Hjem

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
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2 Game Positions and Options
2.
3 Impartial Games: Minding Your Ps and Ns
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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
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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
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2 Case Study: Shove
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3 Stops
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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 Toppling Dominoes
5.
9 Proofs of Equivalence of Games and Numbers Problems 6 Structure
6.
1 Games Born by Day 2
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2 Extremal Games Born By Day n
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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
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2 Coping with Confusion
8.
3 Cooling Things Down
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4 Strategies for Playing Hot Games
8.
5 Norton Products Problems 9 All-Small Games
9.
1 Cast of Characters
9.
2 Motivation: The Scale of Ups
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3 Equivalence Under
9.
4 Atomic Weight
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5 All-Small Shove
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6 More Toppling Dominoes
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7 Clobber Problems 10 Trimming Game Trees
10.
1 Introduction
10.
2 Reduced Canonical Form
10.
3 Hereditary-Transitive Games
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4 Ordinal Sum
10.
5 Stirling-Shave
10.
6 Even More Toppling Dominoes Problems Further Directions 1 Transfinite Games 2 Algorithms and Complexity 3 Loopy Games 4 Kos: Repeated Local Positions 5 Top-Down Thermography 6 Enriched Environments 7 Idempotents 8 Mis'ere Play 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