State-Space Models for Characterizing Engaging Game Design from Gameplay Dynamics

Game designs differ in how strongly they sustain, vary, repeat, and organize interaction during gameplay. Understanding these differences is important for computational game analysis because engagingness is often assessed through player questionnaires or post-hoc behavioral measures, while comparatively less attention has been given to whether properties of the game design itself can be recovered directly from gameplay dynamics. We investigate whether state-space representations can characterize how engaging a game design is through patterns such as rapid changes in gameplay state, repeated or concentrated state usage, exploratory diversity, sensitivity to reward and risk, recurring latent states, and long-range consistency. Our framework uses Mamba selective state-space models to learn sequential representations across both chess and video-game gameplay. Chess sequences combine board configurations, move-level events, game phase, and evaluation dynamics, while video-game sequences integrate visual representations, motion and reward/risk signals, together with vision-language descriptors of Action, Interaction, Reward, Risk, Intensity, and Phase. Mamba is compared with LSTM and Transformer baselines. The learned representations are characterized using latent state volatility (LSV), state entropy, attractor structure, reward sensitivity, consistency, and an aggregate addictive-pattern score (APS). These measures capture complementary properties of game design, including variability, concentration of state usage, recurrence of interaction patterns, and responsiveness to salient reward- or risk-related events. Preliminary results show that, on chess sequences, Mamba achieves the strongest alignment with evaluation-derived gameplay dynamics, with a correlation of 0.568, compared with 0.533 for Transformer and 0.503 for LSTM. Across four video games, LSV is highest for PUBG (67.05), followed by Animal Crossing (34.92), Minecraft (29.69), and FIFA (26.42), indicating distinct design-level interaction signatures. We further compare these learned patterns with an adapted SHARP-G assessment that excludes Gambling-Like Features while retaining Social, Personal Investment, Accessibility, and World Design characteristics. The corresponding scores are PUBG 43, Animal Crossing 36, FIFA 35, and Minecraft 32. The LSV and adapted SHARP-G rankings show a strong positive rank association (Spearman’s (\rho = 0.80)), demonstrating an analogy between learned gameplay dynamics and independently assessed structural design-risk characteristics. This correspondence provides preliminary convergent evidence that the learned representations capture design properties associated with sustained, repetitive, exploratory, and reward-sensitive gameplay. As planned validation, we construct counterfactual gameplay sequences that selectively perturb design-relevant factors such as reward/risk intensity, repetition, exploratory opportunities, and salient-event frequency while preserving the remaining gameplay structure as consistently as possible. We then evaluate whether these controlled perturbations produce corresponding directional shifts in the learned metrics, providing an intervention-based test of what the representations capture. Our key novelty is to shift engagement modeling from player-level psychological inference to a design-level characterization of engagingness learned directly from gameplay dynamics. Overall, the framework combines state-space representation learning, interpretable design metrics, structural comparison, and counterfactual validation to characterize and compare engaging game design directly from gameplay.