I study the impact of novel game manipulations on user engagement using principled computational methods. Maximizing user engagement is important because it results in more profitable games in the commercial arena and better learning outcomes in the educational arena. It is then perhaps unsurprising that the study of user engagement is well established. Most work uses a classical A/B paradigm, in which a few, often binary (on/off), design decisions are manipulated. Recently, optimization studies have begun to explore a range of discrete or continuous levels. The majority of work in both types of studies is concerned with manipulations such as aesthetics, rewards, and difficulty. While many of these manipulations are found to increase engagement, little work has been done on utilizing theories of engagement from other domains, such as gambling and storytelling, to improve user game engagement. For instance, the tension-and-release manipulation, a common technique in storytelling and music composition for controlling event progression, is usually discussed within the gaming context only qualitatively as a way of controlling difficulty over time. The near-win effect--an increase in motivation due to almost winning a game--comes from gambling psychology. Another understudied manipulation is the perception of difficulty, where the user's perception of the challenge is controlled independently from actual challenge or vice versa. Undoubtedly, game designers are using these manipulations--near-win, tension-release and perception of difficulty--in their games but I am not aware of work that systematically explores how different levels of these manipulations influence user engagement. In this thesis I study these manipulations systematically using Gaussian processes, neural network, and preference learning models. Results from multiple Bayesian optimization experiments show that maximum engagement occurs when the user's perception of difficulty is manipulated moderately, suggesting the critical role of a user's self-perception of competence. A/B and random assignment studies show that engagement in a web-based memory training game can be modulated via tension-and-release difficulty curves. Finally, a massive study with thousands of students shows that the near-win effect significantly improves engagement of lower-performing students. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]