Abstract The rise of China has returned attention to the links between power transitions and war. In this literature, three different causal mechanisms can be confused. This essay disentangles them. Power transitions can lead to three kinds of war: preventive, accidental, and revisionist. Formal models tend to study the first, in which a declining state tries to delay or prevent a rival’s ascent. However, major wars during great power transitions are usually initiated by the rising state, not the declining one. To describe these historical cases, less formal theories, especially neorealism and neoclassical realism, focus on accidental and revisionist wars, but these theories tend to fall back on nonrational mechanisms to connect changing power to the risk of conflict. This leaves a theoretical gap: Why would a rising, rational actor deliberately choose conflict, i.e., start a revisionist war? To suggest an answer, this essay demonstrates how a simple change in standard bargaining models—incorporating a nonzero probability of indecisive war—can ground realist intuitions on rationalist foundations. It further shows how this change leads immediately to an intuitive, formal definition of stability that aligns naturally with existing informal work. Then, contrary to existing realist theory, it shows why the rigorous analysis of realist assumptions leads to a nonmonotonic relationship between the offense/defense balance and war. It thus uses realism to inform and potentially redirect formal scholarship; it also uses formal scholarship to sharpen the logical foundations of realism and, in so doing, derive novel empirical predictions. The essay concludes by applying this synthesis to the rise of China today and indicating directions for deepening the formal/realist synthesis.