Game Analysis

Petri Lankoskiaalto.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• Emotions – Lankoski, unpublished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

Game Analysis

Settlers of Catan: Game Elements

Environment

Game Analysis

Settlers of Catan: Game Elements

Game Mechanics

?

Components

Game Analysis

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

1D6

2D6

1 2 3 4 5 61 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

Game Analysis

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…

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

Game Analysis

Settlers of Catan: Balance…

• 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

Game Analysis

Settlers of Catan: Feedback Loops

ResourcesSettlement

& Cities

+

VictoryPoints

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 1978Image source: Wikipedia

Game Analysis

Tetris: EmotionSuccess Fail, goal blocked

Game Analysis

MonopolyChange to end up in a square

1/40 = 2,50%?

3 doublesin a row

1/16 Card takesto Jail

A player can increaseprobability to land to

these squares(out with doubles)

Game Analysis

Monopoly

Land to Jail

If a card moves,these are not counted

Game Analysis

Monopoly

Breakeven Times, assumes short jail stayBased on data from http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml

There is positive feedback loop• Gains are insignificant if no monopoliesPrison: conditional negative feedback• Pay to get out, or• Staying reduces changes of collecting rents