Depth in Strategic Games

This paper explores the question of whether it's possible to discover a well-defined property of game systems that corresponds to what game designers and players mean by the term ``depth.'' We propose a measurable property of a game's formal system, which we call `d', that corresponds to the capacity of a game to absorb dedicated problem-solving attention and allow for sustained, long-term learning. To define this property we develop a formal model that measures how susceptible a game is to partial solutions under conditions of steadily increasing computational resources. We then sketch out several directions for using the model to investigate questions about the structural properties of games that produce these effects.