Two experiments explored whether children’s correct answers to counterfactual and future hypothetical questions were based on an understanding of possibilities. Children played a game in which a toy mouse could run down either 1 of 2 slides. Children found it difficult to mark physically both possible outcomes, compared to reporting a single hypothetical future event, “What if next time he goes the other way …” (Experiment 1: 3–4-year-olds and 4–5-year-olds), or a single counterfactual event, “What if he had gone the other way …?” (Experiment 2: 3–4-year-olds and 5–6-year-olds). An open counterfactual question, “Could he have gone anywhere else?,” which required thinking about the counterfactual as an alternative possibility, was also relatively difficult.