Fig. 9. Design and results of experiment 5.

a Schematic of Rock, Paper, Scissors. On each trial, participants choose one of three symbols (rock, paper, or scissors), then transition to one of three states depending on their (computer) opponent’s symbol (rock, paper, or scissors) with a 33% chance of each state. Depending on the combination of symbols, the end state is a win (worth 3 cents), draw (worth 0 cents), or loss (worth -1 cent). We have illustrated the game with the example choice of “rock” for the participant. b Schematic of Odds vs. Evens. Participants first chose to represent “odds” or “evens” for the duration of the game. On each trial, participants select a number (one or two), then transition to one of two states depending on the number selected by their (computer) opponent (one or two), with a 50% chance of each state. If the sum of the numbers is odd, participants advance to an end state of “win” (worth 3 cents) if they represent “odds”—otherwise they advance to an end state of “lose” (worth -1 cents). If the sum of the numbers if even, participants advance to an end state of “win” if they represent “evens”—otherwise they advance to an end state of “lose.” We have illustrated the game for the example choice of two for a participant who represents “odds.” c Effects of game on flow and enjoyment. Points denote means, and error bars represent 95% CIs. Statistics are derived from LMMs (two-sided) performed over 794 observations across 397 participants. No corrections for multiple comparisons were applied. d Key statistics associated with each game. The values of $I\left(M;E\right)$, expected value (EV), marginal value ($\Delta V$), and the correlation between $M$ and $E$ $\left({\mathrm{\phi }}_{\mathrm{c}}\left(M,E\right)\right)$ were computed analytically. The values for temporal difference prediction error ($\mathrm{\delta }\left(M\right)$) and value of information (VOI) correspond to the average output of 1,000 simulations. The largest value of each variable is highlighted in gray.