## Combinatorial GamesBased on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings in Columbus in August 1990, the ten papers in this volume will provide readers with insight into this exciting field. Because the book requires very little background, it will likely find a wide audience that includes the amateur interested in playing games, the undergraduate looking for a new area of study, instructors seeking a refreshing area in which to give new courses at both the undergraduate and graduate levels, and graduate students looking for a variety of research topics. |

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### Contents

1 | |

Numbers and Games | 23 |

Impartial Games | 35 |

More Ways of Combining Games | 57 |

Introductory Overview of Mathematical Go Endgames | 73 |

Games and Codes | 101 |

Complexity of Games | 111 |

Welters game Sylver Coinage DotsandBoxes | 155 |

Unsolved Problems in Combinatorial Games | 183 |

Selected Bibliography on Combinatorial Games and Some Related Material | 191 |

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### Common terms and phrases

acyclic algorithm analysis annihilation game Berlekamp binary born on day canonical form chess codeword combinatorial games complexity component Comput defined definition digraph Dots-and-Boxes edge Edited ELWYN BERLEKAMP example extended quadratic residue Figure finite Fraenkel frieze pattern game G Game Theory game-graph Go endgames Golay code graph Grundy's Game Hackenbush Hamming code heaps of beans impartial games infinite integers J.H. Conway JOHN HORTON CONWAY Kayles labeled Last player wins Left and Right Left option legal move long chains mated Math misere play move loses nim-addition Nim-sum nim-value Nimstring nodes normal play number of beans Numbers and Games odd number ONAG opponent outcome P-position pair partizan games polynomial position problem Pspace-complete quadratic residue code remoteness reply Right options rules skittles Sprague-Grundy theory square strip Sylver Coinage Table Theorem tokens turn unable to move unique values vertex vertices Welter's Game winning move winning strategy zero