Business leaders are frequently forced to make difficult decisions with incomplete information and uncertain consequences. The goal of this article is to provide an exposure to mathematical decision theory and demonstrate how it can add value in real-world decision making. The randomness of the real world presents a disconnect between the correctness of a decision and the actual outcome experienced. A person can make a correct decision, given all the information available at the time, yet still experience an unlucky bad consequence. Similarly, a person can make an incorrect decision, but get lucky and receive a good consequence. The randomness disconnects the reinforcement learning process and makes it difficult for us to improve as decision makers. Behavioral economists, psychologists, and statisticians have done an enormous amount of research on how to improve decision-making. Some of that research has been formalized, leading to recent advances in artificial intelligence, and business leaders can benefit by understanding the principles and process of handling uncertainty.