First off, why discount suicides? The fact is that in households without guns, people are far less likely to commit suicide. Why? Because suicide is usually a quick decision and if people can’t figure out how to do it right in that moment they’re less likely to do so.
Secondly, what “accidents”? There are no gun accidents. There’s handling a firearm improperly, period. If your child gets hold of your gun and kills himself or someone else, that’s not an “accident.” That’s criminal negligence.