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Asymmetric games
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Because of the weaknesses of symmetric games, many games attempt to establish an asymmetric relationship between the opponents. Each player has a unique combination of advantages and disadvantages. The game designer must somehow balance the advantages so that both sides have the same likelihood of victory, given equal levels of skill. The simplest way of doing this is with plastic asymmetry. These games are formally symmetric, but the players are allowed to select initial traits according to some set of restrictions. For example, in the Avalon-Hill boardgame WIZARD S QUEST, the players are each allowed the same number of territories at the beginning of the game, but they choose their territories in sequence. Thus, what was initially a symmetric relationship (each person has N territories) becomes an asymmetric one (player A has one combination of N territories while player B has a different combination). The asymmetry is provided by the players themselves at the outset of the game, so if the results are unbalanced, the player has no one to blame but himself.
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Other games establish a more explicitly asymmetric relationship. Almost all solitaire computer games establish an asymmetric relationship between the computer player and the human player because the computer cannot hope to compete with the human in matters of intelligence. Thus, the human player is given resources that allow him to bring his superior planning power to bear, and the computer gets resources that compensate for its lack of intelligence.
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Triangularity
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The advantage of asymmetric games lies in the ability to build nontransitive or triangular relationships into the game. Transitivity is a well-defined mathematical property. In the context of games it is best illustrated with the rock-scissors-paper game. Two players play this game; each secretly selects one of the three pieces; they simultaneously announce and compare their choices. If both made the same choice the result is a draw and the game is repeated. If they make different choices, then rock breaks scissors, scissors cut paper, and paper enfolds rock. This relationship, in which each component can defeat one other and can be defeated by one other, is a nontransitive relationship; the fact that rock beats scissors and scissors beat paper does not mean that rock beats paper. Notice that this particular nontransitive relationship only produces clean results with three components. This is because each component only relates to two other components; it beats one and loses to the other. A rock-scissors-paper game with binary outcomes (win or lose) cannot be made with more than three components. One could be made with multiple components if several levels of victory (using a point system, perhaps) were admitted. Nontransitivity is an interesting mathematical property, but it does not yield rich games so long as we hew to the strict mathematical meaning of the term. The value of this discussion lies in the generalization of the principle into less well-defined areas. I use the term "triangular" to describe such asymmetric relationships that extend the concepts of nontransitivity beyond its formal definition. A simple example of a triangular relationship appears in the game BATTLEZONE. When a saucer appears, the player can pursue the saucer instead of an enemy tank. In such a case, there are three components: player, saucer, and enemy tank. The player pursues the saucer (side one) and allows the enemy tank to pursue him unmolested (side two). The third side of the triangle (saucer to enemy tank) is not directly meaningful to the human---the computer maneuvers the saucer to entice the human into a poor position. This example is easy to understand because the triangularity assumes a spatial form as well as a structural one. Triangularity is most often implemented with mixed offensive-defensive relationships. In most conflict games, regardless of the medium of conflict, there will be offensive actions and defensive ones. Some games concentrate the bulk of one activity on one side, making one side the attacker and the other side the defender. This is a risky business, for it restricts the options available to each player. It s hard to interact when your options are limited. Much more entertaining are games that
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