How do I balance a game with lots of interacting systems?

You can balance most things now. It is the complex cases, the many systems all interacting, where the balance gets away from you. Change one number and three other things shift in ways you did not expect. That is the hardest part of balancing, and it humbles everyone who does it. When everything affects everything, you cannot hold it all in your head, and you should stop trying. The way through is to change one thing at a time and watch what it does before touching the next. Chasing several knobs at once is how you lose the thread of what caused what. Pick the single system that most drives the others and stabilize that first, then work outward. Change one variable, test, observe, then move on. It is slower, but it keeps you from spinning. Complex balance is not solved in one grand adjustment. It is solved one careful, isolated change at a time.