Characterizing and Optimizing Game Level Difficulty Glen Berseth 1, M. Brandon Haworth 2, Mubbasir Kapadia 3, Petros Faloutsos 2 1 University of British Columbia, 2 York University, 3 Rutgers University 1

Motivation [Resident Evil, Capcom] [Baldur’s Gate II, Beamdog] [Tomai, et al 2013] [Csikszentmihalyi 90] 2

Goals Calculate the expected difficulty of a scenario Procedurally generate a scenario with respect to some desired difficulty Define a parameterized scenario Develop measure for difficulty Formulate a measure of difficulty based on player state and NPC paths and parameters Optimize over scenario parameters Approach 3

Related Work Game Level Evaluation [Guttler and Johansson 03] Player Experience Flow [Csikszentmihalyi 90] Game Enjoyment [Przybylski et al. 10] Level Optimization for Content Generation Search-Based [Togelius et al. 11] fun optimization [Sorenson and Pasquier 10a] Multi-Objective [Togelius et al. 13] 4

Framework Overview 5

Our Contributions A measure of game level difficulty Expected damage over space-time path A game level parameterization model An optimization framework to procedurally generate game levels with a desired difficulty. User/Designer control over obstacle locations and NPC settings 6

Scenario Parameterization 7

Scenario Annotation 8

NPC Behaviour Difficult to define concrete behaviour Assume too much, system will only work for class of games (e.g. following player) Use generic path calculation which can be replaced by application-specific models 9

Game Level Difficulty Computed as the line integral over a players path 10

Difficulty Visualization Visualizes expected difficulty over time Informed design decisions Changed location of single obstacle Bottom scenario twice as difficult 11

Optimization 12

Penalty Method 13

Optimization Objective 14

Covariance Matrix Adaptation (CMA) CMA-ES [Hansen and Ostermeier 96] Tolerates noise Step-size adjustment Non-convex optimization Parameter bounds Respect scenario constraints Limit search space 15

Benchmarks and Experiments: 16

Benchmarks and Experiments: Warehouse 17

Zombie Street Crossing 18

Baldur’s Gate II 19

20

Limitations and Future Work Player and NPC models could be enhanced Do not recompute Navmesh every evaluation Performance Future Work Explore possible path sampling Cooperative and competitive behaviours Simulation-based analysis User study for subjective difficulty 21

Conclusion Characterized player difficulty by static analysis Visualizing difficulty over time Used optimization to procedurally generate game configurations. Can generate various configurations with similar difficulty Demonstrated on many types of game levels 22

Software Release Brandon and Myself are working on releasing the software on Unity3D SteerSuite-2.0 More Features More Robust 23

Questions? Glen Berseth 1, M. Brandon Haworth 2, Mubbasir Kapadia 3, Petros Faloutsos 2 1 University of British Columbia 2 York University, 3 Rutgers University 24