In chapter 10 of Half-Blood Prince, Dumbledore makes a claim that I can't parse (emphasis mine):
I do not believe that her magical powers appeared to their best advantage when she was being terrorized by her father.
How do I read this? The "their" in the sentence suggests that the subject is "her magical powers", but then what is the "best advantage" that he's talking about? Advantage over/to what? Even if we drop the word "best", I can't see how her magical powers can appear to their own advantage.
The context suggests that the author is trying to tell us that Merope's magical powers didn't show their full strength until her father no longer terrorized her, but I can't see how this sentence actually communicates that. Have I totally missed the correct reading?