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The Rules of Chutes and Ladders
So much for the simplicity of rules. Now that we have taken a closer look at the formal structure of Tic-Tac-Toe, it is clear that the phenomenon of game rules is more complex than it initially appeared. Let us continue our investigation of three kinds of rules by turning to the board game Chutes and Ladders. The printed rules of the game read as follows:
Although these aren't the complete printed rules that accompany the game (the official rules include a narrative introduction and a Setup section), they give us the information that we need for our formal analysis. How do these printed rules relate to the operational, constituative, and implicit rules of the game?
Chutes and Ladders: Operational Rules
Like most rules that are written out as instructions for players, the printed rules of Chutes and Ladders consist primarily of operational rules. The operational rules are explicit instructions that guide the behavior of players. How to Play rule number two, for example, tells players: "On your turn, spin the spinner and move your pawn, square by square, the number shown on the spinner."
This is an overt instruction that engages directly with the materials of the game. Because the physical materials of a board game allow players to interact with the game system, it is important for the operational rules to delineate precisely how a player is to manipulate and interpret the objects of a game. The rule mentions the spinner, pawn, and squares of the board, outlining in a single statement the core mechanism of play.
Chutes and Ladders: Constituative Rules
The primary concern of the operational rules of a game is guiding the behavior of players. In contrast, the constituative rules of a game—the underlying mathematical structure—exist independently from the player. Whereas operational rules are concrete and describe specific actions that players will take, the constituative rules are abstract. Constituative rules are sets of logical relationships that are not necessarily embodied in a material form or in a set of behavioral guidelines for the player. Constituative rules literally have their own logic, which does not explicitly state how a player will make use of them.
What are the constituative rules of Chutes and Ladders? They might look something like this:
Players all begin with a value of zero.
Players alternate turns adding a random number of 1–6 to their current value.
The first player to reach a value of exactly 100 wins (if adding the random number to a player's total would make the total exceed 100, do not add the random number this turn).
When a player's total exactly reaches certain numbers, the total changes. For example, if a player reaches exactly 9, her total becomes 31. If a player reaches exactly 49, her total becomes 11.(This rule covers the "chutes" and "ladders" of the game. For a true set of constituative rules, this rule would have to be expanded to include all of the possible "chute" and "ladder" number adjustments for the particular edition of the game.)
Notice that in these rules, there is no mention of a spinner, a board, or pawns. There is no mention of how players are supposed to generate random numbers or to keep track of their numbers during the game. These mechanisms, which involve particular materials and behaviors, are part of the operational rules of the game.
How do the constituative rules relate to the operational rules? Is there a one-to-one relationship? As a thought experiment, we could use these same four constituative rules to invent new sets of operational rules that differ from the standard Chutes and Ladders game. Say that we wanted to change only the way that players generated the random number on their turn and the way that they kept track of their progress. Here are a few of the many different ways we could redesign the game:
Die and Scoresheet. Players keep track of their total by writing numbers on a scoresheet and roll a die to generate a random number.
Cards and Chips. Players keep track of their total by taking chips from a central pool and they pick from a set of six shuffled cards to generate a random number.
Spinner and Pegs. Players move pegs along a linear track, using pawns to keep their place. Players use a spinner to generate a random number.
Each of these three games would have its own set of operational rules, which would vaguely resemble the original rules of Chutes and Ladders, but the rules would have to be adjusted to take into account the new materials and behaviors we introduced. For each game, we would have to provide an informational sheet for players to track all of the forward and backward jumps, which in the original game take the form of "chutes" and "ladders" graphically depicted on the board.
These three games all require players to behave differently. Each one creates a different experience for players: rolling a die is a different action than drawing a card. Despite these differences, they all still share the same set of underlying constituative rules. There is not, therefore, an intrinsic relationship between a game's operational and constituative rules. The same set of constituative rules can be expressed in many different operational forms.
Chutes and Ladders: Implicit Rules
Let us turn to our third kind of rules, the implicit rules of a game. There are many implicit rules of Chutes and Ladders. For example, the implicit rule we pointed out in Tic-Tac-Toe relating to the time players should take between turns also applies here. But there are other implicit rules of Chutes and Ladders too. Some of them are even included in the printed game rules. Below is the Setup section from the game's rule booklet:
Position the gameboard so that all the players can easily move their pawns from square to square.
All About the Squares: Take a peek at the gameboard.The squares are numbered from 1 to 100. Players' pawns will move back and forth across the board, following the numbers upward—starting at square #1 and moving right toward square #10, then up to square #11 and left toward square #20, etc. Of course, you can also move by climbing ladders and unfortunately fall down, too, by sliding down chutes. More about that later.Everyone chooses a pawn to play. Any extra pawns are out of play. Chosen pawns are placed off the board near square #1. Now get ready for the fun! [4]
Although these rules might seem obvious, they help illustrate some of the implicit rules of Chutes and Ladders. Setup rule number 1 is a classic example of an implicit rule, here made explicit in the printed text. The gameboard must be positioned so that everyone can access it—in other words, it is necessary that everyone be able to physically and logistically enact the operational rules. The Setup rule that instructs players to put extra pawns out of play (leaving them outside the game) is another rule that is usually implicit, but happens to be written out here.
In the case of these two rules, a normally implicit rule is made an explicitly stated, operational rule through its listing in the rules that come with the game. For Chutes and Ladders' audience of young players, the game designers seemed to think that it was necessary in these cases to spell out what is usually implicit. And because the potential number of implicit rules is infinite, there are many other implicit rules that might be stated as well. Which ones should you include when you are writing instructions, manuals, or help sections for a game? It all depends on your audience and the kind of experience you want the participants to have. Ultimately, sets of rules and instructions need to be designed, analyzed, tested, and revised just as other aspects of a game.
For the purposes of our formal analysis, what does it mean to call these written rules "implicit rules"? If a rule is explicitly written out, how can it possibly be implicit? The boundary between operational and implicit rules can be quite fuzzy. Often, a "rule of play" can shift from implicit to operational, depending on the context. To return to our earlier example of the abandoned lot baseball game, the rule about the tree trunk (and not the branches or roots) being second base could be an implicit rule for a group of kids that have a lot of common experience playing baseball in places where trees are used as bases. However, a newer player might need this implicit rule spelled out, at which point it would become an explicit, operational rule.
The value of this three-part rules model is not in being able to definitively decide whether any given rule is constituative, operational, or implicit. There will always be some games and game contexts that don't neatly fit into our model. Like all of the concepts in this book, these three ways of understanding rules is not presented as a definitive explanatory typology: it is offered as a framework for identifying, analyzing, and solving design problems as they arise in your game.
[3]Milton Bradley, Chutes and Ladders.
[4]Ibid.
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