Rules

1. Rules “rules, play, culture”

2. 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

3. 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

4. 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 COSC 4126 rules

5. 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

6. 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

7. 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

8. 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

9. 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

10. Categories of rules in games • operational • constituative (sic) • implicit COSC 4126 rules

11. 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

12. Pick a number… 1 2 3 4 5 6 7 8 9 COSC 4126 rules

13. 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

14. 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

15. Categories of rules in games • operational • constituative • implicit COSC 4126 rules

16. operational rules • rules of play • guidelines for players • usually the explicitly written “rules of the game” COSC 4126 rules

17. constituative rules • underlying formal structures – the formal game space • logical / mathematical rules –the parameters and algorithms of the coded game COSC 4126 rules

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. Designing a digital game • game core as constituative model • interface – inputs plus display plus sound as operational model COSC 4126 rules

25. 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

26. 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

27. 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