Probabilistic models of expected information gain require integrating prior knowledge about causal hypotheses with knowledge about possible actions that might generate data relevant to those hypotheses. Here we looked at whether preschoolers (mean: 54 months) recognize "action possibilities" (affordances) in the environment that allow them to isolate variables when there is information to be gained. By manipulating the physical properties of the stimuli, we were able to affect the degree to which candidate variables could be isolated; by manipulating the base rate of candidate causes, we were able to affect the potential for information gain. Children's exploratory play was sensitive to both manipulations: given unambiguous evidence children played indiscriminately and rarely tried to isolate candidate causes; given ambiguous evidence, children both selected (Experiment 1) and designed (Experiment 2) informative interventions. (Contains 3 figures.)