Causal reasoning is a core component of intelligence. Large language models (LLMs) have shown impressive capabilities in generating human-like text, raising questions about whether their responses reflect true understanding or statistical patterns. We compared causal reasoning in humans and four LLMs using tasks based on collider graphs, rating the likelihood of a query variable occurring given evidence from other variables. LLMs' causal inferences ranged from often nonsensical (GPT-3.5) to human-like to often more normatively aligned than those of humans (GPT-4o, Gemini-Pro, and Claude). Computational model fitting showed that one reason for GPT-4o, Gemini-Pro, and Claude's superior performance is they didn't exhibit the "associative bias" that plagues human causal reasoning. Nevertheless, even these LLMs did not fully capture subtler reasoning patterns associated with collider graphs, such as "explaining away".