QuaRkZ (the last time I'll ever spell it that way) is a game where you and your opponent are putting particles onto a board, I guess.
Each square will change to the color of the player who last added a particle to it.
When a square has enough particles in it to put one in each surrounding square, it's "critical" and will "explode" into the surrounding squares. In and of itself, this is predictable. The unpredictable element comes from the fact that, when two or more critical squares are next to each other and one of them goes off, they all go off, and while I'm sure, given time, that you could analyze and figure out the logic, it's mostly pretty chaotic.
I remember playing this game ages ago and having no luck with it; when I found it again more recently, I realized that I knew how to play it more effectively because I'd watched an episode of Cyberchase, a PBSKids cartoon, that had a somewhat similar game principle. Don't tell me you can't learn stuff watching cartoons.
(The episode is season one's "Problem Solving at Shangri-La." The principle is one of "lethal numbers," in effect, numbers you don't want to be caught with. How does it apply here? Well, against a computer opponent, the computer seems to have a better awareness of chain reactions, so you use the principle of lethal numbers to avoid letting the computer trick you into filling a square to critical, because if you follow the correct principle, you'll always win by attrition.)
All in all, it's a bit of a boring game if you actually know how to play it, and an annoying one if you don't. However, you can probably still have fun with it in the process of learning how every single game goes.