A.I. in Board Games

Topics: Board game, Game, Monopoly Pages: 162 (53631 words) Published: May 3, 2013
Bachelor Thesis
A.I. in board games

Aron Lindberg, s042422

Technical University of Denmark
Informatics and Mathematical Modelling Thesis tutored by Thomas Bolander August 19, 2007

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Abstract
In this thesis, a board game named Kolibrat is implemented in the Objective-C programming language and Apple Computers Cocoa API. Besides from documenting this work, the thesis focus on the development of artificial players.

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Resum´ e
I denne afhandling bliver et brætspil Kolibrat implementeret i programmerings sproget Objective-C og Apple Computers Cocoa API. Udover at dokumenterer dette arbejde fokuserer denne afhandling p˚ arbejdet med a udviklingen af kunstigt intelligente spillere.

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Contents
1 Preface 1.1 Preconditions . . . . 1.2 Aims and limitations 1.2.1 Limitations . 1.3 Structure of thesis . 1 2 3 3 4 5 5 6 6 6 6 6 7 8 9 11 16 16 18 19 20 20 20 23 25 27

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2 Game Development 2.1 Concept design . . . . . . . . . 2.1.1 Graphical user interface 2.1.2 Game Controller . . . . 2.1.3 Game Engine . . . . . . 2.1.4 Players . . . . . . . . . 2.2 User Interface . . . . . . . . . . 2.2.1 Flow control . . . . . . 2.2.2 GUI implementation . . 2.3 Game Implementation . . . . . 2.3.1 Class details . . . . . . 2.3.2 Kolibrat flow diagrams . 2.3.3 C data structures . . . . 2.4 Testing . . . . . . . . . . . . . 2.4.1 Test summery . . . . . .

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3 Artificial intelligence 3.1 Game Analysis . . . . . . . . . . . . 3.1.1 Game state space . . . . . . . 3.1.2 Branching factor . . . . . . . 3.1.3 Complete analysis of Kolibrat 3.1.4 Analyzing forced loops . . . . iv

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CONTENTS 3.2 AI in Kolibrat games . . . . . . . . . . . . . . . . . . 3.2.1 Mini-Max agent . . . . . . . . . . . . . . . . 3.2.2 Optimizing the Mini-Max agent . . . . . . . . Implementing the Mini-Max agent . . . . . . . . . . 3.3.1 Additional possible Mini-Max enhancements Optimizing the Heuristic function . . . . . . . . . . . 3.4.1 Neural network utility function . . . . . . . . 3.4.2 Weighted linear evaluation function . . . . . 3.4.3 Choosing the heuristic parameters . . . . . . 3.4.4 Determining the parameters weight . . . . . . Simulated annealing Implementation . . . . . . . . . 3.5.1 Simulated annealing results . . . . . . . . . . Heuristics Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v 29 29 30 32 33 35 35 36 37 38 39 42 44 48 49 50 51 51 54 58 58 58 59 61 64 69 70 80 81 88 89 92 93 98 99

3.3 3.4

3.5 3.6

4 Conclusions 4.1 Future prospects . . . . . . . . . . . . . . . . . . . . . . . A Kolibrat Rulebook A.1 Game Objectives . . . . . . . . . . . . . . . . . . . . . . . A.2 Rules for movement . . . . . . . . . . . . . . . . . . . . . B Tests Details C Source Code C.1 Kolibrat Source Code . . . . . . . . C.1.1 HumanPlayer.h . . . . . . . . C.1.2 HumanPlayer.m . . . . . . . C.1.3 Datastructures.h . . . . . . . C.1.4 Datastructures.m . . . . . . . C.1.5 GameLogic.h . . . . . . . . . C.1.6 GameLogic.m . . . . . . . . . C.1.7 GameEngine.h . . . . . . . . C.1.8 GameEngine.m . . . . . . . . C.1.9 GameController.h . . . . . ....
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