We consider an approach to blame attribution based on counterfactual reasoning in probabilistic generative models. In this view, people intervene on each variable within their model and assign blame in proportion to how much a change to a variable would have improved the outcome. This approach raises two questions: First, what structure do people use to represent a given situation? Second, how do they choose what alternatives to consider when intervening on an event? We use a series of coin-tossing scenarios to compare empirical data to different models within the proposed framework. The results suggest that people sample their intervention values from a prior rather than deterministically switching the value of a variable. The results further suggest that people represent scenarios differently when asked to reason about their own blame attributions, compared with the blame attributions they believe others will assign.