Fig. 3. Relationships between I(M;E) and variables of interest in experiments 1 and 2.

Effects of all variables of interest on $I\left(M;E\right)$ in experiment 1 (Exp. 1) and experiment 2 (Exp. 2). The variables of interest are expected value (EV), controllability (CTRL), skill-challenge balance (SCB), marginal value ($\Delta V$), the value of information (VOI), temporal difference prediction error ($\mathrm{\delta }\left(M\right)$), and the correlation between $M$ and $E$ (${\mathrm{\phi }}_{\mathrm{c}}\left(M,E\right)$). Statistics are derived from LMMs (two-sided) performed over 720 observations across 365 participants in experiment 1, and 488 observations across 249 participants in experiment 2. Each LMM regresses $I\left(M;E\right)$ on one variable from the predictor column, a nuisance regressor for game order (first game vs. second game), and random subject-level intercepts. Red squares denote standardized regression coefficients, and intersecting red lines represent 95% CIs. No corrections for multiple comparisons were applied.