| Preface to Second Edition |
| Preface |
| Spade-Work! |
| Whose Game? / 1： |
| Blue-Red Hackenbush |
| The Tweedledum and Tweedledee Argument |
| How Can You Have Half a Move? |
| ... And Quarter Moves? |
| Ski-Jumps for Beginners |
| Don't Just Take the Average! |
| What Is a Jump Worth? |
| Toads-and-Frogs |
| Do Our Methods Work? |
| What is a Game? |
| When Is a Move Good? |
| Figure 8(d) Is Worth 3/4 |
| References and Further Reading |
| Finding the Correct Number is Simplicity Itself / 2： |
| Which Numbers Are Which? |
| Simplicity's the Answer! |
| Simplest Forms for Numbers |
| Cutcake |
| Maundy Cake |
| A Few More Applications of the Simplicty Rule |
| Positive, Negative, Zero, and Fuzzy Positions |
| Hackenbush Hotchpotch |
| Sums of Arbitrary Games |
| The Outcome of a Sum |
| The Negative of a Game |
| Cancelling a Game with its Negative |
| Comparing Two Games |
| Comparing Hackenbush Positions |
| The Game of Col |
| A Star is Born! |
| Col Contains Such Values |
| Game Trees |
| Green Hackenbush, The Game of Nim, and Nimbers |
| Get Nimble with Nimbers |
| Childish Hackenbush |
| Seating Couples |
| Winning Strategies |
| The Sum of Two Finite Games Can Last Forever |
| A Theorem about Col |
| Col-lections and Col-lapsings |
| Another Cutcake Variant |
| How Childish Can You Get? |
| Some Harder Games and How to Make Them Easier / 3： |
| Poker-Nim |
| Northcott's Game |
| Bogus Nim-Heaps and the Mex Rule |
| The Sprague-Grundy Theory for Impartial Games |
| The White Knight |
| Adding Nimbers |
| Wyt Queens |
| Reversible Moves in General Games |
| Deleting Dominated Options |
| Toads-and-Frogs with Ups and Downs |
| Game Tracking and Identification |
| What Are Flowers Worth? |
| A Gallimaufry of Games |
| Who Wins Sums of Ups, Downs, Stars, and Numbers? |
| A Closer Look at the Stars |
| The Values {[up arrow] | [up arrow]} and {0 | [up arrow]} |
| The Upstart Equality |
| Gift Horses |
| The Nim-Addition Rule in Several Variations |
| Wyt Queens and Wythoff's Game |
| Answers to Figures 8, 9, and 11 |
| Toad Versus Frog |
| Two Theorems on Simplifying Games |
| Berlekamp's Rule for Hackenbush Strings |
| Taking and Breaking / 4： |
| Kayles |
| Games With Heaps |
| P-Positions and N-Positions |
| Subtraction Games |
| Ferguson's Pairing Property |
| Grundy Scales |
| Other Take-Away Games |
| Dawson's Chess |
| The Periodicity of Kayles |
| Other Take-and-Break Games |
| Dawson's Kayles |
| Variations |
| Guiles |
| Treblecross |
| Officers |
| Grundy's Game |
| Prim and Dim |
| Replication of Nim-Values |
| Double and Quadruple Kayles |
| Lasker's Nim |
| Some Remarks on Periodicity |
| Standard Form |
| A Compendium of Octal Games |
| Additional Remarks |
| Sparse Spaces and Common Cosets |
| Will Grundy's Game Be Ultimately Periodic? |
| Sparse Space Spells Speed |
| Games Displaying Arithmetic Periodicity |
| A Non-Arithmetic-Periodicity Theorem |
| Some Hexadecimal Games |
| Further References and Reading |
| Numbers, Nimbers and Numberless Wonders / 5： |
| Domineering |
| Switch Games |
| Cashing Cheques |
| Some Simple Hot Games |
| The Tiniest Games |
| Modern Management of Cash Flow |
| Tiny Toads-and-Frogs |
| The Opening Dissection of Toads-and-Frogs |
| Seating Boys and Girls |
| Toads-and-Frogs Completely Dissected |
| Toads-and-Frogs with Two Spaces |
| More Domineering Values |
| References |
| The Heat of Battle / 6： |
| Snort |
| A Graphic Picture of Farm Life |
| Don't Move In A Number Unless There's Nothing Else To Do! |
| What's in it for Me? |
| The Left and Right Stops |
| Cooling--and the Thermograph |
| Cooling Settles the Mean Value |
| How to Draw Thermographs |
| When A Player Has Several Options |
| Foundations for Thermographs |
| Examples of Thermographs |
| Who Is To Move From The Final Stop? |
| A Four-Stop Example |
| The Cheque-Market Exchange |
| Equitable Games |
| Excitable Games |
| The Extended Thermograph |
| Getting the Right Slant |
| The Thermostatic Strategy |
| Thermostrat's Not Often Wrong! |
| Heating |
| Does The Excitement Show? |
| Selling Infinitesimal Values To Your Profit-Conscious Friends |
| Nim, Remoteness and Suspense in Hot Games |
| Overheating |
| Cooling the Children's Party |
| But How Do You Cool A Party By One Degree? |
| Three Snort Lemmas |
| A Snort Dictionary |
| Proof of the Number Avoidance Theorem |
| Why Thermostrat Works |
| Blockbusting |
| ... An On We Go! |
| Hotstrat, Thermostrat and Sentestrat |
| Hackenbush / 7： |
| Green Hackenbush |
| Green Trees |
| Fusion |
| Proving The Fusion Principle |
| A More Complicated Picture |
| Impartial Maundy Cake |
| Flower Gardens |
| The Blue Flower Ploy |
| Atomic Weights |
| Atomic Weights of Jungles |
| Making Tracks in the Jungle |
| Tracking Down an Animal |
| Amazing Jungle |
| Smart Game in the Jungle |
| Unparted Jungles |
| Blue-Red Hackenbush Can Be Hard, Too! |
| Redwood Furniture |
| Redwood Beds |
| How Big Is A Redwood Bed? |
| What's The Bottle |
| Ordinal Addition, The Colon Principle, and Norton's Lemma |
| Both Ways of Adding Impartial Games |
| Many-Way Maundy Cake |
| Solution to Figure 15 |
| Tracks Cleared Through the Amazing Jungle |
| How Hard Was The Bed? |
| NP-Hardness |
| The Bottle at the End of Chapter 7 |
| It's a Small Small Small Small World / 8： |
| Uppitiness and Uncertainty |
| Computing Atomic Weights |
| Eatcake |
| Splitting The Atom |
| Turn-and-Eatcake |
| All You Need To Know About Atomic Weights But Were Afraid To Ask |
| Childish Hackenbush Hotchpotch |
| Atomic Weights of Lollipops |
| Proving Things About Atomic Weights |
| Playing Among the Flowers |
| When is g as uppity as h? |
| Go Fly A Kite! |
| All Remote Stars Agree |
| Large and Small Flowerbeds |
| Playing Under a Lucky Star |
| General Multiples of Up |
| Proof of the Remote Star Rules |
| Proof That Atomic Weight = Uppitiness |
| The Wholeness of Hackenbush Hotchpotch |
| Proper Care of the Eccentric |
| Galvinized Games |
| Trading Triangles |
| Multiples of Positive Games |
| Multiples Work! |
| First for the "With" Rule |
| Now for the "Without" Rule |
| Shifting Multiples Of Up By Stars |
| A Theorem on Incentives |
| Seating Families of Five |
| Index |
| Preface to Second Edition |
| Preface |
| Spade-Work! |
| Whose Game? / 1： |
| Blue-Red Hackenbush |
| The Tweedledum and Tweedledee Argument |
