Fig. 3

Overview of guessing game experiment. (a) Game design. Participants interacted with machines producing numbers from Gaussian distributions by adjusting a slider to guess the number the machine would produce next. After each guess, they could decide whether to stay with the current machine or move on to the next one. (b) Simulated learning progress with a Kalman filter. The trajectory of the update of the mean depends on the true underlying variance of the Gaussian distribution. The smaller variances make large updates only during the first step, while the high variances make only small updates directly from the first step onwards. Only intermediate variances continue to make larger updates. (c) Simulated engagement. The simulation samples from the current distribution until the update of the mean lies below a threshold — here set to 0.5 (for other values, see SI). The peak of the inverted-U shapes — the true variance the simulation is interacting with the longest — depends on the prior variance. (d) Behavioral results. Data from 98 participants showed that they liked to interact most with machines with variance 1. (e) Mixed-effects regression analysis. The significant negative squared effect of the variance accounts for the inverted U-shape seen in the human engagement behavior. (f) Influence of the difficulty-expectation disparity on human behavior. The difference between the estimated variance — calculated based on the samples participants have seen in the current distribution — and the estimated expected variance — calculated based on the machines participants have seen so far — shows an inverted-U relationship to the number of guesses with a peak close to 0. This indicates that participants preferred to interact with variances that lie close to their expected variance. The inset plot displays a zoomed-in version of the data. Error bars (in d and e) indicate the standard error of the mean.