Using probabilistic model checking to balance games

Research output: ThesisDoctoral Thesis


In this thesis, we consider problem areas in game development and use probabilistic model checking to address them. In particular, we address the problem of multiplayer game balancing and introduce an approach called Chained Strategy Generation (CSG). This technique uses model checking to generate synthetic player data representing a game-playing community moving between effective strategies. The results of CSG mimic the metagame, an ever-evolving state of play describing the players’ collective understanding of what strategies are effective. We expand upon CSG with optimality networks, a visualisation that compares game material and can be used to show that a game exhibits certain qualities necessary for balance.

We demonstrate our approach using a purpose-built mobile game (RPGLite). We initially balanced RPGLite using our technique and collected data from real world players via the mobile app. The application and its development are described in detail. The gathered data is then used to show that the model checking did lead to a well-balanced game. We compare the analysis performed from model checking to the gameplay data and refine the baseline qualities of a balanced game which model checking can be used to guarantee.

We show how the collected data via the mobile app can be used in conjunction with the prior model checking to calculate action-costs – the difference between the value of the action chosen and the best action available. We use action-costs to evaluate player skill and to consider other factors of the game.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Glasgow
  • Miller, Alice, Supervisor, External person
  • Norman, Gethin, Supervisor, External person
Award date19 Jan 2022
Place of PublicationGlasgow
Publication statusPublished - Nov 2021
Externally publishedYes


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