We don't need to come up with a new board game. How about a board game that has been written about extensively for hundreds of years

LLMs can't consistently win at chess https://www.nicowesterdale.com/blog/why-llms-cant-play-chess

Now, some of the best chess engines in the world are Neural Networks, but general purpose LLMs are consistently bad at chess.

As far as "LLM's don't have understanding", that is axiomatically true by the nature of how they're implemented. A bunch of matrix multiplies resulting in a high-dimensional array of tokens does not think; this has been written about extensively. They are really good for generating language that looks plausible; some of that plausable-looking language happens to be true.

false, chess ELO is pretty good

https://maxim-saplin.github.io/llm_chess/

ets not cherry pick and actually see benchmarks please. i would say even ~1000 elo means that it can reason better than the average human.