a good way to make deer burgers is mix it (2 to 1 ratio) with sausage, I personally use deer sausage made with mixed in pork fat, but I have used regular pork sausage (the cheap stuff no need to get fancy) typically the cheaper the better b/c it wont make the burger taste like a sausage patty, put some liquid smoke, ground pepper, and seasoned salt in it and your good to grill.
keep in mind, my deer meat is ground with 18-20% beef fat. so you may have to adjust your fat % accordingly.