In my opinion the greatest game animal would be big mature Mule Deer. No amount of money and time spent hunting one will guarantee that a hunter will take an animal that size. I have a really good one at home that I accidentally ran into Elk hunting but I long to set my sights on a really tremendous one . I have run into some absolute monsters with no tag in my pocket or already filled out on a smaller buck or being a 1/2 mile away with a bow in my hand and night fall approaching...guess I have reason to be thankful even having gazed at such magnificent creatures and taken one of them .