I hate to guess at the author's intent, but I'm pretty sure there's no magic. At least, within The Folding Knife, there's no magic, nor system thereof. Basso's luck is just luck (or is it "fate"?).
That said, I think it could kind of click with the magical system that's in the Fencer trilogy. I kind of like that theory for its... I dunno... neatness, as it makes a nice RPG-style "rules" for things. But that would also undermine a lot of what Basso says about fate, luck, and belief towards the end, which I think is really important. And I don't like it because, again, that would be a fairly major part of the setting that has nothing to do with the content of this text, and I don't think we can judge what happens here by the rules of a setting (that may or not even be the same setting) introduced in other books.
(If Fencer and TFK are set in the same world - which is possible! - there'd presumably be a hearty time difference between them. Magic is an established, ancient, known 'thing' in Fencer, but goes completely unmentioned in TFK. So TFK would need to be much, much earlier or much, much later than Fencer. AAAH!)