The effectiveness of Chain-of-thought prompting (CoT) has been widely recognized, but the underlying mechanisms behind its success, the reason why it just works for a wide range of tasks, remains an open question. To investigate this, we employ a counterfactual prompting approach, systematically manipulating elements of examples used in a few-shot prompt, and testing the consequences on model behavior. This allows us to understand the relative contributions of prompt elements such as symbols (digits, entities) and patterns (equations, sentence structure) on in-context learning. Our experiments with three different large language models (LLMs) reveal several key findings. First, the specific symbols used in the prompt do not significantly impact the model’s performance. However, consistent patterns in examples and specifying text in style frequently found on the web are crucial. Second, our findings suggest that the necessity of accurate few-shot examples depends on their role in communicating task understanding. We identify tasks where inaccurate few-shot examples hurt and, surprisingly, tasks where they improve performance. Additionally, we find that the intermediate steps in CoT may not necessarily facilitate learning how to solve a task, but instead efficiently convey task understanding (what) to the model. Furthermore, CoT leverages LLMs to fill in missing commonsense information, particularly helping difficult reasoning problems and long-tail questions.