  Large Language Models (LLMs) have recently shown a promise and emergence of
Theory of Mind (ToM) ability and even outperform humans in certain ToM tasks.
To evaluate and extend the boundaries of the ToM reasoning ability of LLMs, we
propose a novel concept, taxonomy, and framework, the ToM reasoning with Zero,
Finite, and Infinite Belief History and develop a multi-round text-based game,
called $\textit{Pick the Right Stuff}$, as a benchmark. We have evaluated six
LLMs with this game and found their performance on Zero Belief History is
consistently better than on Finite Belief History. In addition, we have found
two of the models with small parameter sizes outperform all the evaluated
models with large parameter sizes. We expect this work to pave the way for
future ToM benchmark development and also for the promotion and development of
more complex AI agents or systems which are required to be equipped with more
complex ToM reasoning ability.
