Directed acyclic graph (DAG) approaches to causal inference have helped clarify familiar statistical problems such as confounding (common causes) and mediation (intermediate causes) and offer a common framework for thinking about the consequences of conditioning on a colliders (common effects) e.g. selecting on dependent or independent variables, modeling missing data, and other sample selection problems using selection nodes. Although collider bias is usually considered something to be avoided, this paper argues, first: that collider bias can also have *positive* consequences for causal inference, e.g. in matching analyses, provided it are appropriately generated, and second: that positive uses of collider bias are examples of a more general strategy of inducing 'unfaithfulness' to the presumed underlying DAG. (A set of observed associations are unfaithful to a graph when they do not show all the conditional indepencies that the graph implies - under normal conditions, a measure zero event.) The paper concludes by considering the closely related problem of representing control and other equilibrium-type relations in DAGs. Control and monitoring relationships are both classic examples of graph unfaithfulness and currently hard to represent in a DAG framework, despite their ubiquity in political science research.