No way in h-e--double hockey sticks I can shoot both eyes open- I'm right handed left eye dominant- I've shot both ways, right handed and left handed- have to close one eye regardless- see two of each pin otherwise and they show up pretty far apart. (I also have astigmitism(sp) and this may make matters worse)

Shooting a shotgun was a problem at first as well (used to shoot skeet and alot of upland birds/game/ and waterfowl)- after awhile I started to notice I'd always roll my head over far enough to get my left eye over the vent rib- but it still messed with my sight picture as things always happen too quick shooting birds and I couldn't get focused. Finally started closing my eye and all was good

You do lose some field of view and depth perception, but I can assure you I'd end up shooting every deer in the neck or in the stomach if I didn't close one eye, regardless.