Hex Strategy: Making the Right Connections(AK Peters/CRC Recreational Mathematics Series)

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.

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 How Not to Play -- 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 Comer is a Losing Opening -- D.4 First Player Loses on n*(n + 1) Board Playing Wide -- D.5 No Simultaneously Opposed O-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.