I hunt deer with a muzzleloader most of the time, and I only need one round (but I generally carry 4 reloads just in case). When I hunt with a rifle, I carry a full magazine (3-4 rounds), plus one more magazine worth in my pocket. But again, I've only ever needed one shot. The couple times I missed, having the reloads would have made no difference.
When I hunt small game I'll either carry my shotgun with a full load of appropriate shells in the gun (5 rounds), plus 10 more in my pockets, or my 10/22 with a full mag (10 rounds) plus an extra box in my pocket (40-50 shots).
Mike