Little is known about how individuals make decisions when they must choose several options from a set of options when the outcomes are risky and the payoffs are rival. When researchers model these decisions, they assume people maximize their expected utility. We design an experiment in which subjects face either rival or independent payoffs. While theory predicts different behavior, subjects behave nearly identically under these payoff schemes. This suggests individuals are not maximizing expected utility. Additional treatments demonstrate that this behavior is likely driven by a heuristic used to simplify a complex math problem, rather than a preference for lotteries with the highest independent expected utilities. Our results suggest that using expected utility as peoples' objective function in these types of environments will lead to biased predictions