The terms nested sets, partitive frequencies, inside-outside views and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999) The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis - it uses exactly the same numbers as natural frequencies. We show that non-bayesian reasoning in children, laypeople, and physicians follows multiple rules rather than a general-purpose associative process in a vaguely specified "System 1." It is unclear what the theory in "dual process theory" is: Unless the two processes are defined, this distinction call account hoc for almost everything. In contrast, an ecological view of cognition helps to explain insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures.