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