Mathter of the Game






Introduction

  1. What is that Title?
  2. Mathematical Games
  3. Dots-and-Boxes
  4. Why this site?




Table of Contents




1. Dots Tutorial


  1. An example game
  2. What's your level?
  3. Basic notation




1.1 The Basic Strategy


  1. Chains
  2. Doublecrosses
  3. Control and how to keep it
  4. The Chain Rule



1.2 Getting better

Practice


  1. Yahoo
  2. Dabble

Stages of a Game


All About the Chain Rule


  1. The Chain Rule for Other Boards
  2. The Non-Chain Rule
  3. Good Greed
  4. The Short Chain Rule
  5. The Zero Rule

Getting to Know Chains


  1. Recognizing Chains
  2. Cutting and Connecting
  3. Beware the join!
  4. Chain invasions

Sacrifices

  1. Tactical Sacrifices
  2. Positional Sacrifices

Life and Death


  1. The 4-Corner

How to Count


  1. Using the Chain Rules
  2. Cost of Living

Openings


  1. Basic Concepts
  2. The Fight for the Center
  3. Standard Openings
  4. The Yahoo Opening
  5. The Wilson Opening

Common Mistakes



  1. Forgetting who you are
  2. Sacrificing for Non-Chains
  3. The Doubletrap
  4. Errors in Winning Ways



1.3 Becoming Expert


Beyond the Chain Rule

The Preemptive Sacrifice


  1. Aftermath
  2. Prevention
  3. Care and Feeding of Chains
  4. Skip This Proof

Nibbling


The Quad


  1. One Quad
  2. Two Quads

It's not Easy Being Green

  1. The Standard Ties
  2. The Standard Losses



1.4 Masters and Non-Mathematicians

6x6 Dots

Handicap Dots


Studying Games


  1. Using Dabble
  2. Scoresheet for 5x5 Dots
  3. Scoresheet for 6x6 Dots

Consulting the Oracle

Living on the Edge

  1. The Third Chain
  2. Pivot Moves

The Nimstring Method


  1. Beyond Life and Death
  2. The Mirror Strategy
  3. When are Two Regions Equal?
  4. Beyond Parity
  5. Nimdots: The Theory of Delaying Moves
  6. Nimdots Values
  7. Using Nimdots Values
  8. The Value of the 4-Corner
  9. Nimdots and 5x5 Dots
  10. Nimstring Strategy in Action




2. Mathematical Theory of Dots




The Chain Rule


  1. Proof of the Chain Rule
  2. Euler's Theorem
  3. Toroidal Dots and Other Games



Combinatorial Game Theory


  1. Strings and Coins
  2. Nimstring
  3. Nim
  4. Combinatorial Games



Computer Analysis




3. Can you Mathter Mathematical Games?


  1. The Unreasonable Ineffectiveness of Combinatorial Game Theory
  2. A Brief History of Dots
  3. Dots come of age
  4. The myth of Dots and Boxes
  5. The Failure of Nimstring
  6. Nimstring in Practice
  7. There is no Mathematical Road to Dots
  8. The Natural Limitations of Dots
  9. Specific Problems with Berlekamp's book



Other Games


  1. Go




4. Yahoo Dots

Yahoo Ratings


  1. The Rating System

  2. Dots Hierarchy

  3. Chess Ratings

  4. Comparison with Chess

Abuse


  1. Boosting
  2. Impostors
  3. Dealing with cheating
  4. Being a good games player

Suggestions for Improvement

Chat

  1. Jargon
  2. ASL
  3. Trash Talk




Glossary




References and Comments







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