I don't think it's easier, a bad poker bot will lose a lot over a large enough sample size. But maybe it's easier to incorporate exploitation into your strategy - exploits that rely more on human psychology than pure statistics?
From my experience, their hallucination when playing poker mostly comes from a wrong reading of their hand strength in the current state. E.g., thinking they have the nuts when they are actually on a nut draw. They would reason a lot better if you explicitly give out their hand strength in the prompt.
I like the Tree of Thoughts theory that treat each chain of thoughts 'branch' as a possible hypothesis. They might trained a search system that quickly explore some of these branches and by some metric choose the most likely to be the right one at the moment to answer.