PokeChamp: an Expert-level Minimax Language Agent for Competitive Pokemon

Thank you for the opportunity to address the concerns raised in the review. We appreciate the recognition of our interesting use of LLMs for competitive gameplay and the promising results achieved.

Regarding generalizability: While PokéChamp is indeed designed for Pokémon battles, the underlying methodology of using LLMs for game-theoretic modeling and decision-making is broadly applicable. As noted, breakthroughs in specific games like chess, Go, and poker have historically driven advances in AI and machine learning. Our work similarly aims to push boundaries in a complex, partially observable domain.

The mathematical formalization in Section 2 (page 3) provides a general framework for partially observable Markov games, which can be applied to many competitive scenarios beyond Pokémon. This formalization allows readers unfamiliar with Pokémon to understand the problem structure we are addressing.

Novelty and contribution: Our approach of using online planning with an LLM prior to approximate Nash equilibrium strategies is indeed novel. Unlike methods requiring exhaustive sampling, we achieve expert-level performance in a domain with a vast state space (10^354 possible states, pg. 1) and stochastic outcomes. Achieving top 10% performance against human players (pg. 9, Table 5) demonstrates the effectiveness of this approach.

The integration of LLMs with minimax search and tool use (e.g., damage calculator) represents an innovative combination of techniques. This allows for adaptive gameplay without requiring extensive training or fine-tuning on Pokémon-specific data.

Adaptability and tool use: Our use of tools like the damage calculator actually enhances adaptability by providing accurate, up-to-date information to the LLM. This approach allows PokéChamp to perform well even with an LLM (Llama 3) with a 2023 data cutoff, demonstrating its ability to adapt to current gameplay.

The strong empirical results against rule-based bots, prior work (PokéLLMon), and human players (pgs. 8-9, Tables 3-5) provide evidence of the system's adaptability and effectiveness.

Addressing LLM limitations: Our approach directly addresses the limitations of LLMs in planning and strategy by incorporating the minimax search and tool use. The depth-limited minimax search (pg. 4-5, Section 3) allows for structured planning, while the damage calculator provides precise quantitative information to supplement the LLM's qualitative understanding.

The concern about brittle decision-making is not supported by our empirical results. PokéChamp's performance in the top 10% of human players (pg. 9, Table 5) demonstrates its ability to handle long-term strategy and deep reasoning effectively.

We acknowledge that there is room for improvement, particularly in areas like stall strategies and excessive switching (pg. 9). However, these limitations do not negate the significant advances demonstrated by PokéChamp.

In conclusion, we believe our work makes a substantial contribution to the field by demonstrating a novel approach to game-theoretic modeling using LLMs, achieving strong performance in a complex, partially observable domain. The methodology and insights gained are applicable beyond Pokémon and contribute to our understanding of LLM capabilities in strategic decision-making.

Thank you for your thoughtful review and for highlighting the strengths of our work, particularly the novelty of our application, the nice formulation as a Partially Observable Markov Game (POMG), and our strong empirical results achieving top human performance in real game settings.

We appreciate your feedback and would like to address the concerns raised:

1. Presentation and missing elements: The appendix is indeed provided in the supplemental file, with Appendix B detailing the background on Pokémon game mechanics. Additionally, Section 2 (page 3) provides a comprehensive mathematical formulation to help readers understand the algorithmic problem without extensive knowledge of game mechanics.

2. Damage Calculator explanation: The Damage Calculator serves two crucial purposes: a) It uses historical statistics to produce likely stats and available actions for the partially observable opponent team. b) It predicts the number of turns required to KO (knockout) the opponent's Pokémon, as shown explicitly in Figure 3. This can be thought of as a singular branch of depth-first search. This dual functionality is essential for our approach, and we will revise the text to make this clearer.

3. Applicability to other games: While our framework is demonstrated using Pokémon, the core principles of using LLMs for action sampling, opponent modeling, and state value calculation can be adapted to other games with similar structures. The key innovation is leveraging LLMs to enhance decision-making in complex game environments, which could be extended to other domains where domain knowledge is crucial.

4. Action Prediction and game theory optimality: We assume that by game theory-optimal, we are discussing the approaching a Nash equilibria. The quality of the data varies based on the Elo ratings of the recorded games. It is important to note that even state-of-the-art methods like AlphaZero have shown that additional training continues to increase performance (and Elo). Our approach of predicting opponent actions serves to provide a greedy search that limits the search space for online planning, which is crucial given the vast state space of Pokémon battles (on the order of 10^354 for just the first turn, as mentioned on page 2, lines 69-71).

5. Contribution and novelty: Our work contributes significantly to the field by: a) Demonstrating a novel application of LLMs in competitive game environments. b) Proposing a minimax search method enhanced by LLM capabilities. c) Achieving top human performance in a complex, partially observable game setting.

We believe these contributions are significant and generalizable, offering insights into integrating LLMs with game-theoretic approaches in domains with vast state spaces and partial observability.

6. Empirical results: To further emphasize the strength of our empirical results, we would like to highlight that PokéChamp achieves an expert rating of 1500 Elo on the online ladder, placing it in the top 10% of all players (as shown in Figure 1, page 1). This demonstrates that our approach is not only theoretically sound but also highly effective in practice against skilled human players.

We appreciate your feedback and will work on improving the clarity and presentation of our paper. We hope these clarifications address your concerns and demonstrate the value and potential impact of our work. We believe that PokéChamp represents a significant advancement in applying LLMs to complex game environments and opens up new avenues for research in this area.

Thank you for your thoughtful review and constructive feedback. We appreciate your recognition of our paper's strengths and would like to address your concerns while highlighting the significant contributions of our work.

We are pleased that you recognized the novelty of our approach in integrating LLMs with minimax search. As you noted, our agent leverages LLMs for three novel key components: action sampling, opponent modeling, and value calculation. This integration indeed allows for human-like strategic thinking, resulting in an expert-level game-playing agent.

We appreciate your acknowledgment of our comprehensive experiments, particularly the real-world evaluation against human players on the online ladder. This demonstrates the practical applicability and effectiveness of our approach in a competitive setting.

Thank you for highlighting the clarity and logical structure of our paper. We strived to present both the technical details and high-level motivations in a manner accessible to readers.

Addressing Weaknesses

Generalizability: While our framework is demonstrated using Pokémon, the core principles of using LLMs for action sampling, opponent modeling, and state value calculation can be adapted to other games with similar structures (a 2 player game with a discrete action space, a game that has some occurences in the pretraining on the LLM, but not extensive data). The key innovation is leveraging LLMs to enhance decision-making in complex game environments, which could be extended to other domains where domain knowledge is crucial.

Our approach is generalizable to other partially observable games with large action spaces and complex state representations. We believe this framework can be adapted to various game-playing tasks with appropriate modifications due to the general algorithmic and mathematical formulation.

Related Work: We acknowledge the similarity to Guo et al. (2024) and will include this reference in our related work section. However, our work provides more extensive empirical results in a challenging game setting, demonstrating the practical effectiveness of our approach. Additionally, while our work is related to the inspiration from Minimax, our methodology differs.

Mathematical Formalization: The mathematical formulation in Section 2 formalizes Pokémon battles algorithmically and motivates the structure of our search. This formulation motivates our use of minimax search, which has been shown to find Nash equilibria with full planning. Our method uses an approximate form of planning online to approach a Nash equilibrium.

Additional Points: Regarding fine-tuning, we agree that additional fine-tuning with collected data could potentially improve the agent's performance. This presents an interesting direction for future research, but is not necessary in the current study, which focuses on planning and a frozen LLM.

In conclusion, we believe our work presents a significant contribution to the field of AI in game-playing, demonstrating a novel and effective approach to integrating LLMs with traditional search methods. We hope these clarifications address your concerns and strengthen the case for the acceptance of our paper.

Thank you for the opportunity to address your review. We appreciate your thoughtful comments and positive feedback on our work. We are pleased to provide clarifications and additional information to address your concerns.

Strengths: We thank the reviewer for highlighting our "novel integration of LLM with Minimax", which achieves "competitive performance" and is "adaptive to partially observable info". We are glad you recognized our "high Elo rating" on "real-world benchmarks" as well as our "comprehensive dataset and benchmarks". These points underscore the key contributions of our work.

Weaknesses:

1. Limited Prediction Accuracy for Opponent Modeling: We appreciate this observation. As stated on page 6, Table 1, we provide results on opponent modeling to analyze how to understand the performance of an agent based on a frozen LLM. Rather than being a weakness, this is a highlight of our paper to critically show the shortcomings of a frozen LLM to motivate future work in the area and contextualize the results. For instance, our work shows performance in the top 10% of human players despite weak top-1 opponent modeling. This means that through branching in our minimax planning, we can benefit from exploring opponent actions beyond one predicted directly by the LLM's prompting. In fact, we show that this works quite well based on our winrates. Our work assumes a frozen LLM, so addressing this limitation is beyond the scope of the current work and is intended for future research that relaxes assumptions on fine-tuning the LLM.

2. Role of Nash Equilibrium: We appreciate this point. As with all empirical works, the idea is to try to approach a Nash equilibrium. As shown in AlphaGo (Silver et al., 2016), additional training continues to increase Elo, which demonstrates that empirical Nash equilibria for complex games have not yet been found. Though, the overall structure to solve is the same. We will clarify this connection in the final version.

3. Next-state Prediction Accuracy: The next state prediction uses historical likelihoods in combination with a reverse-engineered game engine, as described on page 5, Section 3.2. The historical likelihoods are accurate in the following way: if an opponent has a Pokémon that uses a move 70% of the time, then the prediction will be 70% correct. We sample from this distribution to reverse engineer partially observable opponents to help the LLM choose actions.

Questions:

1. Computation Time Comparison: As stated on page 5, Section 3, PokéLLMon simply samples K actions and chooses the most likely one (self-consistency). We keep the branching factor (3) to be the same as the self-consistency K=3 for fairness. A large amount of the time to run PokéChamp is taken up by generating our prompts which use the damage calculator, resulting in the clock time limit issue for games. Each game is limited to 2 minutes and 30 seconds so we cannot explore any methods that go beyond this runtime given our assumption and constraints.

2. Number of Human Players in Online Ladder Results: As stated in Table 5 on page 9, each opponent is a unique human, so there are 50 games and 50 human opponents.

We believe these clarifications address the concerns raised and further highlight the strengths and contributions of our work. We are committed to improving the paper based on your valuable feedback. Thank you for your time and consideration.