You got me, the only reason I'm on here is to accumulate XP so I can get more spells and a larger HP pool next level.
Seriously though, I think the OP did a decent job trying to figure things out before posting. S/he read the obvious doc, did some troubleshooting, and had a nearly correct understanding of the ||= operator, but was unsure and needed confirmation and a little guidance. I think the OP's main issue is that the reader of perlop needs to extrapolate some of the function of ||= from the examples for += and the OP may have missed that. Regarding // vs ||, even some of the people answering had some confusion.
OK, that's my two cents. Now I'm off to Reddit, where the votes actually matter!