This paper evaluates the effectiveness of various reasoning strategies for large language models (LLMs) by incorporating computational budget into the evaluation framework. The authors argue that traditional performance metrics often overlook the impact of computational resources, leading to an incomplete understanding of strategy efficiency. They introduce a budget-aware evaluation framework that considers both performance and computational cost, revealing that simpler strategies like chain-of-thought self-consistency (SC) can often outperform more complex strategies when given equivalent computational resources. The study compares several reasoning strategies, including Multi-Agent Debate (MAD), Reflexion, Plan and Solve, Least to Most Prompting, and Tree-of-Thoughts (ToT), across multiple datasets such as GSM8K, MATH, TheoremQA, CSQA, and HotpotQA. The results show that SC consistently performs well, often outperforming other strategies when given the same budget. However, strategies like ToT require significantly more computational resources to achieve comparable performance. The paper also explores the role of self-evaluation in reasoning strategies, finding that while self-evaluation can improve performance, current LLMs are not yet capable of effective self-evaluation. The study highlights the importance of considering computational budget when evaluating reasoning strategies and suggests that future research should focus on improving budget efficiency and self-evaluation capabilities in LLMs. The findings underscore the need for a more balanced approach to evaluating reasoning strategies that accounts for both performance and computational cost.This paper evaluates the effectiveness of various reasoning strategies for large language models (LLMs) by incorporating computational budget into the evaluation framework. The authors argue that traditional performance metrics often overlook the impact of computational resources, leading to an incomplete understanding of strategy efficiency. They introduce a budget-aware evaluation framework that considers both performance and computational cost, revealing that simpler strategies like chain-of-thought self-consistency (SC) can often outperform more complex strategies when given equivalent computational resources. The study compares several reasoning strategies, including Multi-Agent Debate (MAD), Reflexion, Plan and Solve, Least to Most Prompting, and Tree-of-Thoughts (ToT), across multiple datasets such as GSM8K, MATH, TheoremQA, CSQA, and HotpotQA. The results show that SC consistently performs well, often outperforming other strategies when given the same budget. However, strategies like ToT require significantly more computational resources to achieve comparable performance. The paper also explores the role of self-evaluation in reasoning strategies, finding that while self-evaluation can improve performance, current LLMs are not yet capable of effective self-evaluation. The study highlights the importance of considering computational budget when evaluating reasoning strategies and suggests that future research should focus on improving budget efficiency and self-evaluation capabilities in LLMs. The findings underscore the need for a more balanced approach to evaluating reasoning strategies that accounts for both performance and computational cost.