The average is only 19.3 rounds because there is a bugged run where Gemini beats round 6 but the game bugs out when it attempts to sell Invisible Joker (a valid move)[0]. That being said, Gemini made a big mistake in round 6 that would have costed it the run at higher difficulty.
[0]: given the existence of bugs like this, perhaps all the LLMs' performances are underestimated.
It's hit or miss, but I've been able to have it self improve on prompts. It can spot mistakes and retain things that didn't work. Similar to how I learned games like Balatro. Playing Balatro blind, you wouldn't know which jokers are coming and have synergy together, or that X strategy is hard to pull off, or that you can retain a card to block it from appearing in shops.
If the LLM can self discover that, and build prompt files that gradually allow it to win at the highest stake, that's an interesting result. And I'd love to know which models do best at that.