This is a topic that comes up frequently.Personally I don't think it is an ethical shot on a whitetail deer,I don't know enough about other game animals to speak to the validity of taking shots at that distance.
I don't care how good a shot someone is they cannot control the movement of the animal that they are shooting at.The deer takes a step forward,or shifts to one side or the other and your in their guts or shoulder.Drilling bulls eyes on a target at that distance and drilling an animal are night and day different.
What is an acceptable liklihood for someone,if they can make the shot 9 out of 10 times,8 out of 10 times?Some would say 10 out of 10 times,meaning if you absolutely don't know that you can make the shot you shouldn't be taking it.I am of that belief.