Lessons in play : an introduction to combinatorial game theory

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
0: 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 Functions
	2.2 Game Positions and Options
	2.3 Impartial Games: Minding Your Ps and Ns
	2.4 Case Study: Roll the Lawn
	2.5 Case Study: Timber
	2.6 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 Pitch
	4.5 Incentives
	Problems
5: Values of Games
	5.1 Numbers
	5.2 Case Study: Shove
	5.3 Stops
	5.4 A Few All-Smalls: Up, Down, and Stars
	5.5 Switches
	5.6 Case Study: Elephants & Rhinos
	5.7 Tiny and Miny
	5.8 Case Study: 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 Notation
	7.5 Taking-and-Breaking Games
	7.6 Subtraction Games
	7.7 Keypad Games
	Problems
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
	8.6 Domineering Snakes
	Problems
9: All-Small Games
	9.1 Cast of Characters
	9.2 Motivation: The Scale of Ups
	9.3 Equivalence Under ✰
	9.4 Atomic Weight
	9.5 All-Small Shove
	9.6 More Toppling Dominoes
	9.7 Clobber
	Problems
10: Trimming Game Trees
	10.1 Introduction
	10.2 Reduced Canonical Form
	10.3 Hereditary-Transitive Games
	10.4 Maze
	10.5 Ordinal Sum
	10.6 Stirling-Shave
	10.7 Even More Toppling Dominoes
	Problems
ω: Further Directions
	ω.1 Transfinite Games
	ω.2 Algorithms and Complexity
	ω.3 Loopy Games
	ω.4 Kos: Repeated Local Positions
	ω.5 Top-Down Thermography
	ω.6 Enriched Environments
	ω.7 Idempotents
	ω.8 Misère Play
	ω.9 Scoring Games
A: Top-Down Induction
	A.1 Top-Down Induction
	A.2 Examples
	A.3 Why Is Top-Down Induction Better?
	A.4 Strengthening the Induction Hypothesis
	A.5 Inductive Reasoning
	Problems
B: CGSuite
	B.1 Installing CGSuite
	B.2 Worksheet Basics
	B.3 Programming in CGSuite’s Language
C: Solutions to Exercises
D: Rulesets
Bibliography
Index