Hex Strategy: Making the Right Connections

Description

Hex Strategy is the first book to offer a comprehensive look at the game of Hex, from its history and mathematical underpinnings to discussions of advanced playing techniques. This is first and foremost a book on strategy aimed at providing sufficient knowledge to play the game at any level desired. Numerous examples illustrate an algorithmic approach to the game. Hex Strategy is a book for board game enthusiasts, recreational mathematicians and programmers, or simply those who enjoy games and puzzles. Cover Title Page Copyright Page Dedication Page Table of Contents Preface 1 Introduction 1.1 The Game of Hex 1.2 Rules of Play 1.3 History 1.4 Nature of the Game 1.5 The Shannon Switching Game 1.6 Current Literature 1.7 Board Representations Summary 2 Adjacency and Connectivity 2.1 Coordinate Systems and Adjacency 2.2 Chains 2.3 Connectivity Summary 3 Strategy I: Basic 3.1 Structural Development 3.2 Positional Play 3.3 General Strategies 3.4 Applying Basic Strategy Summary 4 Groups, Steps, and Paths 4.1 Groups , 4.2 Steps 4.3 Paths 4.4 Groups from Paths Summary 5 Templates 5.1 Connection Templates 5.2 Template Intrusions 5.3 Multi-Piece Edge Templates Summary 6 Strategy II: Intermediate 6.1 Expand With Templates 6.2 Momentum 6.3 Forcing Moves 6.4 Home Area 6.5 Edge Awareness 6.6 Loose Connections 6.7 Reduce the Opponent's Alternatives 6.8 Edge Defense 6.9 Stages of Play Summary 7 Ladders 7.1 Ladder Basics , 7.2 Ladder Formation 7.3 Ladder Escapes 7.4 Ladder Escape Forks 7.5 Ladder Escape Foils 7.6 Getting Off Ladders 7.7 Partial Ladder Escapes Summary 8 Algorithmic Board Evaluation 8.1 The Algorithm 8.2 An Example 8.3 The Need for Groups 8.4 Optimizations 8.5 Features of the Algorithm Summary 9 Opening Play 9.1 Opening and Swapping 9.2 Common Opening Strategies 9.3 Adapt to the Situation 9.4 Even-Sided Boards Summary 10 Strategy III: Advanced 10.1 Multiple Threats Per Move 10.2 Don't Provide Forcing Moves 10.3 Ladder Handling 10.4 Looking Ahead 10.5 Overall Game Plan Summary 11 Annotated Sample Games 11.1 Notation 11.2 Ladder Escapes Denied 11.3 Premature Resignation 11.4 HowNottoPlay 11.5 Another Point of View 12 Strategy IV: Essential 12.1 Opening Play 12.2 Start Blocking at a Distance 12.3 Bridges 12.4 Play Defensively 12.5 Edge Templates 12.6 Forcing Moves 12.7 Ladders 12.8 Spanning Paths 12.9 Multiple Threats Per Move 12.10 Looking Ahead 13 Hex Puzzles 13.1 Previously Published 13.2 Original 14 Conclusion 15 References 15.1 Publications 15.2 Online Resources Appendices A Solutions to Puzzles B Some Notes on Berge's Hex Problem C Sample Games D Proofs D.l One Player Must Win D.2 First Player to Win D.3 Acute Corner is a Losing Opening D.4 First Player Loses on n*(n + 1) Board Playing Wide D.5 No Simultaneously Opposed 0-Connected Spanning Paths E Hex Variants E.l Variants on the Hex Board E.2 Other Hexagonal Connectivity Games E.3 Non-Hexagonal Connectivity Games E.4 Tile-Based Connectivity Games E.5 Mobile Pieces E.6 Three-Dimensional Connectivity Games F Blank Hex Boards G Polyhexes H Hex Programs I Glossary 1.1 Terms 1.2 Symbols 1.3 Path Algebra 1.4 Move Notation Index