Scott - Every reference I read on the net says everyone has a dominant eye--- classified as "weak" or "strong." Can you reference a site that says there are people with no dominant eye? I read that ocular dominance is required to prevent binocular vision. Hypothetically, if there were people with true non-dominant eyes---or equal dominance--- the % is so small, your question is a moot point.
Folks:
This concept of "ocular dominance" (the technical term for the blue-collar "dominant eye") is actually a MISNOMER. There is no such thing as a dominant eye, because in all human beings, the optic nerve of each eye is connected to a separate hemisphere of the brain. You remember the ol' "left brain -- analytical side" and "right brain -- creative side" thing, right? Believe it or not, this same thing applies to the eyes, precisely for this reason.
And, get this -- there can also be "application" differences (preferences, actually) between the two eyes. And the "dominance" (if you want to call it that) can actually change from eye to eye, depending on what you're doing with your eyes -- i.e. what is it you're trying to see? Here's a very interesting read about the eye dominance fallacies in the Oxford Journals:
http://brain.oxfordjournals.org/content/125/9/2023.full
I'll use myself as an example. Many would say that I'm left-eye dominant. They might say this, because when reading extremely fine print (like those information pamphlets that you find inside the box for medication), I might close my right eye, and read it entirely with my left eye. My right eye has problems focusing on short-distance objects, like extremely fine print in front of my face. My left eye focuses -- forgive the pun -- in the blink of an eye for close-up objects, and does so razor-sharp. However, for long-distance things -- like aligning and sighting the iron sights on my German 8mm Mauser rifle -- I use my right eye. (And that's not because I'm right-handed -- I can actually shoot with both hands, but I prefer my right-eye over the sights because of the long-distance alignment thing, and I get more of a panoramic view with my right eye than my left eye.)
After consultation with an ophthalmologist
(I thought there was "something wrong with me" that my eyes seemed to reveal "distinct" specialties and uses -- I thought I had diabetes or something because the first symptoms can reveal themselves in eyesight anomalies), he assured me what I was observing with the distinct specialties between my left and right eye was NORMAL. I told him that I shoot firearms competitively and also play pool. He asked me how I position my head over the cue (I had them with me, because I knew this question would come up). When I demonstrated to him, he noticed that I'm dead-center over it (my chin centered on the cue, eyes level [head not tilted one way or the other], and the tip of my nose over the center of the cue). He explained to me that my mind is able to overlay and blend the "short distance and detail-focusing specialty" of my left eye, with the "long distance and panoramic specialty" of my right eye, to create one cohesive image of the shot. I was floored to learn this!
So while this talk of "dominant eye" has SOME applicability to pool, I would recommend anyone trying to do any kind of self-diagnosis to seek the advice of your local ophthalmologist first. You may be surprised at what you learn. And, you may also catch the early warning signs of certain diseases (like diabetes) that can show up first in eyesight anomalies.
-Sean
P.S.: in case the question comes, which I know it will, "but Sean, what happens when you move your head left or right over the shot?" If I've gotten down on the shot and I'm comfortable enough to pull the trigger with the assumption that the ball will be pocketed, if I freeze, and take note of where my head is, it's dead-center over the cue, with my chin touching. If I bow my head straight down, the tip of my nose will touch the top of the cue. If I move my head left (so that the cue is closer to being under my right eye), the cue "moves" to the right, and the shot looks out-of-line to me. Likewise if I move my head to the right (i.e. so that the cue is closer to being under my left eye); the cue moves to the left and it looks out-of-line to me. So "doc" was right -- my brain is apparently combining the distinct specialties of my left and right eyes equally to create one image.
P.P.S.: Richard Kranicki's great work
Answers to a Pool Player's Prayers has some great exercises you can do with a dressing mirror positioned near the table, some string, and some other aids. You can find your natural eye "dominance" (if you will) using some of these exercises.