FUNDAMENTALS OF GAME DESIGN, SECOND EDITION

Symmetry and Asymmetry

In a symmetric game, all the players play by the same rules and try to achieve the same victory condition. Basketball is a symmetric game. The initial conditions, the actions allowed, and the victory condition are identical for both teams. Many tradi­tional games such as chess and backgammon are symmetric in every respect except for the fact that one player must move first.

WHO GOES FIRST?

In turn-based games, the fact that one player moves first can confer an advantage to one side or the other. For example, in tic-tac-toe among experienced players, only the person who goes first can win. However, if a game is designed in such a way that the advantage of going first is slight or nonexistent, this asymmetry can be ignored. In chess, only the weakest pieces on the board, pawns or knights, can move on the first turn, and they cannot move very far or establish a dominant position. The asymmetry of going first is considered irrelevant, so for practical purposes chess is a symmetric game.

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People usually feel that if all players start in the same state, they all have an equal chance of winning. This assumes that the definition of fairness ignores the differ­ences in the players' skill levels. Occasionally, people agree that a highly skilled player must take a handicap—that is, they impose a disadvantage on a skilled player to give the less-skilled players a better chance of winning. Amateur golf is the best- known example: Poor players are allotted a certain number of strokes per match that do not count against their score. On the other hand, professional golf, in which prize money is at stake, does not use this system and is purely symmetric.

In an asymmetric game, different players may play by different rules and try to achieve different victory conditions. Many games that represent real-world situa­tions (for example, war games based on historical events) are asymmetric. If you play a war game about World War II, one side is the Axis and one is the Allied powers. The two sides necessarily begin at different locations on the map, with different numbers of troops and different kinds of weapons. As a result, it is often necessary for the two sides to have different objectives to make the game fair.

In asymmetric games, it is much more difficult to determine in advance whether players of equal skill have an equal chance of winning. As a result, people often adjust the rules of asymmetric games to suit their own notions of fairness. Figure 1.3 shows an asymmetric medieval board game called Fox and Geese. One player moves the fox (F) and the other moves the geese (G).

The players take turns each moving one piece. The objective for the fox is to jump over the geese and remove them from the board, while the objective for the geese is to push the fox into a corner so that it cannot move. The geese cannot jump over the fox. Several variants of this game exist because people have adjusted the rules to align it closer to their sense of fairness. Some versions have two foxes; other ver­sions have smaller numbers of geese; in some, the geese may not move on the diagonal lines, and so on.