I've always subscribed to the theory that we have 2 eyes for a reason......I think anytime you take one eye completely out of the equation you are going to promote balance and depth perception problems. Probably just fine for shooting a scoped firearm where you can only use one eye anyway and your visual picture is dominated by the scope, but when shooting a bow you are taking in the environment as you see it and depth perception and balance are more critical.........especially 20 feet up a tree.
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Personally my accuracy is much better when shooting with both eyes wide open