if you go to the top of this page and type 'dominant' in the search button, there is some good reading.
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from Google
For most people, their dominant eye is also their naturally preferenced side for doing other things- writing, eating, basic dexterity things.
The general consensus among athletics and neurologists is that it is easier and more efficient to retrain your larger muscles (arms, chest, legs) than it is to retrain your brain/eye. Howard Hill once said that an archer will never become a championship quality shooter (I am wholly paraphrasing here) if he insists on shooting against eye dominance. So, if a person has cross-eye dominance, he'll find that he will do better in sports (such as archery, pool, golf, baseball, anything that requires the eye to get the job done) if he learns to do it with the dominant eye side.
For example, in my case, I am right-handed, but left-eye dominant. I have a left-handed bow, golf as a lefty and shoot as a lefty. Once I made the switch, my accuracy and ability went through the roof.