Gotcha. Yes, it only matters with both eyes open. If you shoot both eyes open in your situation, your left eye will try to take over just by the nature of it being dominant. If that happens (and you may not know it until you release) your arrow will fly VERY wide, lots of times missing the target by a good bit. You may also experience a bad case of double vision trying to sight properly. I'm certainly not "the expert" but from what I've seen and the folks I have dealt with, its tough to shoot both eyes open unless your dominant eye is sighting through the peep (or whatever you use). Best is probably to continue to shoot one eye closed, unless you want to switch to a LH bow. You can still be very accurate as you do now, leaving the dom eye out of the equation. Hope this helps.