Curdog said:
I shot at an A level for years right-handed/left eye dominant. I never found it necessary to move my left eye over the cue or to tilt my head in a strange way.
I think the truth of the matter is that I shot for probably 25 years or more before I even heard of a dominant eye! It wasn't until I heard of this issue that it became a thought to me. I don't believe that it is terribly important where your dominant eye is positioned as long as it is consistent from shot to shot.
I'm with you, eye-dominance does not matter. Not ever, not a little, none, no way, don't waste your time checking, it won't help you, get over it.
You need DEPTH PERCEPTION to play pool and that takes BOTH eyes. Close one of your eyes and walk around poking things with your finger...try to touch them softly. You'll have a hard time telling how far away things are because there is no depth perception.
If you like the cue under one eye or the other, go for it. I've seen some strong players that shoot like that. If you like to tilt your head, go for it. I've also seen strong players that tilt their head. The only thing that comes to my mind is how do you do something so unusual consistantly? That is the reason why I have my cue under my chin, and my head straight...bottom line, it doesn't matter.