The high rewards people desire are often unlikely. Here, we investigated whether decision-makers exploit such ecological correlations between risks and rewards to simplify their information processing. In a learning phase, participants were exposed to options in which risks and rewards were negatively correlated, positively correlated, or uncorrelated. In a subsequent risky choice task, where the emphasis was on making either a 'fast' or the 'best' possible choice, participants' eye movements were tracked. The changes in the number, distribution, and direction of eye fixations in 'fast' trials did not differ between the risk-reward conditions. In 'best' trials, however, participants in the negatively correlated condition lowered their evidence threshold, responded faster, and deviated from expected value maximization more than in the other risk-reward conditions. The results underscore how conclusions about people's cognitive processing in risky choice can depend on risk-reward structures, an often neglected environmental property. Keywords Risk-reward • Decisions under risk • Ecological rationality • Eye tracking • Drift-diffusion model JEL Classification D91 • D81 Monetary lotteries have been playing a lead role in studies of how people should and do make decisions under risk (e.g.