| Acknowledgments |
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xi | |
| Introduction |
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1 | (6) |
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7 | (27) |
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7 | (3) |
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1.2 Platforming in Three Dimensions |
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10 | (2) |
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1.3 LittleBigPla.net: Exploring Physics through Gameplay |
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12 | (2) |
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1.4 From 2D to 3D: Bending Laws in Portal |
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14 | (4) |
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1.5 Exploring Reality with A Slower Speed of Light |
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18 | (3) |
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1.6 Exploring Alternative Realities |
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21 | (5) |
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1.7 Beyond Physics: Minecraft or Mine Field? |
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26 | (1) |
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27 | (2) |
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1.9 Addendum: Describing Distortion |
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29 | (5) |
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34 | (24) |
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34 | (2) |
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2.2 Game Shows and Birthdays |
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36 | (3) |
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2.3 Beyond the First Duplicate |
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39 | (2) |
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2.4 The Draw Something Debacle |
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41 | (5) |
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2.5 Delayed Repetition: Increasing N |
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46 | (2) |
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2.6 Delayed Repetition: Weight Lifting |
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48 | (5) |
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2.7 The Completionist's Dilemma |
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53 | (2) |
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55 | (1) |
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2.9 Addendum: In Search of a Minimal k |
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55 | (3) |
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3 Get Out the Voting System |
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58 | (28) |
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3.1 Everybody Votes, but Not for Everything |
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58 | (2) |
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3.2 Plurality Voting: An Example |
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60 | (1) |
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3.3 Ranked-Choice Voting Systems and Arrow's Impossibility Theorem |
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61 | (5) |
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3.4 An Escape from Impossibility? |
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66 | (2) |
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3.5 Is There a "Best" System? |
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68 | (3) |
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3.6 What Game Developers Know that Politicians Don't |
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71 | (5) |
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76 | (6) |
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82 | (1) |
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3.9 Addendum: The Wilson Score Confidence Interval |
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83 | (3) |
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86 | (36) |
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86 | (1) |
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87 | (4) |
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91 | (7) |
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98 | (2) |
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4.5 A Mathematical Model of Threes! |
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100 | (5) |
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105 | (4) |
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109 | (7) |
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116 | (5) |
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121 | (1) |
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5 The Thrill of the Chase |
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122 | (36) |
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122 | (1) |
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123 | (2) |
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5.3 Green-Shelled Monsters |
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125 | (4) |
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5.4 Generalizations and Limitations |
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129 | (2) |
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131 | (3) |
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5.6 Apollonius Circle Pursuit |
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134 | (2) |
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5.7 Overview of a Winning Strategy |
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136 | (5) |
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5.8 Pinpointing the Intersections |
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141 | (4) |
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145 | (3) |
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5.10 The Pursuer and Pursued in Ms. Pac-Man |
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148 | (5) |
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153 | (1) |
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5.12 Addendum: The Pursuit Curve for Red Shells and a Refined Inequality |
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153 | (5) |
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158 | (26) |
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158 | (2) |
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6.2 P, NP, and Kevin Bacon |
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160 | (5) |
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165 | (4) |
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169 | (1) |
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6.5 Fetch Quests: An Overview |
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170 | (5) |
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6.6 Fetch Quests and Traveling Salesmen |
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175 | (8) |
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183 | (1) |
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184 | (26) |
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7.1 Taking It to the Next Level |
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184 | (2) |
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7.2 Friendship as Gameplay: The Sims and Beyond |
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186 | (4) |
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7.3 A Game-Inspired Friendship Model |
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190 | (3) |
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7.4 Approximations to the Model |
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193 | (2) |
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7.5 The Cost of Maintaining a Friendship |
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195 | (3) |
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7.6 From Virtual Friends to Realistic Romance |
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198 | (2) |
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7.7 Modeling Different Personalities |
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200 | (3) |
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7.8 Improving the Model (Again!) |
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203 | (6) |
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209 | (1) |
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210 | (17) |
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210 | (1) |
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8.2 Love in the Time of Chaos |
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211 | (5) |
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8.3 Shell Games Revisited |
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216 | (7) |
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223 | (2) |
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225 | (2) |
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227 | (17) |
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9.1 More Important Than Math |
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227 | (3) |
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230 | (12) |
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242 | (2) |
| Notes |
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244 | (25) |
| Bibliography |
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269 | (4) |
| Index |
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273 | |
