Ha !!!...the way I do it you seriously cannot tell the difference, especially when the burger is used in chili, spaghetti, etc. The key to cooking deer meat whether it's deer burger or cubed steak, or tenderloin, or ham/shoulder, is to bleed the meat out several times in water or salted water (brining) to the point where the meat loses its reddish color and turns kinda brownish. The quality as well as the amount of the beef fat which also actually has its own flavor is also very important in taking away that "gamey" deer taste. I typically use 75% deer and 25% beef fat for burger or pork fat when making sausage.
Another key is what the deer actually eat and down here starting in July/August we plant sizable deer food plots of soybeans, radishes, peas, etc., near our deer stands...and about a week before the season opens, we'll start feeding them corn/cracked corn, wild pears and crab apples...this also makes a huge difference in flavor.
Also, a doe or yearling make for the mildest tasing deer meat. Conversely, you don't want the meat from a buck that was shot during the rut because they pretty much stop eating and instead devote all their attention to fighting other bucks with hopes of mating with the does.
I doubt it will happen but if you or ANY of the others who post here are ever down my way, let me know...I'll prove it to you you and show a real good time.