> 3) LLMs do not have a mechanism for sampling from given probability distributions. E.g. if you ask LLM to sample a random number from 1 to 10, it will likely give you 3 or 7, as those are overrepresented in the training data.
You can have them output a probability distribution and then have normal code pick the action. There's other ways to do this, you don't need to make the LLM pick a random number.
It's not like an LLM can play poker without some shim around it. You're gonna have to interpret its results and take actions. And you want the LLM to produce a distribution either way before picking an explicit action from that distribution. Having the shim pick the random number instead of the LLM does not take anything away from it.
You can have them output a probability distribution and then have normal code pick the action. There's other ways to do this, you don't need to make the LLM pick a random number.