Game designers can use computer-aided game design methods to model how players may experience the perceived difficulty of a game. We present methods to generate and analyze the difficulty of a wide variety of minimal action game variants throughout game space, where each point in this abstract design space represents a unique game variant. Focusing on a parameterized version of Flappy Bird, we predict hazard rates and difficulty curves using automatic playtesting, Monte Carlo simulation, a player model based on human motor skills (precision and actions per second), and survival analysis of score histograms. We demonstrate our techniques using simulated game play and actual game data from over 106 million play sessions of a popular online Flappy Bird variant, showing quantitative reasons why balancing a game for a wide range of player skill can be difficult. Some applications of our techniques include searching for a specific difficulty, game space visualization, computational creativity to find unique variants, and tuning game balance to adjust the difficulty curve even when game parameters are time varying, score dependent, or changing based on game progress.