How do people make causal judgments? We propose a counterfactual simulation model (CSM) which predicts that causal judgments are influenced by whether a candidate cause made a difference to whether the outcome occurred as well as to how it occurred. We show how whether-causation and how-causation can be implemented as different counterfactual contrasts one the same generative model of the domain. We test the model in a physics domain where people make judgments about colliding billiard balls. Experiment 1 shows that participants’ counterfactual judgments are well-explained by an approximately Newtonian model of physics. In Experiment 2, participants judged to what extent two balls were causally responsible for a third ball going through a gate or missing the gate. As predicted by the CSM, participants’ judgments increased with their belief that a ball was a whether-cause, a how-cause, as well as sufficient for bringing about the outcome.