Emergence and progression - Game Mechanics: Advanced Game Design - page 27

C. E. Shannon, in his early paper “Programming a Computer for Playing Chess,”
estimated that there are more possible game states in games like chess and Go than
there are atoms on earth (1950). The rules of the game determine the number of
possible states, but it is not necessarily true that more rules will lead to more pos-
sible states. In addition, when a game can create a large number of possible states
without using many rules, the game will be more accessible to players.
Gameplay and Game States
When we speak of the path players take through the possible states of a game—its
probability space—we sometimes describe this path as a trajectory. The possible game
states and play trajectories through a game are emergent properties of the game
rule system. Games that allow many different, interesting trajectories arguably have
more gameplay than games that generate fewer trajectories or less interesting ones.
However, determining the type and quality of the gameplay is hard, if not impos-
sible, by simply looking at the rules. Comparing the rules of tic-tac-toe and Connect
Four serves as a good illustration of these difficulties. The rules for tic-tac-toe are
as follows:
1. The game is played on a three-by-three grid.
2. The players take turns to occupy a square.
3. A square can be occupied only once.
4. The first player to occupy three squares in a row (orthogonally or diagonally) wins.
The rules for Connect Four are as follows (with the differences emphasized):
1. The game is played on a seven-by-six grid.
2. The players take turns to occupy a square.
3. A square can be occupied only once.
4. Only the bottom most unoccupied square in a given column can be occupied .
5. The first player to occupy four squares in a row (orthogonally or diagonally) wins.
While there are only a few differences in the rules for these two games, the differ-
ences in gameplay are immense, much greater than the amount of mental effort
needed to understand the rules. In the commercially available version of Connect
Four , the most complicated rule (number 4) is enforced by gravity: A player's token
will automatically fall to the lowest available space in the upright playing area (see
Figure 2.1 ). This relieves players from manually enforcing this rule and allows them
to focus on the rule's effects instead. Despite the small difference in the complexity
of the rules, tic-tac-toe is suited only for small children, whereas Connect Four can
also be enjoyed by adults. The latter game allows many different strategies, and
it takes much longer to master the game. When two experienced players play the