Fig. 4. Enjoyment results from experiment 2.

Effects of all variables of interest on the continuous measure of enjoyment and the binary choice measure of which game participants would rather play again in experiment 2. The variables of interest are I(M;E), its constituent entropy terms $H\left(M\right)$ and $H\left(M\mid E\right)$, 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 $E$ (${\mathrm{\phi }}_{\mathrm{c}}\left(M,E\right)$). Effects on choice are coded such that positive scores correspond to a tendency to choose the game with the highest value of the relevant variable. Statistics are derived from LMMs (two-sided) performed over 488 observations across 249 participants. Each LMM regresses one variable from the outcome column on one variable from the predictor column (with the exception of $H\left(M\right)$ and $H\left(M\mid E\right)$, which are included in the same model), 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.