In this dissertation, I explore the idea of designing "flexible game systems". A flexible game system allows players (not software designers) to decide on what rules to enforce, who enforces them, and when. I explore this in the context of digital card games and introduce two design strategies for promoting flexibility. The first strategy is "robustness". When players want to change the rules of a game, a robust system is able to resist extreme breakdowns that the new rule would provoke. The second is "versatility". A versatile system can accommodate multiple use-scenarios and can support them very well. To investigate these concepts, first, I engage in reflective design inquiry through the design and implementation of Card Board, a highly flexible digital card game system. Second, via a user study of Card Board, I analyze how players negotiate the rules of play, take ownership of the game experience, and communicate in the course of play. Through a thematic and grounded qualitative analysis, I derive rich descriptions of negotiation, play, and communication. I offer contributions that include criteria for flexibility with sub-principles of robustness and versatility, design recommendations for flexible systems, novel dimensions of design for game play and communications, and rich description of game play and rule-negotiation over flexible systems. A model of rule-negotiation is introduced as well as advancements in theory regarding unexpected use of software and socially-negotiated play. [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/en-US/products/dissertations/individuals.shtml.]