From 686bfe6121176573788e5f46ff2d20ab96181685 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Sun, 21 Aug 2011 23:21:46 +0000
Subject: othelloboard (21aug11)

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+\documentclass[a4paper,12pt]{book}
+
+\setcounter{secnumdepth}{0} % Switches off numbering for sections a la original book.
+
+%%% PAGE DIMENSIONS %%%
+\usepackage{titlesec}
+\titleformat{\chapter}[display]
+{\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}
+% removes excessive "before" spacing (the second length argument) in chapter headings (default is 50pt)
+\titlespacing*{\chapter}{0pt}{0pt}{40pt}
+
+\usepackage[inner=2.5cm, outer=3.2cm, bottom=4cm]{geometry}
+\usepackage{setspace}
+%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
+\addtolength{\belowcaptionskip}{-8pt} % Reduce some of the excessive space after figures
+
+\usepackage[labelsep=newline, textfont=it, figurename=Diagram, justification=centering]{caption}
+\newcommand{\jargon}[1]{\textbf{#1}}
+\newcommand{\exercisenum}[1]{\vspace{8pt}\noindent\makebox[2.8cm][l]{\textbf{#1}}}
+\newcommand{\puzzlenum}[1]{\vspace{8pt}\noindent\makebox[2.2cm][l]{\textbf{#1}}}
+\newcommand{\glossitem}[1]{\vspace{8pt}\noindent\textbf{#1}\hspace{6pt}}
+\renewcommand\thefigure{\arabic{chapter}-\arabic{figure}}
+
+\usepackage{wrapfig}
+%\usepackage{qtree}
+%\usepackage{multirow}
+%\usepackage{color}
+%\usepackage{hyperref}
+%\hypersetup{linktocpage}
+%\definecolor{gray}{RGB}{211,211,211}
+
+%%% OTHELLO DIAGRAMS %%%
+\usepackage{othelloboard}
+\let\Oldothellogrid\othellogrid
+\renewcommand{\othellogrid}{\dotmarkings\Oldothellogrid}
+
+% diagram sizes
+\newcommand{\scalefactorthreeup}{0.64}
+\newcommand{\scalefactortwoup}{0.64}
+\newcommand{\scalefactorfourup}{0.48}
+
+%\usepackage{appendix}
+
+%%% TITLE %%%
+% Title given on title page
+
+%% DOCUMENT %%
+
+\begin{document}
+%\frontmatter
+
+%\begin{titlepage}
+%\begin{center}
+%\vspace*{5cm}
+%\Huge{\textbf{Othello}}\\[0.5cm]
+%\LARGE{A Minute to Learn \ldots\ a Lifetime to Master}\\[1cm]
+%\large{\textsc{Brian Rose}} 
+%\end{center}
+%\end{titlepage}
+
+%\thispagestyle{empty}
+%\null
+%\vfill
+%\begin{center}
+%\noindent Copyright \copyright\ 2005 by Brian Rose\\
+
+%\noindent\emph{Othello} and \emph{A Minute to Learn \ldots\ A lifetime to Master} are registered trademarks of Anjar Co., \copyright\ 1973, 2004 Anjar Co. All Rights Reserved.
+%\end{center}
+
+%\chapter{Acknowledgements}
+%\tableofcontents
+
+%\chapter{Introduction}
+
+%\mainmatter
+
+%\part{}
+\chapter{Rules and notation}
+Diagram 1-1 shows the standard notation for Othello. The columns are labeled
+`a' through `h' from left to right, and the rows are labeled `1' through `8' from top to
+bottom. In this book, squares will be referenced using a small letter followed by a
+number, e.g., `a1' for the upper-left corner and `h8' for the lower-right corner. Certain
+squares are assigned special letters, which will be capitalized, as shown in Diagram
+1-2. This notation was developed by Othello's inventor, Goro Hasegawa, and remains
+in use today. The B-squares are in the center of the edge, the C-squares are on
+the edge next to the corner, and the A-squares lie between the B-squares and C-squares.
+The X-squares are diagonally adjacent to the corners, with the `X' indicating
+danger.
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\annotationsfirstrow{a1}{b1}{c1}{d1}{e1}{f1}{g1}{h1}
+\annotationssecondrow{a2}{b2}{c2}{d2}{e2}{f2}{g2}{h2}
+\annotationsthirdrow{a3}{b3}{c3}{d3}{e3}{f3}{g3}{h3}
+\annotationsfourthrow{a4}{b4}{c4}{d4}{e4}{f4}{g4}{h4}
+\annotationsfifthrow{a5}{b5}{c5}{d5}{e5}{f5}{g5}{h5}
+\annotationssixthrow{a6}{b6}{c6}{d6}{e6}{f6}{g6}{h6}
+\annotationsseventhrow{a7}{b7}{c7}{d7}{e7}{f7}{g7}{h7}
+\annotationseighthrow{a8}{b8}{c8}{d8}{e8}{f8}{g8}{h8}
+\end{othelloboard}
+\caption{}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\annotationsfirstrow{}{C}{A}{B}{B}{A}{C}{}
+\annotationssecondrow{C}{X}{}{}{}{}{X}{C}
+\annotationsthirdrow{A}{}{}{}{}{}{}{A}
+\annotationsfourthrow{B}{}{}{}{}{}{}{B}
+\annotationsfifthrow{B}{}{}{}{}{}{}{B}
+\annotationssixthrow{A}{}{}{}{}{}{}{A}
+\annotationsseventhrow{C}{X}{}{}{}{}{X}{C}
+\annotationseighthrow{}{C}{A}{B}{B}{A}{C}{}
+\end{othelloboard}
+\caption{Square names}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{0}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{1}{0}{0}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+Black and White, written with capital letters, will refer to the players, while
+lowercase letters (black and white) will refer to the color of the discs. For example:
+``at the end of the game there were more black discs than white discs, so Black won
+and White lost''. Black and White are referred to as ``he'', although they could of
+course be ``she'', as many women play Othello, including Carol Jacobs, who won the
+U.S. Othello Championship twice in a row.
+
+Compass directions (north, south, east, west) are sometimes used to refer to
+areas of the board (top, bottom, right, and left, respectively).
+
+\section{Rules of the game}
+
+\begin{enumerate}
+\item The game begins with black discs on d5 and e4, and white discs on d4 and e5, as
+shown in Diagram 1-3.
+
+\item Players alternate taking turns, with Black moving first.
+
+\item A legal move consists of placing a new disc on an empty square, and flipping
+one or more of the opponent's discs.
+
+\item Any of the opponent's pieces which are `sandwiched' between the disc just placed
+on the board and a disc of the same color already on the board should be flipped.
+Sandwiches can be formed vertically, horizontally, or diagonally. To form a sandwich,
+all of the squares between the new disc and the disc of the same color
+already on the board must be occupied by the opponent's pieces, with no blank
+squares in between.
+
+\item Pieces may be flipped in several directions on the same move. Any pieces which
+are caught in a sandwich must be flipped; the player moving does not have the
+right to choose to not flip a disc.
+
+\item A new disc can not be played unless at least one of the opponent's discs is
+flipped. If a player has no legal moves, that is, if no matter where the player
+places a new disc he could not flip at least one disc, that player passes his turn,
+and his opponent continues to make consecutive moves until a legal move becomes
+available to that player.
+
+\item If a player has at least one legal move available, he must make a move and may
+not pass his turn.
+
+\item The game continues until the board is completely filled or neither player has a
+legal move.
+\end{enumerate}
+
+\section{Scoring}
+
+Scoring is done at the end of game. The usual way to determine the score is to
+simply count the number of discs of each color, e.g., if there are 34 black discs and 30
+white discs, then Black wins 34--30. If both players have the same number of discs,
+then the game is a draw.
+
+In tournament play, if one player captures all of his opponents discs, the game is
+usually scored as a 64--0 victory for that player, regardless of the number of discs on
+the board. Further, in certain tournaments, such as the World Championship, empty
+squares are awarded to the winner. For example, if at the end of the game there are 32
+black discs and 29 white discs, with 3 empty squares, the score is recorded as a 35--29
+victory for Black.
+
+\section{Examples}
+
+Diagrams 1-4 through 1-9 show a sequence of moves at the start of the game to
+demonstrate the rules. In Diagram 1-4, Black makes the first move of the game to
+f5, sandwiching the white disc on e5 between this new disc and the black disc on
+d5. In the diagram, the numeral 1 on the disc on f5 indicates that this is where the
+first move is played. The diamond-shaped black disc on e5 indicates that this disc
+was white before the move, and was flipped as the result of Black's move. Below
+the diagram, the phrase `White to move' indicates that White will make the next
+move in the game. In Diagram 1-5, White plays to f6, sandwiching the disc on e5
+diagonally using the existing white disc on d4. In Diagram 1-7, White plays to f4,
+flipping discs in two directions. The black disc on f5 is sandwiched between the
+new disc on f4 and the white disc on f6, while the black disc on e4 is sandwiched
+between f4 and d4. In Diagram 1-9, White plays to c5, sandwiching the black discs
+on d5 and e5 using the existing white disc on f5.
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{0}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{4}{2}{0}{0}
+\annotationsfifthrow{}{}{}{}{}{1}{}{}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{0}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{3}{2}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{0}{0}{1}{0}{0}
+\annotationssixthrow{}{}{}{}{}{2}{}{}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{0}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{4}{2}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{0}{2}{1}{0}{0}
+\annotationssixthrow{}{}{}{}{3}{}{}{}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+ 
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfourthrow{0}{0}{0}{1}{3}{1}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{2}{3}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{0}{2}{1}{0}{0}
+\annotationsfourthrow{}{}{}{}{}{4}{}{}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\othelloarraythirdrow{0}{0}{0}{0}{2}{0}{0}{0}
+\othelloarrayfourthrow{0}{0}{0}{1}{4}{1}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{0}{2}{1}{0}{0}
+\annotationsthirdrow{}{}{}{}{5}{}{}{}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\othelloarraythirdrow{0}{0}{0}{0}{2}{0}{0}{0}
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{1}{0}{0}
+\othelloarrayfifthrow{0}{0}{1}{3}{3}{1}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{0}{2}{1}{0}{0}
+\annotationsfifthrow{}{}{6}{}{}{}{}{}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+Suppose that in the position shown in Diagram 1-10, Black moves to f8. Diagram
+1-11 shows the correct position after this move. The white disc on e6 is completely
+surrounded by black discs, but Black does not get to flip this disc, as it was not
+sandwiched by the move to f8. Diagram 1-12 shows a position in which White does
+not have a legal move. White passes, and Black moves again.
+
+\begin{figure}[h!]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow{0}{0}{0}{2}{2}{2}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarraythirdrow{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarrayfourthrow{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{2}{1}{1}{0}{0}
+\othelloarrayseventhrow{0}{0}{0}{2}{2}{1}{0}{0}
+\othelloarrayeighthrow	{0}{0}{0}{0}{2}{0}{0}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+%\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow{0}{0}{0}{2}{2}{2}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{2}{2}{4}{0}{0}
+\othelloarraythirdrow{0}{0}{0}{2}{2}{4}{0}{0}
+\othelloarrayfourthrow{0}{0}{0}{2}{2}{4}{0}{0}
+\othelloarrayfifthrow{0}{0}{0}{2}{2}{4}{0}{0}
+\othelloarraysixthrow{0}{0}{0}{2}{1}{4}{0}{0}
+\othelloarrayseventhrow{0}{0}{0}{2}{2}{4}{0}{0}
+\othelloarrayeighthrow	{0}{0}{0}{0}{2}{2}{0}{0}
+\annotationseighthrow{}{}{}{}{}{1}{}{}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow{0}{0}{1}{2}{2}{2}{2}{2}
+\othelloarraysecondrow	{0}{0}{1}{2}{2}{1}{2}{1}
+\othelloarraythirdrow{0}{0}{1}{2}{2}{2}{2}{2}
+\othelloarrayfourthrow{0}{0}{0}{1}{2}{2}{2}{2}
+\othelloarrayfifthrow{0}{0}{1}{2}{2}{2}{2}{2}
+\othelloarraysixthrow{2}{2}{2}{2}{2}{2}{2}{2}
+\othelloarrayseventhrow{2}{2}{2}{2}{2}{2}{2}{2}
+\othelloarrayeighthrow{2}{2}{2}{2}{2}{2}{2}{2}
+\end{othelloboard}
+\caption{White passes}
+\end{minipage}
+\end{center}
+\end{figure}
+
+\section{Playing through a transcript}
+
+Diagram 1-13 shows an example of a transcript of a complete game. The numbers
+indicate the order in which the moves were made, but not which pieces were
+flipped. To replay the game, place a black disc on the square marked 1 (f5 in this
+case), and flip pieces according to the normal rules of the game (e5 should be flipped
+to black in this case). Continue by playing a move for White on the square marked 2,
+a move for Black on the square marked 3, etc. Diagram 1-14 shows the position
+created after move 30, while Diagram 1-15 shows the final position. Partial transcripts
+are sometimes used to indicate a sequence of moves (see Diagram 2-9 for an
+example).
+
+\begin{figure}[h!]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{2}{1}{1}{2}{2}{1}{2}{1}
+\othelloarraysecondrow	{1}{1}{2}{1}{1}{1}{2}{1}
+\othelloarraythirdrow		{2}{1}{2}{1}{2}{2}{1}{2}
+\othelloarrayfourthrow	{2}{1}{2}{1}{2}{1}{2}{1}
+\othelloarrayfifthrow		{2}{1}{1}{2}{1}{2}{1}{2}
+\othelloarraysixthrow	{1}{2}{2}{1}{2}{1}{2}{2}
+\othelloarrayseventhrow	{2}{1}{2}{2}{1}{1}{2}{1}
+\othelloarrayeighthrow	{1}{2}{2}{1}{1}{2}{2}{1}
+\annotationsfirstrow	{49}	{44}	{38}	{39}	{33}	{40}	{59}	{60}
+\annotationssecondrow	{46}	{48}	{31}	{42}	{10}	{12}	{47}	{52}
+\annotationsthirdrow	{29}	{20}	{27}	{22}	{5}	{11}	{36}	{51}
+\annotationsfourthrow	{45}	{34}	{7}	{}	{}	{4}	{13}	{32}
+\annotationsfifthrow	{43}	{18}	{6}	{}	{}	{1}	{14}	{15}
+\annotationssixthrow	{30}	{21}	{9}	{16}	{3}	{2}	{23}	{35}
+\annotationsseventhrow{55}	{56}	{53}	{17}	{8}	{28}	{37}	{54}
+\annotationseighthrow	{58}	{57}	{25}	{24}	{26}	{19}	{41}	{50}
+\end{othelloboard}
+\caption{Transcript}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{0}{1}{1}{0}{0}
+\othelloarraythirdrow{2}{2}{2}{1}{1}{1}{0}{0}
+\othelloarrayfourthrow{0}{0}{2}{2}{2}{1}{2}{0}
+\othelloarrayfifthrow{0}{1}{2}{1}{2}{1}{2}{2}
+\othelloarraysixthrow{1}{3}{1}{1}{1}{1}{2}{0}
+\othelloarrayseventhrow{0}{0}{0}{1}{1}{1}{0}{0}
+\othelloarrayeighthrow	{0}{0}{2}{1}{1}{2}{0}{0}
+\annotationssixthrow{30}{}{}{}{}{}{}{}
+\end{othelloboard}
+\caption{After move 30}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow{2}{2}{2}{2}{2}{2}{2}{1}
+\othelloarraysecondrow	{2}{2}{1}{1}{1}{2}{1}{1}
+\othelloarraythirdrow{2}{2}{2}{1}{2}{1}{2}{1}
+\othelloarrayfourthrow{2}{2}{2}{2}{1}{1}{2}{1}
+\othelloarrayfifthrow{2}{2}{2}{1}{2}{1}{2}{1}
+\othelloarraysixthrow{2}{2}{1}{2}{2}{2}{1}{1}
+\othelloarrayseventhrow{2}{1}{2}{1}{1}{1}{1}{1}
+\othelloarrayeighthrow{1}{1}{1}{1}{1}{1}{1}{1}
+\end{othelloboard}
+\caption{Final position}
+\end{minipage}
+\end{center}
+\end{figure}
+
+\chapter{Corners and stable discs}
+Perhaps the most basic strategy in Othello is to take the corners. By the rules of
+play, it is impossible to flip a disc in a corner, so that if you are able to take a corner,
+that disc will be yours for the rest of the game. In Diagram 2-1, the disc on h8 must be
+white at the end of the game: even if Black later moves to both g8 and h7, he can not
+capture the disc on h8. Moreover, once you have a corner, it is often possible to build
+a large number of discs that are protected by the corner and can never be flipped.
+Such discs are called \jargon{stable discs}.
+
+\begin{figure}[h!]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{---------------------------OX------OOX-----OOO--------O--------O}
+\end{othelloboard}
+\caption{}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{--------------------O------OO------OOX-----OXX-----XOOO--OOOOOOO}
+\end{othelloboard}
+\caption{}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{---------------O---XXX-O---XXXXO---XXXOO---XXOOO--OOOOOO-OOOOOOO}
+\end{othelloboard}
+\caption{}
+\end{minipage}
+\end{center}
+\end{figure}
+
+In Diagram 2-2, the discs on the bottom row are stable discs, and in Diagram 2-3, 
+all 21 white discs are stable discs. If this is not obvious to you, then take some time
+now to convince yourself. Set up the positions on a board, then try to flip the stable
+discs by placing black discs wherever you like. There is simply no way for Black to
+get ``behind'' these discs to surround and flip them. The possibility of building up
+stable discs usually makes corners very valuable, especially early in the game.
+
+If taking corners is that good, then it should be obvious that you usually do not
+want to give any to your opponent! Given the rules of the game, the only way for your
+opponent to take a corner is if you play in one of the squares next to a corner, i.e., the
+C-squares or X-squares. The X-squares are particularly dangerous, and a move to an
+X-square early in the game is almost certain to give up the adjacent corner. For example, in Diagram 2-4, White has just moved to the X-square at g7. Although Black
+can not take the h8 corner immediately, if he can establish even one disc on the c3-f6
+diagonal, then Black will be able take the corner.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.35\textwidth}
+\begin{othelloboard}{\scalefactortwoup}
+\dotmarkings
+\drawboardfromstring{-----------O-O----OOOOO---OOOOX---OOOOX--XXOXO----XOO3O---XXXXX-}
+\posannotation{g7}{28}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hspace{24pt}
+%\hfill
+\begin{minipage}[t]{.35\textwidth}
+\begin{othelloboard}{\scalefactortwoup}
+\dotmarkings
+\drawboardfromstring{-----------O-O----OOOOO---OOOOX--X4444X--XXOXO----XOOOO---XXXXX-}
+\posannotation{b5}{1}
+
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+One possibility is for Black to play b5, capturing the disc on e5, as shown in
+Diagram 2-5. No matter where White plays, he will not be able to recapture the e5
+disc, and Black will be able to take the h8 corner on his next turn. Once black has the
+corner, all of his discs on row 8 become stable discs, and later in the game he is likely
+to be able to create stable discs on the right edge as well. In general, the earlier in the
+game a corner is taken the more valuable it is, as the potential for building up stable
+discs around the corner is greater. In most cases, moving to an X-square early in the
+game will prove to be a fatal error, although later in the book we will examine some
+exceptional circumstances under which early X-square moves are useful.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{---------------X--XXXO4O--XXX4O----X4OO---XXXO-------O----------}
+\posannotation{h2}{1}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{-----------XOO-X--XXOO4---XOX4XX--OXXXX----OXX------------------}
+\posannotation{h2}{1}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\drawboardfromstring{-------------X-X----OX4----OOXO----OOXOO---OXX------OX----------}
+\posannotation{h2}{1}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+While moves to the X-square will usually allow the opponent to take the adjacent
+corner, for C-squares the degree of danger depends largely on the rest of the
+squares on the same edge. For example, in Diagrams 2-6, 2-7, and 2-8, Black will
+quickly lose the h1 corner. In Diagram 2-6, White simply takes the corner on the next
+move. In Diagram 2-7, White can play h3; Black has no way of capturing the h3 disc,
+and White will be able to play h1 on his next turn. Can you see the way that White can capture the h1 corner in Diagram 2-8?
+
+Starting from Diagram 2-8, White should play h3, gaining access to the h1 corner.
+Even if Black captures the h3 disc by playing h4, as in Diagram 2-9, White still
+has access to the corner, as shown in Diagram 2-10. As these diagrams suggest, C-squares are often the most dangerous when the adjacent A-square is empty, allowing
+the opponent to attack the corner by playing into the A-square. We will see many
+more examples like this in later chapters.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.35\textwidth}
+\begin{othelloboard}{\scalefactortwoup}
+\dotmarkings
+\drawboardfromstring{-------------X-X----OXXO---OOXOX---OOXOO---OXX------OX----------}
+\posannotation{h3}{1}
+\posannotation{h4}{2}
+\end{othelloboard}
+\caption{}
+\end{minipage}
+\hspace{24pt}
+%\hfill
+\begin{minipage}[t]{.35\textwidth}
+\begin{othelloboard}{\scalefactortwoup}
+\dotmarkings
+\drawboardfromstring{-------------X-X----OOXX---OOXXX---OOXXO---OXX------OX----------}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+While there are many circumstances under which C-squares are bad moves, they are quite often perfectly good moves, and frequently they involve no danger of giving up a corner despite being adjacent to it. Diagrams 2-11, 2-12, and 2-13 all show examples where Black has a good C-square move at h2. In Diagram 2-11, h2 builds on Black's stable discs, and offers no prospect of white taking the h1 corner. In Diagram 2-12, Black must play h2 to prevent White from capturing the h8 corner. Once he does so, he is in no immediate danger of losing a corner. In Diagram 2-13, black can play h2 and later play another C-square at h7, all with no danger of losing a corner. As these diagrams suggest, the best time to take a C-square is often when you have pieces of your own color in the other squares along the edge.
+\addtolength{\belowcaptionskip}{-8pt}
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{.6}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{1}{0}{1}{0}{0}
+\othelloarraythirdrow	{0}{0}{1}{1}{1}{1}{1}{2}
+\othelloarrayfourthrow	{0}{1}{1}{1}{1}{1}{2}{2}
+\othelloarrayfifthrow		{1}{1}{1}{2}{2}{2}{2}{2}
+\othelloarraysixthrow	{0}{2}{2}{1}{2}{2}{1}{2}
+\othelloarrayseventhrow	{0}{0}{2}{2}{2}{1}{2}{2}
+\othelloarrayeighthrow	{0}{0}{2}{2}{2}{2}{2}{2}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{.6}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{0}{0}{1}{0}{0}
+\othelloarraythirdrow	{0}{0}{0}{1}{2}{1}{1}{1}
+\othelloarrayfourthrow	{0}{0}{0}{2}{2}{2}{1}{2}
+\othelloarrayfifthrow		{0}{0}{2}{2}{2}{2}{1}{2}
+\othelloarraysixthrow	{0}{0}{2}{2}{2}{1}{2}{2}
+\othelloarrayseventhrow	{0}{0}{0}{0}{0}{0}{0}{2}
+\othelloarrayeighthrow	{0}{0}{0}{0}{0}{0}{0}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{.6}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraythirdrow	{0}{0}{2}{2}{2}{1}{1}{1}
+\othelloarrayfourthrow	{0}{0}{2}{2}{2}{2}{2}{2}
+\othelloarrayfifthrow		{0}{0}{0}{2}{1}{1}{1}{2}
+\othelloarraysixthrow	{0}{0}{0}{1}{1}{1}{1}{2}
+\othelloarrayseventhrow	{0}{0}{0}{0}{1}{1}{0}{2}
+\othelloarrayeighthrow	{0}{0}{0}{0}{0}{0}{0}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+\clearpage
+\section*{Exercises}
+\addtolength{\belowcaptionskip}{8pt}
+\captionsetup{figurename=Exercise}\setcounter{figure}{0}
+In each diagram, find the best move. Answers begin on page \pageref{answersc2}.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{2}{0}{0}{2}{0}
+\othelloarraysecondrow	{0}{0}{2}{2}{2}{2}{2}{0}
+\othelloarraythirdrow	{2}{2}{2}{2}{2}{2}{2}{1}
+\othelloarrayfourthrow	{2}{2}{2}{2}{2}{1}{2}{0}
+\othelloarrayfifthrow		{2}{2}{2}{2}{1}{2}{2}{0}
+\othelloarraysixthrow	{2}{2}{2}{2}{2}{2}{2}{0}
+\othelloarrayseventhrow	{2}{0}{0}{0}{0}{0}{0}{0}
+\othelloarrayeighthrow	{0}{0}{0}{0}{0}{0}{0}{0}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{1}{1}{1}{1}{1}{1}{0}
+\othelloarraysecondrow	{0}{0}{1}{1}{1}{1}{1}{1}
+\othelloarraythirdrow	{2}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayfourthrow	{2}{2}{1}{1}{1}{1}{1}{1}
+\othelloarrayfifthrow		{2}{2}{1}{1}{2}{1}{1}{1}
+\othelloarraysixthrow	{2}{2}{1}{1}{1}{1}{1}{1}
+\othelloarrayseventhrow	{2}{0}{2}{2}{1}{2}{0}{1}
+\othelloarrayeighthrow	{0}{2}{2}{2}{2}{2}{2}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{2}{2}{2}{2}{0}{0}
+\othelloarraysecondrow	{0}{0}{2}{2}{2}{2}{0}{0}
+\othelloarraythirdrow	{0}{0}{2}{2}{2}{2}{0}{0}
+\othelloarrayfourthrow	{0}{2}{2}{1}{2}{2}{0}{0}
+\othelloarrayfifthrow		{0}{2}{1}{2}{1}{2}{0}{0}
+\othelloarraysixthrow	{0}{2}{2}{2}{2}{2}{0}{0}
+\othelloarrayseventhrow	{0}{1}{1}{1}{1}{1}{0}{0}
+\othelloarrayeighthrow	{1}{1}{1}{1}{1}{1}{1}{0}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraysecondrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarraythirdrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayfourthrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayfifthrow		{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarraysixthrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayseventhrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayeighthrow	{2}{2}{2}{2}{2}{2}{1}{0}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{1}{1}{1}{0}{1}{0}{0}
+\othelloarraysecondrow	{0}{0}{2}{1}{1}{1}{0}{0}
+\othelloarraythirdrow	{0}{0}{1}{2}{2}{0}{0}{0}
+\othelloarrayfourthrow	{0}{0}{1}{1}{2}{2}{2}{0}
+\othelloarrayfifthrow		{0}{0}{1}{1}{2}{2}{2}{0}
+\othelloarraysixthrow	{0}{0}{1}{1}{2}{2}{0}{0}
+\othelloarrayseventhrow	{0}{0}{0}{1}{2}{2}{0}{0}
+\othelloarrayeighthrow	{0}{0}{0}{0}{0}{0}{0}{0}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarrayfirstrow		{0}{0}{0}{0}{2}{0}{0}{0}
+\othelloarraysecondrow	{0}{0}{0}{2}{2}{1}{0}{2}
+\othelloarraythirdrow	{0}{0}{2}{2}{2}{1}{2}{2}
+\othelloarrayfourthrow	{0}{0}{2}{2}{2}{2}{2}{0}
+\othelloarrayfifthrow		{0}{0}{0}{2}{2}{2}{1}{0}
+\othelloarraysixthrow	{0}{0}{0}{1}{2}{0}{0}{1}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+\chapter{Frontier discs and walls}
+\captionsetup{figurename=Diagram}
+
+In chapter 2, we learned about the value of corners, and the danger of moving to
+X-squares and C-squares. While knowing this alone might be enough to let you win
+against a complete novice, it will not get you far against more seasoned competition.
+In games between players that are both aware of the strategies presented in chapter 2,
+neither player will voluntarily make the sort of bad X-square and C-squares moves
+that give up corners for no reason. If you want your opponent to make these moves,
+then you will have to force him to do so. That is, you want to create a situation where
+the \emph{only} moves available to your opponent are bad moves. How to go about doing this
+is the subject of this chapter, and indeed most of the rest of the book.
+
+\begin{figure}[h]
+\begin{center}
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarraythirdrow	{0}{2}{2}{2}{2}{2}{1}{1}
+\othelloarrayfourthrow	{2}{2}{2}{2}{2}{2}{1}{0}
+\othelloarrayfifthrow		{0}{1}{2}{2}{1}{1}{1}{2}
+\othelloarraysixthrow	{1}{1}{1}{1}{1}{1}{1}{0}
+\othelloarrayseventhrow	{0}{0}{0}{0}{1}{0}{0}{0}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarraythirdrow		{1}{3}{3}{3}{3}{3}{1}{1}
+\othelloarrayfourthrow		{2}{3}{2}{2}{2}{2}{1}{0}
+\othelloarrayfifthrow		{0}{1}{3}{2}{1}{1}{1}{2}
+\othelloarraysixthrow		{1}{1}{1}{1}{1}{1}{1}{0}
+\othelloarrayseventhrow	{0}{0}{0}{0}{1}{0}{0}{0}
+\posannotation{a3}{1}
+\end{othelloboard}
+\caption{Black to move}
+\end{minipage}
+\hfill
+\begin{minipage}[t]{.32\textwidth}
+\begin{othelloboard}{\scalefactorthreeup}
+\dotmarkings
+\othelloarraysecondrow	{2}{0}{0}{0}{0}{0}{0}{0}
+\othelloarraythirdrow		{4}{4}{1}{1}{1}{1}{1}{1}
+\othelloarrayfourthrow		{2}{1}{2}{2}{2}{2}{1}{0}
+\othelloarrayfifthrow		{0}{1}{1}{2}{1}{1}{1}{2}
+\othelloarraysixthrow		{1}{1}{1}{1}{1}{1}{1}{0}
+\othelloarrayseventhrow	{0}{0}{0}{0}{1}{0}{0}{0}
+\posannotation{a2}{2}
+\end{othelloboard}
+\caption{White to move}
+\end{minipage}
+\end{center}
+\end{figure}
+
+Diagram 3-1 shows the sort of position that often arises in games between an
+expert (Black) and a novice (White). Many novices choose their moves mainly on the
+basis of the number of discs that are flipped, with the more discs flipped the better.
+After all, the object of the game is to end up with as many pieces as possible, so it
+seems logical to want to take a lot of pieces at every point during the game. Following
+this logic, the novice chooses to play a3, flipping 7 discs, as shown in Diagram 3-2.
+The problem with this move becomes apparent after Black replies with a2, resulting
+in the position shown in Diagram 3-3.
+
+In Diagram 3-3, White's only legal option is the b2 X-square, which White is
+obliged to play whether he wants to or not (Diagram 3-4). This immediately surrenders
+the a1 corner (Diagram 3-5), and Black will eventually gain many \ldots
+
+%% Answers %%
+
+\chapter*{Answers to Exercises}
+\label{answersc2}
+\subsection*{Chapter 2}
+\exercisenum{Exercise 2-1} White should play e1, capturing the disc at e4, which will provide access to the h2 corner.
+
+\exercisenum{Exercise 2-2} Black should play a2. Although this is a C-square, there is no
+danger of White gaining access to the a1 corner. Further, this move flips the
+disc at d5, which will allow Black to take the h1 corner.
+
+\exercisenum{Exercise 2-3} White should play a7, using the a8 corner to build more stable
+discs.
+
+\exercisenum{Exercise 2-4} This is an extreme example of building up stable discs. The
+correct sequence of moves is shown in the diagram.
+
+\begin{center}
+\begin{othelloboard}{.8}
+\othelloarrayfirstrow			{2}{2}{2}{2}{2}{2}{2}{2}
+\othelloarraysecondrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarraythirdrow		{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayfourthrow		{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayfifthrow		{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarraysixthrow		{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayseventhrow	{1}{1}{1}{1}{1}{1}{1}{1}
+\othelloarrayeighthrow		{2}{2}{2}{2}{2}{2}{1}{2}
+\annotationsfirstrow			{1}{2}{3}{4}{5}{6}{8}{9}
+\posannotation{h8}{7}
+\end{othelloboard}
+\end{center}
+
+\exercisenum{Exercise 2-5} Black should fill in the hole at e1. Since White can not capture
+this disc, Black will be able to take the a1 corner.
+
+\exercisenum{Exercise 2-6} White should play h4, threatening to take the h1 corner. If Black
+tries to prevent this by playing h5, the white disc at h6 still allows White to take
+the corner.
+
+
+\end{document}
\ No newline at end of file
-- 
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