Operationalising Difficulty in Puzzle Games

The main line of investigation of this industrial PhD has been determining and modelling difficulty in games, specifically in mobile puzzle games. Difficulty plays a crucial role in player engagement in such games, so gaining a deeper understanding and being able to predict the perceived difficulty on a player level are important goals not only for researchers but for the industry at large.The initial work focused on creating a playtesting agent that would be able to automatically play through new content in a commercial puzzle game. For this purpose, we developed a reinforcement learning setup that could operate within a number of technical constraints, such as no possibility of using player play traces or tree-search. While the agent did not reach human-level performance on the full-scale problem, a key finding was that the top ~10% performances of the agent on a level were strongly correlated with player data. Additionally, we proposed ways to train the playtesting agent in a quick and robust way.With the agent not being enough by itself to predict the difficulty of new levels, we started to address the question of how to link agent behaviour to player behaviour. The first line of research was more focused on answering the question of what difficulty actually is in puzzle games and what it entails to predict difficulty for any content a player has not yet encountered. There were two main findings from this work: first, we proposed a parametric distribution for modelling the number of actions players spend for completing a level, paving the way for dynamic difficulty adjustment, and second, how individual difficulty predictions for the players are possible using factorization machines by capturing player skill and intrinsic level difficulty with latent factors.In the last line of research, the objective was to tie it all together – how can agent behaviour data be used together with personalised predictions for estimating the difficulty of not just old content but also new, novel content? The results showed that agent data does indeed have high predictive power on new content and can improve personalised predictions. While the factor-ization machine approach is useful for personalised predictions on old content, for predictions on new content, non-personalised predictions using a standard artificial neural network worked better. There is therefore not one approach that works the best in all use-cases, but in each of the use-cases, the accuracy of the methods is high enough for being used in a commercial context

Difficulty Modelling in Mobile Puzzle Games: An Empirical Study on Different Methods to Combine Player Analytics and Simulated Data

Difficulty is one of the key drivers of player engagement and it is often one of the aspects that designers tweak most to optimise the player experience; operationalising it is, therefore, a crucial task for game development studios. A common practice consists of creating metrics out of data collected by player interactions with the content; however, this allows for estimation only after the content is released and does not consider the characteristics of potential future players. In this article, we present a number of potential solutions for the estimation of difficulty under such conditions, and we showcase the results of a comparative study intended to understand which method and which types of data perform better in different scenarios. The results reveal that models trained on a combination of cohort statistics and simulated data produce the most accurate estimations of difficulty in all scenarios. Furthermore, among these models, artificial neural networks show the most consistent results

Combining Sequential and Aggregated Data for Churn Prediction in Casual Freemium Games

In freemium games, the revenue from a player comes from the in-app purchases made and the advertisement to which that player is exposed. The longer a player is playing the game, the higher will be the chances that he or she will generate a revenue within the game. Within this scenario, it is extremely important to be able to detect promptly when a player is about to quit playing (churn) in order to react and attempt to retain the player within the game, thus prolonging his or her game lifetime. In this article we investigate how to improve the current state-of-the-art in churn prediction by combining sequential and aggregate data using different neural network architectures. The results of the comparative analysis show that the combination of the two data types grants an improvement in the prediction accuracy over predictors based on either purely sequential or purely aggregated data

Difficulty Modelling in Mobile Puzzle Games: An Empirical Study on Different Methods to Combine Player Analytics and Simulated Data

Difficulty is one of the key drivers of player engagement and it is often one of the aspects that designers tweak most to optimise the player experience; operationalising it is, therefore, a crucial task for game development studios.A common practice consists of creating metrics out of data collected by player interactions with the content; however, this allows for estimation only after the content is released and does not consider the characteristics of potential future players.In this article, we present a number of potential solutions for the estimation of difficulty under such conditions, and we showcase the results of a comparative study intended to understand which method and which types of data perform better in different scenarios.The results reveal that models trained on a combination of cohort statistics and simulated data produce the most accurate estimations of difficulty in all scenarios. Furthermore, among these models, artificial neural networks show the most consistent results

Statistical Modelling of Level Difficulty in Puzzle Games

Successful and accurate modelling of level difficulty is a fundamental component of the operationalisation of player experience as difficulty is one of the most important and commonly used signals for content design and adaptation. In games that feature intermediate milestones, such as completable areas or levels, difficulty is often defined by the probability of completion or completion rate; however, this operationalisation is limited in that it does not describe the behaviour of the player within the area. In this research work, we formalise a model of level difficulty for puzzle games that goes beyond the classical probability of success. We accomplish this by describing the distribution of actions performed within a game level using a parametric statistical model thus creating a richer descriptor of difficulty. The model is fitted and evaluated on a dataset collected from the game Lily's Garden by Tactile Games, and the results of the evaluation show that the it is able to describe and explain difficulty in a vast majority of the levels.Comment: Conference on Games 2021 conference pape