OK guys, quick lesson...Take your index finger, like a pistol when you were a kid, point it at a door knob or light switch with BOTH eyes open...
Now close the left eye, if the finger is pointed to the object then you are right eyed dominant and should shoot all weapons from your right shoulder and with both eyes open...You will naturally point the weapon at the object because the dominate eye takes over...

Any good game shot with a shotgun knows this and wouldn't dream of trying to mount the gun, close one eye and try to shoot...The same goes with a bow...If you are left eye dominate and shooting a right handed bow then you are handicapping yourself, you can "get by" by closing the other eye but you will miss shots that you should have made just because you aren't shooting in the natural position...