways towards allowing them to control the entire fight.
Not my idea of good planning...