Major advances in Question Answering technology were needed for Watson to play Jeopardy! at championship level -- the show requires rapid-fire answers to challenging natural language questions, broad general knowledge, high precision, and accurate confidence estimates. In addition, Jeopardy! features four types of decision making carrying great strategic importance: (1) selecting the next clue when in control of the board; (2) deciding whether to attempt to buzz in; (3) wagering on Daily Doubles; (4) wagering in Final Jeopardy. This talk describes how Watson makes the above decisions using innovative quantitative methods that, in principle, maximize Watson's overall winning chances. We first describe our development of faithful simulation models of human contestants and the Jeopardy! game environment. We then present specific learning/optimization methods used in each strategy algorithm: these methods span a range of popular AI research topics, including Bayesian inference, game theory, Dynamic Programming, Reinforcement Learning, and real-time ""rollouts."" Application of these methods yielded superhuman game strategies for Watson that significantly enhanced in its overall competitive record. Joint work with David Gondek, Jon Lenchner, James Fan and John Prager.