Games are often designed to shape player behavior in a desired way; however, it can be unclear how design decisions affect the space of behaviors in a game. Designers usually explore this space through human playtesting, which can be time-consuming and of limited effectiveness in exhausting the space of possible behaviors. In this paper, we propose the use of automated planning agents to simulate humans of varying skill levels to generate game playthroughs. Metrics can then be gathered from these playthroughs to evaluate the current game design and identify its potential flaws. We demonstrate this technique in two games: the popular word game Scrabble and a collectible card game of our own design named Cardonomicon. Using these case studies, we show how using simulated agents to model humans of varying skill levels allows us to extract metrics to describe game balance (in the case of Scrabble) and highlight potential design flaws (in the case of Cardonomicon).
 Characteristics of Games offers a new way to understand games: by focusing on certain traits--including number of players, rules, degrees of luck and skill needed, and reward effort ratio--and using these characteristics as basic points of comparison and analysis. These issues are often discussed by game players and designers but seldom written about in any formal way. This book fills that gap. By emphasizing these player-centric basic concepts, the book provides a framework for game analysis from the viewpoint of a game designer. The book shows what all genres of games--board games, card games, computer games, and sports--have to teach each other. Today's game designers may find solutions to design problems when they look at classic games that have evolved over years of playing. Characteristics of Games--written by three of the most prominent game designers working today--will serve as an essential reference for game designers and game players curious about the inner workings of games. It includes exercises (which can also serve as the basis for discussions) and examples chosen from a wide variety of games. There are occasional mathematical digressions, but these can be skipped with no loss of continuity. Appendixes offer supplementary material, including a brief survey of the two main branches of mathematical game theory and a descriptive listing of each game referred to in the text.  Motivated by our ongoing efforts in the development of Refraction 2, a puzzle game targeting mathematics education, we realized that the quality of a puzzle is critically sensitive to the presence of alternative solutions with undesirable properties. Where, in our game, we seek a way to automatically synthesize puzzles that can only be solved if the player demonstrates specific concepts, concern for the possibility of undesirable play touches other interactive design domains. To frame this problem (and our solution to it) in a general context, we formalize the problem of generating solvable puzzles that admit no undesirable solutions as an NPcomplete search problem. By making two design-oriented extensions to answer set programming (a technology that has been recently applied to constrained game content generation problems) we offer a general way to declaratively pose and automatically solve the high-complexity problems coming from this formulation. Applying this technique to Refraction, we demonstrate a qualitative leap in the kind of puzzles we can reliably generate. This work opens up new possibilities for quality-focused content generators that guarantee properties over their entire combinatorial space of play.  The pace at which challenges are introduced in a game has long been identified as a key determinant of both the enjoyment and difficulty experienced by game players, and their ability to learn from game play. In order to understand how to best pace challenges in games, there is great value in analysing games already demonstrated as highly engaging. Play-through videos of four puzzle games (Portal, Portal 2 Co-operative mode, Braid and Lemmings), were observed and analysed using metrics derived from a behavioural psychology understanding of how people solve problems. Findings suggest that; 1) the main skills learned in each game are introduced separately, 2) through simple puzzles that require only basic performance of that skill, 3) the player has the opportunity to practice and integrate that skill with previously learned skills, and 4) puzzles increase in complexity until the next new skill is introduced. These data provide practical guidance for designers, support contemporary thinking on the design of learning structures in games, and suggest future directions for empirical research. Behavioral datasets from major commercial game titles of the “AAA” grade generally feature high dimensionality and large sample sizes, from tens of thousands to millions, covering time scales stretching into several years of real-time, and evolving user populations. This makes dimensionality-reduction methods such as clustering and classification useful for discovering and defining patterns in player behavior. The goal from the perspective of game development is the formation of behavioral profiles that provide actionable insights into how a game is being played, and enables the detection of e.g. problems hindering player progression. Due to its unsupervised nature, clustering is notably useful in cases where no prior-defined classes exist. Previous research in this area has successfully applied clustering algorithms to behavioral datasets from different games. In this paper, the focus is on examining the behavior of 62,000 players from the major commercial game Tomb Raider: Underworld, as it unfolds from the beginning of the game and throughout the seven main levels of the game. Where previous research has focused on aggregated behavioral datasets spanning an entire game, or conversely a limited slice or snapshot viewed in isolation, this is to the best knowledge of the authors the first study to examine the application of clustering methods to player behavior as it evolves throughout an entire game. It is easy to create new combinatorial games but more difficult to predict those that will interest human players. We examine the concept of game quality, its automated measurement through self-play simulations, and its use in the evolutionary search for new high-quality games. A general game system called Ludi is described and experiments conducted to test its ability to synthesize and evaluate new games. Results demonstrate the validity of the approach through the automated creation of novel, interesting, and publishable games. Non-negative matrix factorization (NMF) has recently received a lot of attention in data mining, information retrieval, and computer vision. It factorizes a non-negative input matrix V into two non-negative matrix factors V = WH such that W describes "clusters" of the datasets. Analyzing genotypes, social networks, or images, it can be beneficial to ensure V to contain meaningful cluster centroids'', i.e., to restrict W to be convex combinations of data points. But how can we run this convex NMF in the wild, i.e., given millions of data points? Triggered by the simple observation that each data point is a convex combination of vertices of the data convex hull, we propose to restrict W further to be vertices of the convex hull. The benefits of this convex-hull NMF approach are twofold. First, the expected size of the convex hull of the candidate set typically grows much slower than the data set. Second, distance preserving low-dimensional embeddings allow one to compute candidate vertices efficiently. Our extensive experimental evaluation shows that convex-hull NMF compares favorably to convex NMF for large data sets both in terms of speed and reconstruction quality. Moreover, we show that our method can easily be applied to large-scale, real-world data sets, in our case consisting of 1.6 million images respectively 160 million votes on World of Warcraft guilds.  This paper presents a first attempt at evolving the rules for a game. In contrast to almost every other paper that applies computational intelligence techniques to games, we are not generating behaviours, strategies or environments for any particular game; we are starting without a game and generating the game itself. We explain the rationale for doing this and survey the theories of entertainment and curiosity that underly our fitness function, and present the details of a simple proof-of-concept experiment.  We present initial results from ACCME, A Co-operative Co-evolutionary Metroidvania Engine, which uses co-operative co-evolution to automatically evolve simple platform games. We describe the system in detail and justify the use of co-operative co-evolution. We then address two fundamental questions about the use of this method in automated game design, both in terms of its ability to maximise fitness functions, and whether our choice of fitness function produces scores which correlate with player preference in the resulting games.