Human and animal decision-making is known to violate rational expectations in a variety of contexts. Statistical structures of real-world environments may account for such seemingly irrational behavior. In a computerized experiment, 16 capuchins, 7 rhesus monkeys, and 30 humans chose between up to three options of different value. The options disappeared and became available again with different probabilities. Subjects overwhelmingly chose transitively (A>B, B>C, and A>C) in the control condition, where doing so maximized overall gain. However, most subjects also adhered to transitivity in the test condition, where it was suboptimal but led to negligible losses compared to the optimal strategy. Only a few of the capuchins were able to maximize long-term gain by violating transitivity. Adhering to rational choice principles may facilitate the formation of near-optimal decision rules when short- and long-term goals align. Such cognitive shortcuts may have evolved to preserve mental resources.