The gravity of play: Quantifying what we enjoy about games

Games and the very act of playing have been around since before the cradle of human civilization. However, games have constantly evolved over time, with various rulesets and modes of play falling in and out of favor throughout history. In turn, this implies that people at different times enjoyed different aspects of each game, which may constitute a vivid reflection of the cultural tendencies of each era. Unfortunately, the attractiveness of games is tied to human psychology, and finding objective evidence in topics related to the realm of the human mind is a difficult task. Could there possibly be a way to quantify universal characteristics of games so as to put them under rigorous mathematical analysis?

Professor Hiroyuki Iida, vice president and trustee of the Japan Advanced Institute of Science and Technology (JAIST), thinks that there is. Under his guidance, the Iida laboratory has put much effort into developing theories and models that explain, using concepts from mathematics and psychology, what players enjoy about different games and why they feel motivated to play. Now, in their most recent study published in IEEE Access, scientists at JAIST have developed a novel approach to quantify the psychological appeal of games from a perspective analogous to the basic laws of motion in physics.

Ms Kang Xiaohan, Ph.D. student and lead author of the study, explains that their research is based on a combination of game refinement theory, reinforcement schedules and ‘motion in mind.’ Game refinement theory is a methodology for assessing the enjoyment and entertainment value of a game based on variables such as uncertainty, match duration and difficulty. On the other hand, reinforcement schedules are a concept widely studied in psychology that explains how rewards and punishments (and their frequency) motivate specific human behaviors. In this case, a ‘reward’ in the psychological sense can be winning a game in a given match. Finally, “motion in mind” is a novel theory pioneered at Iida laboratory, which proposes an analogy between physical measures of motion (such as potential energy, force and momentum) and game-related measures perceived by players, including pace of the game, effort required to progress, and randomness.

One key measure in the model of motion in mind is the acceleration or ‘gravity in the mind,’ in analogy with the earth’s gravitational acceleration. In sufficiently refined games, the model establishes a relationship between the effort that the player has to make to advance and the degree of challenge a game represents. The scientists calculated the gravity associated with a wide variety of games as they evolved through history, including classic board games like Chinese Go, Chess and Shogi, popular sports like soccer, tennis and basketball, and videogames, such as fighting games and strategy games.

Surprisingly, they found that the value of gravity in the mind changed, for each type of game, in sync with historical and cultural trends (Figure 1). For example, whereas people living 4000 years ago valued slow-paced games like ancient Go with a long period between rewards, the medieval and industrial era favored more aggressive and mid-paced games like Chess and Shogi (Figure 2). Similar trends were also found for various sports and videogames of the modern era. Excited about the results, Ms Xiaohan comments, “The gravity in the mind seems to be a good indicator of the core culture of people from a specific era or time. We can analyze how it changes to gain insight into people’s cultural tendencies based on the type of playing experience they seek and their relative comfort.”

The methodology and framework adopted in this study can be equally useful in other contexts where effort and motivation are critical factors, such as gamified activities, education and rehabilitation. It can also be used to analyze the nature of a given game or task so as to identify the psychological requirements for it, as well as the profiles of people that would be most comfortable or satisfied with it. In this regard, Prof Iida concludes, “We think the perspective of game-related research could shift naturally from the psychological realms to a more physical realm, making the generally complicated abstractions of the mind easier to understand.” One thing is certain: as our understanding of the appeal of games increases, so does our understanding of ourselves and our history.

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Founded in 1990 in Ishikawa prefecture, the Japan Advanced Institute of Science and Technology (JAIST) was the first independent national graduate school in Japan. Now, after 30 years of steady progress, JAIST has become one of Japan’s top-ranking universities. JAIST counts with multiple satellite campuses and strives to foster capable leaders with a state-of-the-art education system where diversity is key; about 40% of its alumni are international students. The university has a unique style of graduate education based on a carefully designed coursework-oriented curriculum to ensure that its students have a solid foundation on which to carry out cutting-edge research. JAIST also works closely both with local and overseas communities by promoting industry?academia collaborative research.

Kang Xiaohan obtained a master’s degree in game informatics from JAIST in 2020. She is currently pursuing a Ph.D. degree at Professor Iida’s laboratory at JAIST. Her research interests are distributed game refinement theory in the field of psychology, reinforcement learning, gamification in education, physics in games, mathematical modeling, data science in gaming, and reward function in deep reinforcement learning and its relation to addiction. Her current works focus on establishing the link between psychology and game refinement theory.

Dr. Hiroyuki Iida received his Ph.D. in 1994 on Heuristic Theories on Game-Tree Search from the Tokyo University of Agriculture and Technology, Japan. Since 2005, he has been a Professor at JAIST, where he is also Trustee and Vice President of Educational and Student Affairs. He is the head of the Iida laboratory and has published over 300 hundred papers, presentations, and books. His current research interests include artificial intelligence, game informatics, game theory, mathematical modeling, search algorithms, game-refinement theory, game tree search, and entertainment science.

This research is funded by a grant from the Japan Society for the Promotion of Science, in the framework of the Grant-in-Aid for Challenging Exploratory Research (Grant Number: 19K22893).