The solid (red) and dotted (blue) curves are the hyperbolic and exponential functions respectively, best fitted to the experimental data in delay and probability discounting tasks (a-b) (see Methods). Fig. 1a: Vertical axis indicates group median of indifference point in delay discounting task (discounted present value) and horizontal axis indicates delay (days). Data points are represented by the black diamonds. Fig. 1b: Vertical axis indicates group median of indifference point in probability discounting task (certainty equivalent discounted value) and horizontal axis indicates odds-against = (1/probability)-1 (an average waiting time in Rachlin's virtually-repeated gambling ). Note that hyperbolic models (red) better fit than exponential models (blue) (see Table 1 for AICc for each model).