Lessons in Play An Introduction to Combinatorial Game Theory, Second Edition

This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results.FeaturesEmploys a widely accessible style to the explanation of combinatorial game theory Contains multiple case studies Expands further directions and applications of the field Includes a complete rewrite of CGSuite material

Combinatorial Games 0.1 Basic Terminology Problems 1 Basic Techniques 1.1 Greedy 1.2 Symmetry 1.3 Parity 1.4 Give Them Enough Rope! 1.5 Strategy Stealing 1.6 Change the Game! 1.7 Case Study: Long Chains in Dots & Boxes Problems 2 Outcome Classes 2.1 Outcome Functions2.2 Game Positions and Options 2.3 Impartial Games: Minding Your Ps and Ns 2.4 Case Study: Roll The Lawn2.5 Case Study: Timber2.6 Case Study: Partizan Endnim Problems 3 Motivational Interlude: Sums of Games 3.1 Sums 3.2 Comparisons 3.3 Equality and Identity 3.4 Case Study: Domineering Rectangles Problems 4 The Algebra of Games 4.1 The Fundamental Definitions 4.2 Games Form a Group with a Partial Order 4.3 Canonical Form 4.4 Case Study: Cricket Pitch4.5 Incentives Problems 5 Values of Games 5.1 Numbers 5.2 Case Study: Shove5.3 Stops 5.4 A Few All-Smalls: Up, Down, and Stars 5.5 Switches 5.6 Case Study: Elephants & Rhinos5.7 Tiny and Miny 5.8 Toppling Dominoes 5.9 Proofs of Equivalence of Games and Numbers Problems 6 Structure 6.1 Games Born by Day 2 6.2 Extremal Games Born By Day n 6.3 More About Numbers 6.4 The Distributive Lattice of Games Born by Day n 6.5 Group Structure Problems 7 Impartial Games 7.1 A Star-Studded Game 7.2 The Analysis of Nim 7.3 Adding Stars 7.4 A More Succinct Notation7.5 Taking-and-Breaking Games 7.6 Subtraction Games 7.7 Keypad GamesProblems 8 Hot Games 8.1 Comparing Games and Numbers 8.2 Coping with Confusion 8.3 Cooling Things Down 8.4 Strategies for Playing Hot Games 8.5 Norton Products Problems 9 All-Small Games 9.1 Cast of Characters 9.2 Motivation: The Scale of Ups 9.3 Equivalence Under 9.4 Atomic Weight9.5 All-Small Shove 9.6 More Toppling Dominoes 9.7 Clobber Problems 10 Trimming Game Trees 10.1 Introduction10.2 Reduced Canonical Form10.3 Hereditary-Transitive Games10.4 Ordinal Sum10.5 Stirling-Shave10.6 Even More Toppling DominoesProblems Further Directions1 Transfinite Games 2 Algorithms and Complexity 3 Loopy Games 4 Kos: Repeated Local Positions 5 Top-Down Thermography 6 Enriched Environments 7 Idempotents 8 Mis`ere Play 9 Scoring GamesA Top-Down Induction A.1 Top-Down Induction A.2 Examples