I chose to base a card on one of my new favorite exhibits, the Stone Trolls. As soon as I collected all the pieces and noticed they were playing "Rock, Paper, Scissors", I was geeking out.
I only learnt about this bounty 3 days ago, so I haven't had much time to design the card or come up with a fully fledged game. But, I do know it would be similar to The Witcher's "Gwent", mixed with the classic silliness of Two Point. For the card design itself I used a mix between the style of "Flesh and Blood" and "Magic".
Gamewise, similar to Gwent there would be character or item cards with several types, and a mix of them at play at once.
Curators - they can find item cards in your deck to use for play;
Janitors - have some healing factors or can repair broken item cards (use an item card once, it breaks);
Guards - the opponents card gets peppered, loses hp;
Assistant - helps the player, boosts hp for 1 card;
Analyst - can analyze the opponents hand;
Bandage box - regain hp;
Curators Tools - reveal a hidden card;
And so on.
Cards based on exhibits such as the pictured Stone Trolls, would have goofy executions. As another example-
Fates O' Twenty - Roll a D20 dice, the resulting number is the damage counters put on your opponent. If you roll a 20, double it. If you roll 5 or lower, add 20 damage counters to one of your own cards.
The Trolls would be a goofy break during play, and an easy way to win or lose a round. High risk, high reward, right? Would you play the card?