PS: Of course you could think of poker, but that is nearly solved by fb https://ai.facebook.com/blog/pluribus-first-ai-to-beat-pros-in-6-player-poker/
1. Hidden State. Not necessarily by itself, but the less the player knows about what the state transitions look like, the harder it is.
2. Visual interactions. Dixit is a really cool game with a known deck of cards, but I haven't seen any bots tackle it yet. The game involves giving a phrase about a specific card which isn't too specific.
3. Game Complexity. Easy to explode by having card effects, such as in MTG, which becomes Turing complete. If you have cards that change the game state too much, the game state becomes too chaotic to easily account for.
4. Social interactions. Some research exists on Mafia, but most of it is rudimentary and doesn't take into account the hundreds of different characters and emergent character behavior.
5. Games which force you to model your opponenet's strategy. For eg, some games have a mechanic where if you play the same card as your opponent, the action cancels out (actions are picked and revealed simultaneously). Unless you can build a model of your opponent, it becomes hard to win.
6. Random start states (and implement something like the Pie rule to ensure fairness)
Try to stay away from games which have a small state space (Blackjack), or have easy state-transitions, or are perfect information.