Dude, I would not get hyped up over horoscopes and other magical superstition. I once checked those out, and none of it coincided with me. None of it was me. If she does happen to display the traits of a sign, that's just coincidence.
So if the lady wants mind games, then give her mind games. Play games of riddles with her, chess, whatever. The key to any intellectual thing that you do with her is to make it entertaining. Get her on something that will not only get her intellectually involved, but will also get her to have a load of fun.
"There is no better than adversity. Every defeat, every heartbreak, every loss, contains its own seed, its own lesson on how to improve your performance the next time." - Malcolm X