This dissertation tells a history of how games have been employed as model systems. By focusing on the influence of games upon the theory and design of symbolic computation from the seventeenth century till the end of the twentieth, it argues that games are the paradigmatic technologies for a still-ongoing revolution in modeling practice. From probability theory to general-purpose computers and from game theory to artificial intelligence and machine learning, the domains and technologies emerging from this modeling revolution define every aspect of industrial and post-industrial life.My first chapter argues that games were central to Gottfried Wilhelm Leibniz’s philosophy as modeling tools by which situations arising in the world could be formalized and subsequently rationalized. By contextualizing Leibniz's project within the earlier Llullian art, the theory of probability derived from games of chance, and other discourses of games in medieval and early modern Europe, I describe how his approach to games was unique in European history and synthesized many different discourses into a general science of games. In chapter two, I describe how Charles Babbage’s earliest work on a machine for general computation was inspired by his mathematical study of games. This research on games, which Babbage explicitly credits to Leibniz’s own study of the “geometry of situation” through games, was also a topic of interest in the early correspondence of Babbage and Ada Lovelace. Games provided crucial tools for notational description of mechanisms, the depiction of computational processes using abstract spatial grids, and temporal sequences of operations that would allow for the development of techniques like the “anticipating carry” mechanism. In my third chapter, I take a broader view of twentieth- and twenty-first century systems thinking—comprising formal mathematics, cybernetics, computer science, AI/ML, cognitive science, operations research, economics, and other related domains—to argue that the game of chess modeled for these domains the twentieth-century concept of a formal-symbolic system. I index the ubiquitous discussion and study of chess in systems thinking in the first half of the twentieth century to changes in the concepts, strategies, and institutions of chess in the decades immediately prior. Subsequent changes in chess, including the creative ‘hypermodernist’ movement and its crosspollination with competitive Go, continued to have impacts on how games were understood, discussed, and studied in the sciences. In chapter four, I focus more specifically on chess in the first half of the twentieth century, arguing that it transformed in the early USSR into a tool for modeling dialectical materialism. Chess was understood by Soviet scientists, politicians, and competitors as a tool for cultural uplift and social rationalization, as well as a neutral site for the empirical demonstration of the superiority of socialism over capitalism, because it allowed both ideologies to be represented simultaneously across the board. Finally, I describe a 1926 state-sponsored psychotechnical study on the game of chess as a (now forgotten) exemplar of a Marxist theory of games as modeling technologies that provides a far more nuanced description of games as evolutionary tools than that of Johan Huizinga a decade later. Chapter five returns to the topic of symbolic computation as a global domain of technoscientific research to argue that differing conceptions of chess were central to the twentieth-century development of symbolic computation, cybernetics, organizational research, and artificial intelligence. By recontextualizing the pivotal ITEP-Stanford match between Soviet and American AI researchers in light of Soviet theories of chess and intelligence, I argue that, far from being a ‘fall from grace’ for AI, the ideological neutrality of chess allowed computer chess research to influence systems thinking far more broadly than AI alone could have done. I conclude by describing the chess theory of Soviet control systems engineer, computer chess researcher, and world chess champion Mikhail Botvinnik. I suggest that Botvinnik’s project of formalizing “the algorithm” of historical chess masters into computer language in order to optimize economic planning and other massive social projects represents a revolutionary theory of modeling practice that can help us to reimagine the possibilities of games and computer technology alike in our moment. The mid-century synthesis of communist and capitalist game research produced all the necessary tools for us to construct entirely new futures, and these tools are everywhere around us. It is time to understand them as such.