To expand on this - an LLM will try to play (and reason) like a person would, while a solver simply crunches the possibility space for the mathematically optimal move.
It’s similar to how an LLM can sometimes play chess on a reasonably high (but not world-class) level, while Stockfish (the chess solver) can easily crush even the best human player in the world.
How would an LLM play like a human would? I kind of doubt that there is enough recounting of poker hands or transcription of filmed poker games in the training data to imbue a human-like decision pattern.
You are of course correct but to be pedantic:
Stockfish isn't really a solver it's a neural net based engine
Unlike Chess, in poker you don’t have perfect information, so there’s no real way to optimize it.
How does a poker solver select bet size? Doesn't this depend on posteriors on the opponent's 'policy' + hand estimation?