Preverbal infants manifest probabilistic intuitions in their reactions to the outcomes of simple physical processes and in their choices. Their ability conflicts with the evidence that, before the age of about 5 years, children's verbal judgments do not reveal probability understanding. To assess these conflicting results, three studies tested 3-5-year-olds on choice tasks on which infants perform successfully. The results showed that children of all age groups made optimal choices in tasks that did not require forming probabilistic expectations. In probabilistic tasks, however, only 5-year-olds made optimal choices. Younger children performed at random and/or were guided by superficial heuristics. These results suggest caution in interpreting infants' ability to evaluate chance, and indicate that the development of this ability may not follow a linear trajectory. (C) 2016 Elsevier B.V. All rights reserved.