First order stochastic dominance is a core principle of rational decision making. If lottery A has a higher or equal chance of winning x or more than lottery B for all x, and strictly higher for at least one x, then A should be preferred to B. Previous research has shown that violations of dominance can result from violations of coalescing equivalence. In expected utility theory (EUT) and cumulative prospect theory (CPT), gambles are represented as probability distributions, which implies that if two events yield the same outcome, they can be coalesced by adding their probabilities. Hence, whether a choice problem is presented in split or coalesced form should not matter, and stochastic dominance must be satisfied. By contrast, in the transfer of attention exchange (TAX) model, gambles are represented as trees with branches having probabilities and outcomes, which allows that people can violate coalescing and therefore violate stochastic dominance. We reasoned that if people could be trained to understand and apply coalescing in these choice problems, they could be trained to recognize and satisfy stochastic dominance. However, even with targeted training, violations of stochastic dominance remained surprisingly robust: training had smaller effects than we anticipated. People don’t coalesce spontaneously and struggle to learn it, consistent with the TAX trees-with-branches representation.