A contest here is one in which each side makes its move and the gains and losses of each are bound up with the other's. Balance is the refusal to let one side grow too strong. This class is about these two ideas in the Warring States period: how, when one is behind overall, to win a local advantage by choosing what to give up.
In the middle of the Warring States period Sun Bin devised a horse-race plan for Tian Ji: set his own lowest-grade horses against the other side's top-grade ones, giving up one race, and use the rest of his horses in the other races. This trades a local loss for victory in the whole contest.
In 329 BCE Zhang Yi entered Qin service and promoted the Horizontal Alliance, which came into conflict with the Vertical Alliance. The two were opposite ways of forming alliances, and the states held one another in check between them.
The horse race is about choosing what to give up within a single contest, and the Vertical and Horizontal Alliances are about checks among many states. One is on the racecourse and the other among the states, but both seek balance when strength is not on one's side.
Balance of Power is the class in the chapter on Strategies on alliance and balance: the Warring States art of winning a local advantage from a weak position by alliance, balance and choice of plan. Sun Bin devised a horse-race plan for Tian Ji, and Zhang Yi entered Qin service to promote the Horizontal Alliance against the Vertical Alliance, so that balancing among many states became the main thread of Warring States diplomacy.
