I don't think games are stupid. I just like them to be a bit in depth. Why would I spend time looking at a more interesting version of the game, how to cheat it, and how to add twists otherwise?
Also, if you want to take a game theory approach, you're wrong about the warden. If the warden is just playing a sadistic mind game, and wants to fuck with the players before feeding them to the alligators, the correct "solution" to the game for the players (should they catch on to the warden), is to never declare, thus extending the game infinitely, or barring that maximally, before the warden bores of the game and offs them.
Also, if you want to take a game theory approach, you're wrong about the warden. If the warden is just playing a sadistic mind game, and wants to fuck with the players before feeding them to the alligators, the correct "solution" to the game for the players (should they catch on to the warden), is to never declare, thus extending the game infinitely, or barring that maximally, before the warden bores of the game and offs them.