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This paper is an extension of previous work on capturing and modeling the affective state of entertainment (''fun'') grounded on children's physiological state during physical game play. The goal is to construct, using representative statistics computed from children's physiological signals, an estimator of the degree to which games provided by the playground engage the players. Previous studies have identified the difficulties of isolating elements of physical activity attributed to reported entertainment derived (solely) from heart rate (HR) recordings. In the present article, a survey experiment on a larger scale and a physical activity control experiment for surmounting those difficulties are devised. In these experiments, children's HR, blood volume pulse (BVP) and skin conductance (SC) signals, as well as their expressed preferences of how much ''fun'' particular game variants are, are obtained using games implemented on the Playware physical interactive playground. Given effective data collection, a set of numerical features is computed from these measurements of the child's physiological state. A comprehensive statistical analysis shows that children's reported entertainment preferences correlate well with specific features of the recorded signals. Preference learning techniques combined with feature set selection methods permit the construction of user models that predict reported entertainment preferences given suitable signal features. The most accurate models are obtained through evolving artificial neural networks and are demonstrated and evaluated on a Playware game and a control task requiring physical activity. The best network is able to correctly match expressed preferences in 69.64% of cases on previously unseen data (p-value=0.0022) and indicates two dissimilar classes of children: those that prefer constantly energetic play of low mental/emotional load; and those that report as fun a dynamic play that involves high mental/emotional load independently of physical effort. The generality of the methodology, its limitations, its usability as a real-time feedback mechanism for entertainment augmentation and as a validation tool are discussed.