In the past, with my old Konica that only had manual focus, when grabbing a quick shot, I would almost always settle for a front focus shot first - with the rationale that at least some of the subject was likely to be in focus, with DOF increasing exponentially behind the point of focus. I still use that sometimes, even if the subject is completely still, and I can't see well enough to get the exact point that I want in focus (more and more common the older I get).

Interesting that in your example, Loupey, that the deer was clearer in the rear focus than in front focus. I guess it all depends on how close or distant your points are relative to the subject. I know that I would have had a lot of difficulty getting the deer in clear focus being that far away. My eyes just don't do detail anymore. Gotta save up for that laser surgery - hmmm - since my photography is a business expense due to all of the photos I take for the job, maybe my laser surgery could count as well?? Hmmmm.