Finding Your Dominant Eye for Billiards
When you process an image, your brain complies the images from each eye. It combines the information to produce a third image. This third image is actually what affects your aim, and motor skills during the billiard shot. When you are aiming your shot and looking down the cue, your dominant eye takes over, and is responsible for the alignment that you choose when you finally release the shot. Because of this, the dominant eye should be the one looking directly down the cue and aiming the shot and the weaker eye should be looking to the periphery or the pocket.
You can find your dominant eye by holding your arms straight out in front of you and fully extended. (Paralell to the ground.) Connect your index fingers to a point toward the ceiling, and then join your thumbs at the bottom to form a triangle. With both eyes open, focus on a distant but stationary object as normal. While remaining focused on that object, slowly bring the triangle closer to your face. As it is moving closer, you will notice that your dominant eye will begin to take over focus, and hone in on the object, and your hands will naturally move toward that eye. Whichever eye your triangle is aligned with is your dominant eye. At first when you do this, you may only notice a slight movement of your triangle to one eye. If you are unsure, try forcing it to the other one while remaining focused on the distant object. Notice how awkward it feels?
Use this knowledge for finding your dominant eye for billiards. Then you can ensure that the dominant eye is always placed over your cue when shooting.