Idea: Monty hall door problem... With a twist!
I am suggesting some Monty Hall element in the game.
A classic Monty Hall game is when a player is confronted with three doors: Two doors hide nothing the third hides a prize. After choosing a door Monty opens ones of the doors that contains nothing and asks the player if he wants to switch. The math says it is better to switch.
There can be different twists:
1. More players. Or more doors. Or more Montys.
2. Monty tree: Doors lead to more Monty Hall games. Monty loops: Doors lead back to previous games.
3. Monty cheats and moves the prize (so you always lose, or always win)... Only way forward is to kill Monty...