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> These machines are not made to play games like online poker deterministically

I thought you're supposed to sample from a distribution of decisions to avoid exploitation?

You're correct that the theoretically optimal play is entirely statistical. Cepheus provides an approximate solution for Heads Up Limit, whereas these LLMs are playing full ring (ie 9 players in the same game, not two) and No Limit (ie you can pick whatever raise size you like within certain bounds instead of a fixed raise sizing) but the ideas are the same, just full ring with no limit is a much more complicated game and the LLMs are much worse at it.

This invites a game where models have variants with slightly differing system prompts. Don't know if they could actually sample from their own output if instructed, but it would allow for iterations on the system prompt to find the best instructions.

You could give it access to a tool call which returns a sample from U[0, 1], or more elaborate tool calls to monte carlo software that humans use. Harnessing and providing rules of thumb in context is going to help a great deal as we see in IMO agents.

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