I'm not an expert, but as I understand it there are existing solvers for poker/holdem? Perhaps one of the players could be a traditional solver to see how the LLMs fare against those?
The solvers don't typically work in real time, I don't think. They take a while to crunch a hand.
While others have commented about solvers, I'd also like to bring up AI poker bots such as Pluribus (https://en.wikipedia.org/wiki/Pluribus_(poker_bot)).
This also wouldn't even be a close contest, I think Pluribus demonstrated a solid win rate against professional players in a test.
As I was developing this project, a main thought came to mind as to the comparison between cost and performance between a "purpose" built AI such as Pluribus versus a general LLM model. I think Pluribus training costs ~$144 in cloud computing credits.