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Rules. “rules, play, culture”. Rules of Tic-Tac-Toe. Play occurs on a 3 by 3 grid of 9 squares. Two players take turns marking empty squares, the first marking X’s, the second O’s. A row is any three squares on the grid, adjacent diagonally, vertically or horizontally.

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### Rules

“rules, play, culture”

Rules of Tic-Tac-Toe

- Play occurs on a 3 by 3 grid of 9 squares.
- Two players take turns marking empty squares, the first marking X’s, the second O’s.
- A row is any three squares on the grid, adjacent diagonally, vertically or horizontally.
- If one player places three of the same marks in a row, the player wins.
- If the spaces are all filled and there is no winner, the game ends in a draw.

COSC 4126 rules

Which game structure is part of the rules?

- e.g. rules are distinct from aesthetics
- rules specify the constitution of the deck used in a card game (jokers included?)
- the formal relationship of the cards is part of the rules (e.g. 4 parallel sets of 13 ordered values) but the suits (diamonds, hearts, spades, clubs) and ordered sequences (A,2,3,4,5,6,7,8,9,10,J,Q,K) are not

COSC 4126 rules

Which game structure is part of the rules?

- strategies are not rules
- Two players take turns marking empty squares, the first marking X’s, the second O’s.
is a rule of Tic-Tac-Toe but

- If an opponent has two marks in a row, place a mark to fill the third in the row.
is a strategy

- Two players take turns marking empty squares, the first marking X’s, the second O’s.

COSC 4126 rules

Game rules compared to rules in other activities

Rules: guidelines that direct, restrict or guide behaviour

- etiquette: rules of polite behaviour
- laws: rules of legal behaviour
- policies: rules of acceptable activity

COSC 4126 rules

Qualities of rules

- limit/restrict player action – what can be done with the artifacts of the game
- are unambiguous and explicit
- are shared by all players (does not imply symmetry)
- are fixed
- are binding
- are repeatable / portable

COSC 4126 rules

Rules in context

- game rules create artificial, clear conditions inside the magic circle
- a temporary escape from the ambiguous, shifting, unfair conditions of real life.

COSC 4126 rules

Game space and rules

- the formal structure of games can be regarded as a parameter space where the current state of the game is a point in the parameter space
- rules define the possible edges in the space connecting states
- a particular game is a path through the state space

COSC 4126 rules

Game space example

- Tic-Tac-Toe is a set of 9 parameters, each of which can take on three values: {X, O,e}
- The start state of the game space is
[e,e,e,e,e,e,e,e,e]

- [e,e,e,X,e,e,e,e,e] is connected to the start state by an edge but there is no path to [e,e,O,e,O,e,e,e,e]

COSC 4126 rules

3 to 15: another game

- Two players alternate turns.
- On your turn, pick a number from 1 to 9; you may not pick a number already chosen.
- If any three of your numbers add to 15 you win.
Let’s play….

COSC 4126 rules

3 to 15 == Tic-Tac-Toe

2

9

4

7

5

3

6

1

8

The space of Tic-Tac-Toe is isomorphic with the space of 3 to 15

they share a mathematical structure below the level of the rules

COSC 4126 rules

Implicit rules of games

- What if O player refuses to move?

X

O

O

X

X

implicit rules can be formalized (e.g. clock in chess matches) and often must be considered explicitly in digital games

COSC 4126 rules

operational rules

- rules of play
- guidelines for players
- usually the explicitly written “rules of the game”

COSC 4126 rules

constituative rules

- underlying formal structures – the formal game space
- logical / mathematical rules –the parameters and algorithms of the coded game

COSC 4126 rules

constituative rules - example

- all players begin with value total of zero
- players alternate turns adding a random value of 1 to 6 to their total
- first player with to achieve value total of 100 wins
- if the random value would take the total beyond 100, it is not added
- if a player achieves a value in this table, the other value in the pair is substituted

value

8

16

28

44

67

71

83

96

substitute

19

23

7

30

79

47

55

72

COSC 4126 rules

Making constituative rules operational

- how to measure progress
- write score, amass chips, follow number line

- how to make random move
- throw die, use spinner, draw card

- how to substitute values
- look-up table, links on line

COSC 4126 rules

Making constituative rules operational

in code

- constituative rules are coded in the underlying game algorithms
- operational rules are coded in the interface
question for educational game:

where is the knowledge to be learned?

COSC 4126 rules

implicit rules

- etiquette, sportsmanship, other rules of behaviour
- infinite in number
- “house rules” - may not have some of the ‘qualities’

- are unambiguous and explicit
- are shared by all players (does not imply symmetry)
- are fixed
- are binding
- are repeatable / portable

COSC 4126 rules

Designing a game

- constituative rules and operational rules both determine a game’s identity
- both are part of creation of meaning for the players
- action and response involves both

COSC 4126 rules

Designing a game

- formal (mathematical / algorithmic) model
- operational, concrete model

dictionary

defines relation between abstract symbols and operations

and

concrete objects and player actions

COSC 4126 rules

Designing a digital game

- game core as constituative model
- interface – inputs plus display plus sound as operational model

COSC 4126 rules

Elegant design

- The core of good design is in the operationalization of the constituative rules.
- Salen and Zimmerman, p.136-7, 149

- Designs can be evaluated for meaning by the criteria of
discernability and integration

COSC 4126 rules

Examples

- variations on Tic-Tac-Toe
- variations on Chutes and Ladders
compare with interface alternatives:

e.g. – inputting an integer:

- type in text field; select from menu; position a slider; click on a button

COSC 4126 rules

Designing a game

- original idea can be at either level – constituative or operational
- where is your content?
- is it an interaction model that needs a constituative algorithm behind it?
- is it a conceptual model that needs an operational interface to make it accessible?

COSC 4126 rules

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