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Game Analysis
Petri Lankoski
aalto.fi
Goals
• To develop skills for analyzing, describing, and
discussing games and their structures using concepts
and theories
What
Games
• Examples Today
– The Settlers of Catan
– Monopoly
– Space Invaders
– Tetris
• Wed to Fri
– Group assignments &
discussions
• Essay
Theories, Concepts
• Game elements
– Järvinen, 2008. Games without
Frontiers
• Emotions
– Lankoski, unpublished
manuscript
• Feedback systems
– Further reading: Salen &
Zimmerman, 2004. Rules of
Play
• Probabilities
Essay
• Choose a game or a part of the game
– Except: example and exercise games
• 8-12 pages, 12 pt Times or equivalent, double spaced
• You should describe the game (or the part) using the
concepts or theories from
– Lankoski, “Computer Games and Emotions”
– Järvinen, “Chapter Four: Theory of Game Elements”
– (Salen & Zimmerman, “Chapter 18: Games as Cybernetic Systems”)
• Deadline Friday 10.12.
– Writing tutoring (at latest) in the week 48
• Missing the deadline will decrease the grade (1/week), unless new
schedule is agreed beforehand!
Essay…
• A game analysis essay should be independent work
that should be readable and understandable by a
person who is not expert on subject matter. Essay
should contain:
1. Introduction: a description of the goals of the essay, short
introduction to a game analyzed, description of the main
concept used in the essay (with references);
2. Main part structured by the needs of analysis;
3. Conclusions summarizing main findings;
4. References
• References should be formatted according to Harvard
system.
Assignment
• Become familiar with the game
– the Settlers of Catan
• One game box (4 players)
• http://www.playcatan.com/ (introductory game)
– Space Invaders
• Taito Legends, PS 2
• http://www.freespaceinvaders.org/
– Tetris
• http://www.tetris.com/how-to-play-tetris/
• http://www.tetrisfriends.com/games/Marathon/game.php?ref=from-homepage-ad
– Monopoly
• One game box
• 1 hour to play
Settlers of Catan: Game Elements
Game Analysis
Environment
Settlers of Catan: Game Elements
Game Analysis
Game Mechanics
?
Components
Settlers of Catan: Game Elements
• Procedures
– Build Board
– Player Setup -> Game Mechanics: Place the settlements and roads
– Yield
• rand_num = random(1-6) + random(1-6) DICE!
• if rand_num=7:
– player_move_robber -> Game Mechanic: Move Robber & Select Player whom to steal
– all_discard -> Game Mechanic: Select Resources to Discard
• foreach hex=rand_num :
– if hex not disabled_by_robber: collect_yield
– Buy (road, settlement, city, development_card) <- initiated by Game Mechanic
• if player[active] have_enough_resources and can_place:
– place (road, settlement, city) OR add (development_card)
• Not completed list of procedures
Game Analysis
Settlers of Catan: Balance
• A multiplayer game is balanced when each player have equal change of
winning in the beginning
– In terms of formal features
• Symmetry creates balance
– Not the only way to balance a game
• Setters of Catan is symmetric in terms of
– Game Mechanics
– Component-of-self
• Not symmetric in terms of setup
– Setup
• Asymmetry is compensated with setup order player1–player2–player3–player4–
player4–player3–player2–player1
• Game board?
Game Analysis
Probabilities
1 2 3 4 5 6
Probability 1/6 1/6 1/6 1/6 1/6 1/6
Game Analysis
1D6
2D6
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Prob
2 1/36
3 2/36
4 3/36
5 4/36
6 5/36
7 6/36
8 5/36
9 4/36
10 3/36
11 2/36
12 1/36
Probabilities
• Dice throws are always independent events
– Previous event does not influence the probability of the
next event!
• But cards are dependent events
– The probability to get two aces from the unused deck is 4/52
(four aces in 52 cards) * 3/51 (three aces and 51 cards left)
Game Analysis
Settlers of Catan: Balance…
Game Analysis
5.56%
11.11%
13.89%
3 OR 5 OR 8:
5.56+11.11+13.89 = 30.56%
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
11/36=30.56%
Or calculate using table
Settlers of Catan: Balance…
Game Analysis
• Now we can calculate probabilities
for the board
– But what these probabilities tell…
• Does the board afford balanced
play?
– Is there enough good locations to
place initial settlement for all the
players?
– Is there good locations to expand
later?
- YES
- YES, unless on made a
bad choices in the setup
Settlers of Catan: Feedback Loops
Game Analysis
Resources
Settlement
& Cities
+
Victory
Points
Positive Feedback Loop Negative Feedback Loop
Probability of Negative feedback
activating 1-4 times in a round:
1-(30/36)^4 = 51,8%
• no robbers in a round: (30/36)^4
Resources
If more than 7 resource
cards in one’s hand & 7
7
-
Space Invaders
• Components
– Invaders, the ship, bullets
– Bunkers (or environment?)
• Game mechanics
– Move left, move right, shoot
• Goals
– Shoot invaders, stay alive, high score
• Procedures
– ship move, can shoot?, bullet move, bunker
damage, invader move, ufo appear, ufo move,
invader hit, invader shoot, lost life, new wave,
game over, …
• Feedback loops
– Less the invaders, faster they move, extra lives
Space Invaders, Taito 1978
Image source: Wikipedia
Tetris: Emotion
Game Analysis
Success Fail, goal blocked
Monopoly
Game Analysis
Change to end up in a square
1/40 = 2,50%?
3 doubles
in a row
1/16 Card takes
to Jail
A player can increase
probability to land to
these squares
(out with doubles)
Monopoly
Game Analysis
Land to Jail
If a card moves,
these are not counted
Monopoly
Game Analysis
Breakeven Times, assumes short jail stay
Based on data from http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml
There is positive feedback loop
• Gains are insignificant if no monopolies
Prison: conditional negative feedback
• Pay to get out, or
• Staying reduces changes of collecting rents

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Game Analysis, lecture 1

  • 2. Goals • To develop skills for analyzing, describing, and discussing games and their structures using concepts and theories
  • 3. What Games • Examples Today – The Settlers of Catan – Monopoly – Space Invaders – Tetris • Wed to Fri – Group assignments & discussions • Essay Theories, Concepts • Game elements – Järvinen, 2008. Games without Frontiers • Emotions – Lankoski, unpublished manuscript • Feedback systems – Further reading: Salen & Zimmerman, 2004. Rules of Play • Probabilities
  • 4. Essay • Choose a game or a part of the game – Except: example and exercise games • 8-12 pages, 12 pt Times or equivalent, double spaced • You should describe the game (or the part) using the concepts or theories from – Lankoski, “Computer Games and Emotions” – Järvinen, “Chapter Four: Theory of Game Elements” – (Salen & Zimmerman, “Chapter 18: Games as Cybernetic Systems”) • Deadline Friday 10.12. – Writing tutoring (at latest) in the week 48 • Missing the deadline will decrease the grade (1/week), unless new schedule is agreed beforehand!
  • 5. Essay… • A game analysis essay should be independent work that should be readable and understandable by a person who is not expert on subject matter. Essay should contain: 1. Introduction: a description of the goals of the essay, short introduction to a game analyzed, description of the main concept used in the essay (with references); 2. Main part structured by the needs of analysis; 3. Conclusions summarizing main findings; 4. References • References should be formatted according to Harvard system.
  • 6. Assignment • Become familiar with the game – the Settlers of Catan • One game box (4 players) • http://www.playcatan.com/ (introductory game) – Space Invaders • Taito Legends, PS 2 • http://www.freespaceinvaders.org/ – Tetris • http://www.tetris.com/how-to-play-tetris/ • http://www.tetrisfriends.com/games/Marathon/game.php?ref=from-homepage-ad – Monopoly • One game box • 1 hour to play
  • 7. Settlers of Catan: Game Elements Game Analysis Environment
  • 8. Settlers of Catan: Game Elements Game Analysis Game Mechanics ? Components
  • 9. Settlers of Catan: Game Elements • Procedures – Build Board – Player Setup -> Game Mechanics: Place the settlements and roads – Yield • rand_num = random(1-6) + random(1-6) DICE! • if rand_num=7: – player_move_robber -> Game Mechanic: Move Robber & Select Player whom to steal – all_discard -> Game Mechanic: Select Resources to Discard • foreach hex=rand_num : – if hex not disabled_by_robber: collect_yield – Buy (road, settlement, city, development_card) <- initiated by Game Mechanic • if player[active] have_enough_resources and can_place: – place (road, settlement, city) OR add (development_card) • Not completed list of procedures Game Analysis
  • 10. Settlers of Catan: Balance • A multiplayer game is balanced when each player have equal change of winning in the beginning – In terms of formal features • Symmetry creates balance – Not the only way to balance a game • Setters of Catan is symmetric in terms of – Game Mechanics – Component-of-self • Not symmetric in terms of setup – Setup • Asymmetry is compensated with setup order player1–player2–player3–player4– player4–player3–player2–player1 • Game board? Game Analysis
  • 11. Probabilities 1 2 3 4 5 6 Probability 1/6 1/6 1/6 1/6 1/6 1/6 Game Analysis 1D6 2D6 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 Prob 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36
  • 12. Probabilities • Dice throws are always independent events – Previous event does not influence the probability of the next event! • But cards are dependent events – The probability to get two aces from the unused deck is 4/52 (four aces in 52 cards) * 3/51 (three aces and 51 cards left) Game Analysis
  • 13. Settlers of Catan: Balance… Game Analysis 5.56% 11.11% 13.89% 3 OR 5 OR 8: 5.56+11.11+13.89 = 30.56% 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 11/36=30.56% Or calculate using table
  • 14. Settlers of Catan: Balance… Game Analysis • Now we can calculate probabilities for the board – But what these probabilities tell… • Does the board afford balanced play? – Is there enough good locations to place initial settlement for all the players? – Is there good locations to expand later? - YES - YES, unless on made a bad choices in the setup
  • 15. Settlers of Catan: Feedback Loops Game Analysis Resources Settlement & Cities + Victory Points Positive Feedback Loop Negative Feedback Loop Probability of Negative feedback activating 1-4 times in a round: 1-(30/36)^4 = 51,8% • no robbers in a round: (30/36)^4 Resources If more than 7 resource cards in one’s hand & 7 7 -
  • 16. Space Invaders • Components – Invaders, the ship, bullets – Bunkers (or environment?) • Game mechanics – Move left, move right, shoot • Goals – Shoot invaders, stay alive, high score • Procedures – ship move, can shoot?, bullet move, bunker damage, invader move, ufo appear, ufo move, invader hit, invader shoot, lost life, new wave, game over, … • Feedback loops – Less the invaders, faster they move, extra lives Space Invaders, Taito 1978 Image source: Wikipedia
  • 18. Monopoly Game Analysis Change to end up in a square 1/40 = 2,50%? 3 doubles in a row 1/16 Card takes to Jail A player can increase probability to land to these squares (out with doubles)
  • 19. Monopoly Game Analysis Land to Jail If a card moves, these are not counted
  • 20. Monopoly Game Analysis Breakeven Times, assumes short jail stay Based on data from http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml There is positive feedback loop • Gains are insignificant if no monopolies Prison: conditional negative feedback • Pay to get out, or • Staying reduces changes of collecting rents