In a pure-exchange economy with no aggregate uncertainty, we characterize in closed-form and in full generality Pareto-optimal allocations between two agents who maximize rank-dependent utilities (RDU). We then derive a necessary and sufficient condition for Pareto-optima to be no-betting allocations (i.e., deterministic allocations - or full insurance allocations). This condition depends only on the probability weighting functions of the two agents, and not on their (concave) utility functions. Hence with RDU preferences, it is the difference in probabilistic risk attitudes given common beliefs, rather than heterogeneity or ambiguity in beliefs, that is a driver of a bet. As by-product of our analysis, we answer the question of when sunspots matter in this economy.