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.