A two-person game is any competition or conflict between two opponents, called players. A two-person zero-sum game is any two-person game where the amount won (or gained) by one player is lost by the other player.
In two-person zero-sum games we use a matrix, called a payoff matrix, to denote the gains and losses to player 1, called the row player. Gains appear as positive entries in the matrix and losses appear as negative entries in the matrix.
In a game with payoff matrix P, the row player can choose any of the rows of P and the column player can choose any of the columns of P. A player who makes the same choice each time the game is played is using a pure strategy. In terms of risk, the best pure strategy is the pure strategy that garantees the greatest gain to the player, not knowing the other player’s choise. The concept of best method to play is not based on the actual winnings but rather the notion that a player does the best he can under the circunstances.