  Sequential decision-making refers to algorithms that take into account the
dynamics of the environment, where early decisions affect subsequent decisions.
With large language models (LLMs) demonstrating powerful capabilities between
tasks, we can't help but ask: Can Current LLMs Effectively Make Sequential
Decisions? In order to answer this question, we propose the UNO Arena based on
the card game UNO to evaluate the sequential decision-making capability of LLMs
and explain in detail why we choose UNO. In UNO Arena, We evaluate the
sequential decision-making capability of LLMs dynamically with novel metrics
based Monte Carlo methods. We set up random players, DQN-based reinforcement
learning players, and LLM players (e.g. GPT-4, Gemini-pro) for comparison
testing. Furthermore, in order to improve the sequential decision-making
capability of LLMs, we propose the TUTRI player, which can involves having LLMs
reflect their own actions wtih the summary of game history and the game
strategy. Numerous experiments demonstrate that the TUTRI player achieves a
notable breakthrough in the performance of sequential decision-making compared
to the vanilla LLM player.
