ABSTRACT
A saddlevalue confers safety for both constant and nonconstant sum games. Safety is especially precious when there is no pure saddlevalue. A saddlevalue based on a mixed strategy provides protection from any adverse effects of being found out. Even if your adversary knows your mixed strategy, he cannot know your actual choice in advance because it depends on probabilities as determined by your mixed strategy. At most he can calculate the expected value of the outcome given by the saddlevalue. Moreover, in a nonconstant sum game the minimax protects you from an aggressive adversary. If your adversary is not aggressive but you are defensive, then your return exceeds your saddlevalue. Therefore, a defensive minimax offers not only safety but also a chance of gain.
