This is speculation but i don't think this information (how it came to be) is actually irrelevant information for the LLM. Your state, which transformer LLMs n

This is speculation but i don't think this information (how it came to be) is actually irrelevant information for the LLM. Your state, which transformer LLMs notably have no way of transferring is "just" the computation that preceded the prediction. I think LLMs use previous tokens to compute the likely state vector that preceded the tokens and make predictions that continue this computed state. So the 2 board positions at time x may be identical but the state preceding it or "strategy" was not and so the next move is not identical. This way also, you can make a decision based on the perceived competence of your opponent. These 2 papers kind of touch on what i've been thinking for a while now. They demonstrate task vectors and function vectors here for explicit in context learning tasks. In the absence of explicit tasks, perhaps state vectors would be more appropriate. In-Context Learning Creates Task Vectors - https://arxiv.org/abs/2310.15916 https://arxiv.org/abs/2310.15916 Function Vectors in Large Language Models - https://arxiv.org/abs/2310.15213 https://arxiv.org/abs/2310.15213