Research on risky choice has been predominantly based on studies of choices between two alternatives, but their findings are often generalized to environments with more than two alternatives. One prominent claim of this research is that choices differ with respect to risk when alternatives are described (the description paradigm) as opposed to sampled (the sampling paradigm). Here, we demonstrate that the difference in choices is sensitive to the number of alternatives in a choice set: with a growth in set size, alternatives with rare payoffs become more likely to be chosen in the sampling paradigm. This increased risk‐taking is due to the statistical property of payoffs: with a growth in set size, at least one riskier alternative becomes much more likely to deliver an attractive sample payoff at a higher frequency than its underlying probability. The increased risk‐taking eventually diminishes the difference between the description and the sampling paradigms in the gain domain. Further, we show that the increase in risk‐taking is difficult to avoid, even if each alternative is thoroughly sampled. Copyright © 2015 John Wiley & Sons, Ltd.