  While large language models have made strides in natural language processing,
their proficiency in complex reasoning tasks requiring formal language
comprehension, such as chess, remains less investigated. This paper probes the
performance of ChatGPT, a sophisticated language model by OpenAI in tackling
such complex reasoning tasks, using chess as a case study. Through robust
metrics examining both the legality and quality of moves, we assess ChatGPT's
understanding of the chessboard, adherence to chess rules, and strategic
decision-making abilities. Our evaluation identifies limitations within
ChatGPT's attention mechanism that affect its formal language comprehension and
uncovers the model's underdeveloped self-regulation abilities. Our study also
reveals ChatGPT's propensity for a coherent strategy in its gameplay and a
noticeable uptick in decision-making assertiveness when the model is presented
with a greater volume of natural language or possesses a more lucid
understanding of the state of the chessboard. These findings contribute to the
growing exploration of language models' abilities beyond natural language
processing, providing valuable information for future research towards models
demonstrating human-like cognitive abilities.
