Fig. 4
From: Leveling up fun: learning progress, expectations, and success influence enjoyment in video games
Overview grid exploration game. (a) Game design: Participants explored tiles of a grid produced by an underlying Gaussian Process. We manipulated the smoothness and the point values of the grids. After each sample, participants could decide to open another tile or go on to the next grid. (b) Simulated error over time with a Gaussian Process. The trajectory of the error — calculated as the mean squared error between the true values and the predicted values of the grid — is dependent on the smoothness of the grid, defined by the underlying lengthscale parameter (\(\lambda\)). Smaller values plateau quickly, while larger values quickly reach an error of 0. Only intermediate values continue reducing their error over a longer time frame. (c) Simulated engagement. The simulation samples new tiles until the error lies below a threshold — here set to 0.5 (for other values, see SI). We see an inverted U-shape relationship between the smoothness — defined by the lengthscale parameter (\(\lambda\)) — and the number of samples. (d) Behavioral results based on smoothness. We gathered data from 44 participants. They interacted the most with grids with a \(\lambda\) value of 8. (e) Behavioral results based on the magnitude of point values. Values are summarized in bins of 5. Participants interacted the most with grids that had high point values. (f) Mixed-effects regression analysis. The significant negative squared effect of smoothness accounts for the inverted U-shape seen in the behavioral plot. The linear effect of magnitude showed that participants engaged most in environments with higher point values. Error bars indicate the standard error of the mean.
