Analyses of human reaction to economic incentives reveal contradictory deviations from maximization. For example, underinvestment in the stock market suggests risk aversion, but insufficient diversification of financial assets suggests risk-seeking. Leading explanations for these contradictions assume that different choice environments (e.g., different framings) trigger different biases. Our analysis shows that variation in the choice environment is not a necessary condition. It demonstrates how certain changes in the incentive structure are sufficient to trigger six pairs of contradictory deviations from maximization even when the choice environment is fixed. Moreover, our analysis shows that the direction of these deviations can be captured by assuming that choice propensities reflect reliance on small samples of past experiences. In order to clarify the underlying processes, we considered distinct models of the reliance on small samples assumption, and compared them to classical models of choice (including prospect theory). The comparison focused on both within-individual, and between-group predictions (based on a preregistered study with 120 new tasks). The results reveal large advantage of "wide sampling" models that (in the static settings we examine) approximate an effort to rely on the most similar past experiences. Surprisingly, we also found that assuming that the parameters reflect stable individual traits impairs predictions; it seems that the number of "most similar past experiences" for each individual varies from task to task. These results suggest that ignoring the predictable impact of the incentive structure can lead to exaggeration of the importance of environment-and individual-specific decision biases.