The only issue I see...and I'm assuming none of you have probably ever exchanged gunfire...is that most people don't want to die and wouldn't rather die or risk serious injury instead of go to jail. If you have a gun pointed at you, the safe thing to do is to assume it's loaded. Most people have an instinct that tells them to stay alive.
Now, maybe there are a few guys out there who are willing to die for your TV. First assumption is that they're going to kill you regardless. I don't think that's the case, as life in prison isn't worth your TV either.
In reality, the gun itself is a deterrent, as is the potential outcomes:
1. Get killed
2. Get really hurt
3. Commit aggravated battery / attempted murder, probably get caught, go to jail.
4. Commit murder
5. Any mix of the above
6. None of the above
7. Walk away
If I merely point my gun at someone, they'll throw hands-up and/or run away. In that case, owning ammo would have made no difference.
If they reach for their gun they're hoping that, at close range, they're faster at retrieving their weapon and firing it accurately before me (who already has weapon drawn and aimed). If they know they're a faster, better aim and can kill me before I can, than owning ammo would have a small benefit but chances are I might lose because I'm facing someone with Navy Seals skills.
If they draw first and I pull out a piece I'm losing because I was not in the Navy, a SEAL, nor am I exceptionally fast. I'm a pretty good aim for a non-owner. Hell, even if I were 99% better I'm not winning that match.
If we're both already drawn upon meeting, my mind is better for survival than my ammo. If I fire, I could miss or he could also fire and one or both of us lose. More likely we'll figure out an agreement to walk away unhurt. Ammo would have some benefit here in case I wanted to take a large risk, but my chances of survival are just as good without ammo.
So owning a gun has an advantage, yes. Owning ammo has a small advantage. It's based on the assumption that Hollywood style drama will ensue and their will be an exchange of fire.