Consider the game with the payoff matrix shown in Table 1. The payoff matrix has no saddle point; therefore in this case A and B do not have single best plans as their best strategies. Consequently, each player has to devise some mixed strategy in order to maximize his gain or minimize his loss. What is the best mixed strategy for the players? Can A insure some minimum gain and what is this gain? Similarly, can B insure that he will not lose more than some maximum amount?