Interesting question, Scott. It seems to me that chance has a much greater influence on personal outcomes than most of us are able to emotionally accept. If you make the arduous effort to look at life dispassionately for a few minutes, it seems clear enough that much of what happens, happens in a more or less chance fashion.
But I think most of us are far from emotionally comfortable with that idea. It implies life is not secure, not safe, and that is a thought or feeling that humans instinctively fear and hate. Just look at everything we do -- every length we go to -- to feel secure. People make huge sacrifices to feel secure, and rationalize those sacrifices in such ways they come to believe they are both good and necessary.
Chance, to my mind, is a significant to major factor in most of life's outcomes. But I'm not always very happy with that. In fact, despite believing chance routinely impacts us, I spend considerable time in daily denial that it plays much more than a rare and unusual role at all. It's psychologically very hard to allow oneself to grasp how insecure life really is.
By the way, I find another useful way to distinguish between luck and chance is to define chance as random, and luck as the notion that one in someway is personally favored or disfavored by chance. But I suspect that to use that definition here would amount to changing the subject of the thread -- unless it were used carefully. The reason I bring it up is because I believe that a whole lot of us believe in luck -- believe chance personally favors or disfavors us -- and that that belief amounts to a denial of chance, a way of feeling secure in a chancy world.