Even without other tokens before it the LLM is probably showing the probability of dice rolls based on its training data. I’d guess humans tend to prefer “3” or “4” as it’s nearer the avg/median and feels fairer.

AFAICT, the LLMs aren’t creating new mental mappings of “dice are a symmetric and should give equal probability to land on any side followed by using that info to infer they should use a RNG.”