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Abstract: This chapter starts by considering the simplest possible strategic game, which includes two intelligent opponents who try to outwit each other in a game, where the winnings of one player translate into losses for the other. These types of games are called strategic zero-sum games because one player's profit equals the loss of its opponents. When a rational player has a dominant strategy, one can be fairly sure that he will play exactly that strategy. When dominant or dominated strategies are present, the solution of a game can often be obtained by applying a few insights discussed in the chapter. A more general approach to solving games uses the fact that a Nash equilibrium corresponds to the pair of strategies that are mutual best responses. The chapter summarizes the best responses for each of the two players.