Closing your non-dominant eye altogether is the most precise way to aim because it removes any doubt about which eye is in control. One hundred percent consistency is the result. This is the method preferred by Full Draw columnist Randy Ulmer. Randy is arguably one of the best with a compound bow that ever lived so it is hard to argue with his perspective.
I snipped that from an article by Randy Ulmer. If you go to that website there is a nice article on pros and cons of shooting with both eyes open or one closed.
I'd rather drag out a 4 pointer with my father than a 10 pointer alone.