summaryrefslogtreecommitdiff
path: root/macros/latex/contrib/othelloboard/example-rose-chps1-2.tex
blob: b8766c9897006c223001ecc397c260db2d47921d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
\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}