I'm in a tourist area. 50/50 maybe the person talking to me is from Chicago, Milwaukee, Madison, or Minneapolis.
I start off with the premise that it is a genuine question and go from there. I don't really think the best starting point is "I have a gun, and I'm a jerk." Maybe there is a time to go there, but not the place to start. With children I would say it is 100 percent a genuine question. If parents see me treating their children with respect, it might be the difference of them treating me with respect? Who knows?
I say I'm 1000/4 good/bad encounters in 5 years. I talk to a lot of people about the gun on my hip. The 1000 just means "a lot", but I wouldn't be surprised if I'm close to 1000 actual conversations about firearms. I just about always have my dog with me when I walk, as I'm out to walk the dog. 1/5 conversations probably mention a gun, the vast majority don't say anything about it. I suspect a different state, or a big city might have different results. We're a pretty strong gun/hunting culture here.