I tried a few recently on Civ 6 Deity, and they all lose pretty quickly.

Sounds like an experiment I'd like to give a try--what integration layer did you use to get LLMs to control the civ?

Just running coding harnesses like Codex, Claude Code, and Cursor locally and having them do computer use.

To be fair, Deity on Civ games is brutal. I'd be interested in where the cutoff is.

Doesn't the AI (the computer players, I mean) "cheat" at that high of difficulty level?

That's moot- it's a comparison vs humans who can beat it.