Most work interpreting reasoning models studies only a single chain-of-thought (CoT), yet these models define distributions over many possible CoTs. We argue that studying a single sample is inadequate for understanding causal influence and the underlying computation. Though fully specifying this distribution is intractable, we can measure a partial CoT's impact by resampling only the subsequent text. We present case studies using resampling to investigate model decisions. First, when a model states a reason for its action, does that reason actually cause the action? In "agentic misalignment" scenarios, we find that self-preservation sentences have small causal impact, suggesting they do not meaningfully drive blackmail. Second, are artificial edits to CoT sufficient for steering reasoning? Resampling and selecting a completion with the desired property is a principled on-policy alternative. We find that off-policy interventions yield small and unstable effects compared to resampling in decision-making tasks. Third, how do we understand the effect of removing a reasoning step when the model may repeat it post-edit? We introduce a resilience metric that repeatedly resamples to prevent similar content from reappearing downstream. Critical planning statements resist removal but have large effects when eliminated. Fourth, since CoT is sometimes "unfaithful", can our methods teach us anything in these settings? Adapting causal mediation analysis, we find that hints that causally affect the output without being explicitly mentioned exert a subtle and cumulative influence on the CoT that persists even if the hint is removed. Overall, studying distributions via resampling enables reliable causal analysis, clearer narratives of model reasoning, and principled CoT interventions.