In my experience, you don't hit a running a deer. They usually seem more then happy to hit you while traveling on the PA turnpike.

In all seriousness, I'm very confident in my shooting abilities and have no problem hitting a target 500 yards away without a scope. But when it comes to a running deer, I'd probably pass on it. It's not worth the risk of just injuring the sucker and never seeing the deer again. Patience.