Higher order risk preferences are important determinants of choices under uncertainty. We build a questionnaire different from usually adopted ones: our questionnaire is simpler in order to reduce the number of random choices, and it includes questions with largely diversified stake sizes to observe different gaps between moments. Moreover, we collect results from a large and heterogeneous population to provide more general and unbiased results. Our results confirm the preference of the majority of the respondents for higher odd and lower even moments of the expected return distribution. However, we highlight three features: (i) the importance of the gap between the values of the corresponding moments of the two choices, (ii) the behavioral change in presence of a positive/zero/negative expected value, (iii) the huge heterogeneity in behaviors, also due to the complexity of the choice as an important driver of the propensity to switch from choosing on the basis of preferences to choo sing randomly. We also find that age and geographical location are important determinants of risk propensity.