For a while my daughter has said she wanted to "be the monsters." So one day I saw she had built a dungeon on her own, which kind of looked like a T stuffed with tons of monsters. Unfortunately, the pics we took of this awesome dungeon were lost to a backup/restore gap. After pruning the monster count I allowed her to setup the story: A princess has been captured by a family of dragons and the queen needed some heroes to get her back.
I assumed at first that I was still going to keep track of hitpoints, but she was ADAMANT about keeping it herself on a sheet of paper. During the encounters she proceeded to do an impression of me during our games, doodling on the sheet and constantly saying things like, "ok, he's down to... 15 hitpoints" or "uh oh, he only has... 3 hitpoints left!" None of these assertions came from actual math. She cooked the books to enhance the drama and probably assumed I'm doing the same in our games haha.
When I reached the dragon family at the end, I tried to role play a non-violent end to the encounter by trading money and food for the princess to which my daughter replied as the dragons, "Sorry, you're just going to have to kill us."
This game showed me I have a lot of work to do in our games to introduce more personalities into the encounters. I always try to add more game mechanics (keys, secret doors, portals, etc.) and occasionally throw in a random friendly character, but haven't tried to have her puzzle her way out of battles.
I wish I had a picture of that dungeon!