Altruism and the selfish gene

I haven't read the book, but I have glanced over the selfish gene explanations and I think what he's getting at is this:Altruism is a kind of genetic selfishness because there could be situations where an organism actually propagates more of its genes by giving its life for several of its close relatives. Consider that you share half of your genetic material with your siblings, as well as 100 percent between your two parents. giving your life to save the lives of your siblings, parents, or other family actually protects MORE of your genes than the other way around.Ergo, even self-sacrifical behaviors have a genetic advantage. That's a loose explanation, I'm sure Dawkins gets into it a little better.