Kain would never describe himself as particularly lucky. In fact, he'd argue that luck rarely, if ever, worked in his favour. In fact, whenever something 'lucky' did happen to him, he'd likely become more paranoid about what horrible tragedy he could expect to come his way soon.
Just thinking about his life—both his past and present one— would reiterate this.
When he got into the college of his dreams in his past life—his entire family died on the drive up to see him.
When he got the internship position of his dreams—he died a painful and gruesome death from some kind of mystery disease.
And in this life, it feels as though every month or so he is having to somehow scrape his way through one life-threatening event after another…
However, surviving millions of tons of collapsing ice, stone, and snow with only mild injuries had to count for something—probably at the cost of every shred of good luck he had left.