I might not be dealing with a full deck, but I have two answers. North American game - Yes. African game - No. Unless it was a highly discounted cull.
I live in a province with an excellent variety of wildlife, except the mountain and Arctic species. I have killed several typicals of whitetail, mule deer, pronghorn, black bear and moose (have only shot a cow elk so far) and would shoot an oddball specimen gladly.
For African game however, I want a specimen that looks like it's supposed to look as that may be the only one I am ever able to hunt. The exception would be if I was on a cull hunt, or happened upon a particular animal that the outfitter wanted removed from the population. And at that, I would want a substantial discount.