Sid Meier the creator of the civilization series of games when asked what is a game answered “A game is a series of interesting choices”.
If the decisions available to the player were to be mapped out you would begin to see distinct patterns in the game that was being mapped. To illustrate let’s look at two games tic tac toe, and Chess.
In Tic tac toe the player has to chose where to place their piece on a grid of nine spaces. However on turn two their are only seven spaces available as their opponent has chosen one position. On turn three the decision space is reduced to five. Thus we begin to see a collapsing decision tree as the options reduce the longer play takes place.
In contrast in chess on the first move the player has ten pieces that they can chose to move legally (eight pawns and the two knights). on turn two the number of decisions available is dependent on the first move. So for example if the player moves the kings rook pawn on turn one the decisions space for turn two increases to eleven movable pieces (the pawns, the knights and the kings rook). This analysis does not take into account the decisions opened up by not moving a piece to its maximum move distance. So in chess the first turn move which has ten choices sets up the second turn move to have between nine(assuming a knight moves and blocks one of the pawns) and twelve choices (kings pawn moves opening the queen and bishop) in a branching expanding form.
Games can therefore be described as having an expanding or collapsing decision tree. Although this is based on the point at which you measure the available decisions. Because while chess is initially expanding eventually as the pieces begin to interact and pieces on the board are removed the decision tree will begin to contract thus leading to the victory conditions of the game.
What relevance does this have to classroom activity design?
The first impact of the decision tree on game or activity design is in the length of play. A collapsing decision tree will create a much quicker game as the choices get fewer and fewer with each passing round. Whereas an expanding decision tree requires longer for the player to think through the decisions that are available to them. The expanding tree may also include many more rules to explain to students.
The second effect is on replay ability. Games which have a collapsing tree structure are much easier to solve. (see my post on solved games here) This means that strategies to win are easy to find and they can become boring for the students to engage with.
Examples of classroom activities with collapsing decision trees
Matching activities (race style game)
Battleship (Brawl style)
Examples of classroom activities with expanding decision trees
student created Interviews
As with all things in teaching and learning knowing how to categorize an activity or game can help you to select the type that best serves your educational purpose.