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! |