Academic path to get into video game design?

I’m really interested in getting into some area of video game design, but it’s so broad that I’m not sure how to narrow it down.

Is a a video game “degree” actually worth it, or is it a joke in the industry? Right now I’m taking a mix of computer science classes and art classes, but I’ve only just begun college so I can still move around a bit. Where would a computer science degree put me in the industry? A graphic design degree? Any help at all is much appreciated! Thanks!