How damaging is zero-sum thinking to an agent's interests when the world is positive-sum?
We study whether zero-sum decision rules, maximin and minimax, harm agents' interests in positive-sum games relative to Nash equilibrium behaviour or, more generally, than best response behaviour. Contrary to an influential evolutionary view, we give illustrations where maximin serves an agent's interests better than Nash equilibrium behaviour. Two new sets of results show that these illustrations are not idiosyncratic. First, for any selected Nash equilibrium in cardinal games, we construct a strategically equivalent game where a maximin profile yields the same pay-offs and we fully characterise when maximin can be made to Pareto dominate that Nash equilibrium and the entire Nash equilibrium set. Second, we show that the relevant Maximin Pareto dominance classes are not knife-edge: they are generically interior, and strict maximin profile dominance occurs on a non-empty open set if and only if a player has at least two actions and the other has at least three.