I have never shot at a deer with a shotgun. I did once carry a double shotgun on a deer hunt but did not get a shot. This was some 45 years ago when deer weren't the Vermin they are now in my area. Just prior to this my Wife had gone on a ladies only hunt on a wildlife management area where only shotguns were allowed. She carried my Richland 707 20 gauge double & killed a doe with it. We had sighted it in & the left (full choke) barrel hid dead center, with the right barrel shooting off by around 6". I don't recall for certain now but as I recall it crossed & hit to the left. I told her if she got a shot to pull the back trigger first, which she did. She was using standard Foster 2 3/4" factory loaded shells, Remington, as I recall.
