I don't know if anyone remembers, but years ago I was all alone in advocating the UniDot on this board for "cross eyed" shooters like me and Brian.
I spent much time trying to explain and it seems folks have finally figured it out.
As Brian explained, if you are dominant in your off eye, you will see two barrels.
With the UniDot only one of the two will have the glowing dot (it is the correct one over your shooting shoulder).
It does take some mental training, but if you stick to it, you can train your brain to focus -- I mean tight, clear, primary focus, on the target (this it the opposite of pistol shooting where you focus on the front sight and the target is blurry) -- and your brain will pick up on the glowing dot to make the right bird/bead relationship to break the target.
Contrary to much popular myth, which seems to be finally fading away, you need a good bird/bead relationship to break the target.
Where you'll run into trouble, as Brian explained, is when you try to focus on the bead rather than the target. That much is not myth, it will lead to misses.
I am still awaiting getting a custom fit stock, which I believe is essential to consistent shooting, but believe that once I get one and dial in the fit and POI I will be at very little, if any, disadvantage shooting with a UniDot vis a vie having my dominant hand and eye the same.
To me, trap is nearly identical to golf in the physical and mental skills involved. Assuming everything is set up right to fit you and shoot where you are looking (with the right bird/bead relationship (shooting where you are looking means nothing if the bead and POI are matched up to where you look)) you will probably find that most of your misses are due to errors between the ears (like thinking about breaking the next ten rather than the one you are shooting at or what your wife will wear to bed that night).
The UniDot is not magic, but if you are willing to train your brain it should work for you. If you believe it won't, well then I'm pretty sure your brain will make sure it doesn't.
If you can afford them, or if your comb is pretty high, the Keensight (by Vicky Keen) are really freaking cool, as Brian from Oregon said. They have the fiber optic bar set in a channel down the middle of the rib. They keep your off eye (the dominant eye if you are a cross-eyed shooter) from seeing the dot so that when you see the double vision barrels, only one will have the glowing dot on the end and you can train your brain to match that one up with the target and ignore the other.
If you are focusing on the target and not the end of the barrel/bead, you will see only ONE target, even if you are cross dominant.
Many folks will tell you this is all crapola, but they just don't understand what is happening or are just stubborn mules.
For other folks who are reading this, understand that cross dominance can be occasional as well. This is what happens to me. I can shoot most targets fine without the dot, but on targets that cross to the left across my left eye (with the gun shouldered on my right), my left eye will take over and the eye (functionally your rear sight) alignment between my rear sight (eye) and front bead will cross and I will miss the target.
If you have a kid like this just switch them over to shouldering the gun on the side of their dominant eye. It can be done and is preferred. Did you know that Phil Mickelson golfs wrong handed? It is true.
For those of you that are already grown up and just can't get used to the feel of switching shoulders, put the time in with the UniDot and you may just find it the greatest thing since [fill in the blank].
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