There are quite a few cases where armed civilians needed more than 6 rounds.
1) Lance Thomas, the watchshop owner. He was in at least 4 different gunfights, and in three of them, he needed more than one gun to finish the fight (shooting multiple guns dry and going for another). The Ayoob files; An urban gunfighter: The lessons of Lance Thomas
American Handgunner , March-April, 2002 by Massad Ayoob

2) Richard Davis. He was delivering pizzas when he was ambushed by three armed robbers. He shot his revolver dry, hitting all three of them, and then he got plugged in the guts by one of his assailants when he ran dry. (this story can be found in many places on google...I think Ayoob writes about it too).

3).There was the Circuit City shooting in 1996. An off duty officer, Jason Hendrix(I'll consider him an armed citizen, since he was caught in the middle of a public shooting / domestic violence attack, just like any armed citizen might be caught there). He fired all 5 rounds from his Chief Special, hitting the bad guy at least 4 times in the torso. The bad guy had a Glock 17, and walked up to Hendrix and kept shooting him while on the ground. Hendrix survived. Shots Fired: Palm Desert, California 03•30•1996 - Article - POLICE Magazine

There was another story about a home invasion, I cannot find the link. Homeowner was a competitive shooter, confronted the assailants with a scandium 5 shot snub. Fired all five rounds, scoring hits with all 5, and when he went dry, the assailants remaining standing shot him dead.

All of these cases ARE ONES IN WHICH WE MIGHT ALL FIND OURSELVES FACING. It matters not that we are not watch shop owners in the ghetto, nor off duty officers, or pizza delivery men. All of these events happened in public places, and none of them involved a uniform officer performing his or her duties of arrest or engagement.

We all go to shopping malls, we all walk on sidewalks where pizzamen walk, and we all frequent little shops where multiple armed robbers might decide to shoot it out with the owner or even patrons.

It does no good to argue, "Well, I'll just run away"...if we all had that luxary, then we wouldn't need to carry any gun. Some of us go out in public with dependents, who cannot run with you to escape danger. That means we will need to stay and fight, just like all of the above armed civilians had to do.

Odds are, zero shots will be enough. But that doesn't mean that we might not encounter the lottery and win