Motivated partly by this MO question, I am wondering if it's possible to design a board game where there is a simple winning strategy but it's hard to find. For example, the game of picking a random number, applying your public crypto key to it and asking what the original number was, would be a trapdoor game, but I am looking for something more like a board game. For example, chess with different rules about how the pieces can move, or some Nim like game.
To make the question more clear - what I am looking for is a simple recipe using which I can generate myself a board game in which I can beat everyone and playing many times won't reveal my strategy. (Yes, I've recently been beaten too many times by my wife in memory...)