FWIW, I always figured 3-shot groups were adequate for a big game rifle. Five-shot groups are what I use for a varmint rifle and, if I had a true target rifle, I'd use 10-shot groups.
I remember an old Jack O'Connor article about the "1-shot" group. Jack wrote about an old geezer who fired one shot per day for five days in a row. He would fire two from sitting, two from prone, and one over an improvised rest such as a log. That way he knew what his rifle would do under field conditions from a cold barrel. I think that idea has some merit but I've never tried it.