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3 <!-- Mirrored from users.eniinternet.com/bradleym/Ch5.html by HTTrack Website Copier/3.x [XR&CO'2014], Sun, 06 Nov 2022 06:57:08 GMT -->
4 <head>
5 <title> Improve Fast In Go - Milton N. Bradley</title>
6 <link rel="stylesheet" href="style2.css">
7 </head>
8 <body bgcolor="#E0FFFF">
9 <a name="top">
10
11 <center><br><br>
12 <font class="booktitle">
13 Improve <I>Fast</I> In Go
14 </font>
15 <br><br>
16
17 <h1>
18 <font class="chaptitle">
19 &copy; Milton N. Bradley 2008
20 </font>
21 <hr></h1></center>
22 <br><br>
23
24
25 <center><a name="Chapter5">
26 <font class="chaptitle">
27 Chapter 5 - Sector Lines, Enclosure & Connectiivity
28 </font><br>
29
30 </center>
31 <font size= +1>
32 <br><br>
33
34 In the previous chapters we discussed the principles upon which fighting must be based if it’s to be productive, and then spelled out how to identify the weak, important stones which should be the objects of any attack. In this chapter we begin the discussion of the criteria for deciding whether and when to initiate or avoid such attacks.<br><br>
35 Among the key operative themes in attack/defense are the closely related factors of enclosure and connectivity. These often become significant almost from the very earliest moves in the game as both sides maneuver for advantage, especially but not exclusively in the complex local (usually, but not exclusively corner) confrontations called Joseki.<br><br>
36 Another important issue, closely related to enclosure, is how to act against an opponent’s moyo. Moyo situations are typically quite complex, so without some simplifying concept to provide guidance the average player would find it virtually impossible to accurately assess their often subtle interactions, and then make the correct decisions.<br><br>
37 The ingenious concept known as a Sector Line efficiently satisfies the critical need for guidance in both the attack/defense and moyo situations.<br><br>
38 Although the Sector Line concept has been applied implicitly for centuries in the Orient, the first explicit description of it of which I’m aware was in a mid 1970's article by Bruce Wilcox in the American Go Journal.<br><br>
39
40 But just what is a Sector Line?<br><br>
41
42 <center>
43 <br><table class="txtbox">
44 <tr>
45 <td width="30">&nbsp;</td>
46 <td align="middle" valign="top">
47 <br>
48 <font class="txtboxsmall">
49
50 A Sector Line Is An Imaginary Straight Line<br><br>
51 Extending Across An Open Board Area<br><br>
52 Joining Two Stones Of The Same Color,<br><br>
53 Or Extending From A Single Stone<br><br>
54 To The Board Edge.<br>
55 </font>
56
57
58 <br><br>
59 </td>
60 <td width="30">&nbsp;</td>
61 </tr>
62 </table><br><br>
63 </center>
64
65 The Sector Line’s conceptual rationale is that a solid wall of stones of that color could theoretically be constructed along that line.
66 The fact that such a wall will almost never be realized in practice does not affect the Sector Line’s value as a guide to making the appropriate
67 strategic and tactical decisions.<br><br>
68
69 <table>
70
71 <tr>
72 <td align="left" valign="top">
73 <img src="C5D1.jpg" border="1">
74
75 </td>
76
77
78 <td width="10">&nbsp;</td>
79 <td align="left" valign="top">
80 <img src="C5D2.jpg" border="1">
81
82 </td>
83
84
85
86 <td width="10">&nbsp;</td>
87 <td valign="top" align="left">
88 <br><br><br>
89 <strong>Diagram 1</strong> When B2 approaches W1, the squeeze play of W3 is particularly effective because ...<br><br>
90
91 <strong>Diagram 2</strong> Now the lone Black stone is enclosed within the indicated White Sector Lines, as both players would visualize them.<br><br>
92
93 </td>
94 </tr>
95 </table>
96
97
98 <br><br>
99 <strong>When To Use Sector Lines</strong><br><br>
100
101 <strong>&nbsp;&nbsp;&nbsp;- Sector Lines are primarily (but not exclusively) useful in dealing with <U>weak stones</U></strong>, which might be captured if they can’t make eyes or escape.<br>
102
103 <strong>&nbsp;&nbsp;&nbsp;- Sector Lines are most often applicable in the Fuseki and early middle game</strong>, because it is usually only then that enough of the board is still vacant to make them really meaningful.<br><br>
104
105 <strong>The seriousness of the situation for the enclosed stones is primarily a function of:<br>
106 &nbsp;&nbsp;&nbsp;- The proximity of the nearest Sector Line.<br>
107 &nbsp;&nbsp;&nbsp;- The spacing between the stones forming that Sector Line.</dd></strong><br><br>
108
109 In each case closer is more serious, with the effect diminishing rapidly with increasing distance. No exact criteria exist for determining this spacing/distance effect, so each situation must be individually evaluated using the player’s best judgment.<br><br>
110
111 <strong>How Sector Lines Function</strong><br>
112
113 <strong>&nbsp;&nbsp;&nbsp;- Sector Lines act as a kind of “early warning system”</strong> to indicate which weak stones are in danger of becoming fully enclosed (and thus before the necessity of fighting a life-or-death battle for survival is thrust upon them).<br>
114 <strong>&nbsp;&nbsp;&nbsp;- Sector Lines provide only generally appropriate action guidelines</strong>, and do not specifically identify:<br>
115 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the preferred strategy to be followed<br>
116 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the best move itself, or even an explicit identification of the set of feasible alternatives from which the best move should be &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;selected.<br><br>
117
118 Caution! Although the Sector Line concept is both simple and extremely valuable, it’s not always determinative!<br><br>
119
120
121 <strong>A Sector Line is not valid if it:<br><br>
122 <strong>&nbsp;&nbsp;&nbsp;- Intersects an opposing stone.</strong><br><br>
123
124 <table>
125 <tr>
126 <td align="left" valign="top">
127 <img src="C5D3.jpg" border="1">
128
129 </td>
130
131 <td width="10">&nbsp;</td>
132 <td valign="top" align="left">
133 <br><br><br><br><br><br>
134 <strong>Diagram 3</strong> When B1 is played, it breaks the outer Sector Line and negates it, so that Black is no longer enclosed!<br><br>
135 </td>
136 </tr>
137 </table>
138
139 <br><br>
140 <strong>A Sector Line is not valid if it:<br><br>
141 &nbsp;&nbsp;&nbsp;- Intersects an opposing Sector Line.</strong><br><br>
142
143 <table>
144 <tr>
145 <td align="left" valign="top">
146 <img src="C5D4.jpg" border="1">
147
148 </td>
149
150 <td width="10">&nbsp;</td>
151 <td valign="top" align="left">
152 <br><br><br><br><br><br><br>
153 <strong>Diagram 4</strong> Here we see that W72 is within Black Sector Lines, but Black’s 69-77 group is similarly enclosed by White Sector Lines which intersect Black’s.<br><br>
154 The two B49, 59 stones are within White Sector Lines, but are also an anchor point of the Black Sector Lines which enclose W72.<br><br>
155 The result is that none of these Sector Lines are valid for determining the appropriate action to be taken in this area. This sort of situation is quite common when the board becomes relatively
156 crowded, but in no way detracts from the general utility of the Sector Line concept.<br><br>
157
158 </td>
159 </tr>
160 </table>
161 <br><br>
162 Despite these very real limitations, <strong>the information Sector Lines provide is invaluable:</strong><br>
163 &nbsp;&nbsp;&nbsp;A. To The Attacker, Sector Lines indicate whether or not to try to either:</strong><br>
164 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>1. Steal the opponent’s eyespace</strong>, and therefore drive his weak group out into the center. Or<br><br>
165
166 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>2. Cut off flight into the center</strong>, and so force the weak group to attempt to live, either by making eyes in place or by capturing &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;some of the attacking stones.<br><br>
167 &nbsp;&nbsp;&nbsp;<strong>B. To The Defender, Sector Lines indicate whether it’s best to either:<br>
168 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1. Run into the center to escape.<br>
169 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2. Try to connect to nearby friendly stones.<br>
170 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3. Make eyes.<br>
171
172 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;4. Abandon the threatened stones (at least temporarily).<br>
173 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5. Counterattack.</strong><br><br>
174
175 Caution!<br><br>
176 In any given position not all of these alternatives may be feasible, and choosing among those that are is a matter of the player’s judgment - a subject on which the Sector Lines themselves offer no direct help!
177 Now let’s examine each of these Sector Line characteristics in detail.<br><br>
178 &nbsp;&nbsp;&nbsp;<strong>A. The Attacker’s Uses Of Sector Lines<br><br>
179 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1. Steal the opponent’s eyespace</strong><br><br>
180
181 The sequence shown in the following diagrams occurred in a championship game between two 9 Dan professionals, who were then among the top 10 players in the world. Yet the simple Sector Line concept explains and helps
182 predict their moves to a remarkable degree!<br><br>
183
184 <table>
185 <tr>
186 <td align="left" valign="top">
187 <img src="C5D5.jpg" border="1">
188
189 </td>
190
191 <td width="10">&nbsp;</td>
192
193 <td valign="top" align="left">
194 <br><br><br><br><br><br><br>
195 <strong>Diagram 5</strong> The position in the lower right corner begins with the same popular 3-4 point Joseki we saw earlier in Dia 1, in which White has just squeezed the lone Black stone
196 from above, enclosing it within the indicated Sector Lines.<br><br>
197 These Sector Lines are close enough to constitute a fairly serious threat, so under normal circumstances Black would respond immediately. But because this 9P Black calculated that he can still
198 readily live locally even if White is first to play again here, he instead chose to take Sente elsewhere.<br><br>
199 Although this was a rational global strategic decision, it gave White the opportunity to maximize his local advantage, as we see in the following diagrams.<br><br> <br><br>
200 </td>
201
202 </tr>
203 </table>
204 <br><br>
205
206 <table>
207 <tr>
208 <td align="left" valign="top">
209 <img src="C5D6.jpg" border="1">
210
211 </td>
212
213 <td width="10">&nbsp;</td>
214 <td valign="top" align="left">
215 <br><br><br><br><br><br>
216 <strong>Diagram 6 W1</strong> takes advantage of Black’s failure to defend by blocking him from the corner, making territory for White while making it harder for Black to secure eyespace locally.<br><br>
217 If White were to be allowed to continue at 2 next , that would not only make perfect shape for his own stones but would also make it extremely hard for the Black stone to make life locally.<br><br>
218 So with little choice, <strong>B2</strong> occupies the key shape point himself, while cutting the White Sector Line! (A strong clue that this is a desirable move!)<br><br>
219
220 A (slightly lesser) problem with B2 is that it also makes his unit “heavy”.
221 <strong>W3</strong> With this stylish Knight’s move extension, White increases the scope of his control of the corner by extending to the left, at the same time creating a new Sector line which once again encloses Black.(thereby maintaining Sente!)
222 <br>
223 </td>
224 </tr>
225 </table>
226 <br><br>
227
228 <table>
229 <tr>
230
231 <td align="left" valign="top">
232 <img src="C5D7.jpg" border="1">
233
234 </td>
235
236 <td width="10">&nbsp;</td>
237 <td valign="top" align="left">
238 <br><br><br><br><br><br>
239 <strong>Diagram 7</strong> In order to escape that enclosure it’s necessary to break White’s new Sector Line, and in this position the stylish diagonal extension of B4 is the best way to achieve this end.<br><br>
240
241 An alert reader will have noticed that B4 not only broke the White Sector Line but also established Black’s own Sector Line enclosing the lone White stone on the right side.<br><br>
242 But because the Black star point stone anchoring the upper end of that Sector Line is so far away, the lone White stone is only mildly affected by this. So for the moment White can afford to ignore that Black Sector Line, to continue his own attack.<br><br>
243 White’s natural response to B4 is to extend once again on the bottom with the one point skip of <strong>W5</strong>, increasing his local territory while also initiating the new Sector Line shown, to once again enclose the 3 Black stones.<br><br>
244
245 </td>
246 </tr>
247 </table>
248
249 <br><br>
250
251 <table>
252 <tr>
253 <td align="left" valign="top">
254 <img src="C5D8.jpg" border="1">
255
256 </td>
257
258 <td width="10">&nbsp;</td>
259 <td valign="top" align="left">
260
261 <br><br><br><br>
262 <strong>Diagram 8</strong> When <strong>B6</strong> breaks the latest White Sector Line, there is no further White move that will simultaneously enclose the Black stones within a new White Sector Line while also extending White’s lower side territory.<br><br>
263 That means that, for the moment at least, it is no longer profitable for White to continue playing on the lower side, because it would be Gote.<br><br>
264 On the other hand, we see that Black has now established his own Sector Line enclosing White’s lone right side stone.<br><br>
265 But because the upper anchor stone of this Black Sector Line is so distant, this lone White stone has more than ample maneuvering room to either make a base or escape into the center if attacked further.<br><br>
266
267 So the Sector Line analysis tells us that White can now afford to play elsewhere if his evaluation of the global board position indicates that would be more productive - and that in fact is what the 9 Dan pro playing White in this game actually did!<br><br>
268 <br><br>
269 </td>
270 </tr>
271 </table>
272 <br><br>
273 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>2. Cut off flight into the center.</strong><br><br>
274
275 <table>
276 <tr>
277 <td align="left" valign="top">
278 <img src="C5D9.jpg" border="1">
279
280 </td>
281
282 <td width="10">&nbsp;</td>
283 <td valign="top" align="left">
284 <br><br><br><br>
285
286 <strong>Diagram 9</strong> This is a situation that frequently arises in both even and handicap games when Black fails to respond locally to the kakari of W1.<br><br>
287 W3 (which is also often played at “a”) encloses the Black corner stone within White Sector Lines as shown. But Black can still easily break out safely via a play at
288 any of “a”, “b”, or “c”. But if he doesn’t ...<br><br>
289 <br><br>
290 </td>
291 </tr>
292 </table>
293 <br><br>
294
295 <table>
296 <tr>
297 <td align="left" valign="top">
298 <img src="C5D10.jpg" border="1">
299
300 </td>
301
302 <td width="10">&nbsp;</td>
303 <td valign="top" align="left">
304 <br><br><br>
305
306 <strong>Diagram 10</strong> Most often, White’s strongest continuation is with W1 here, to solidly enclose Black within his Sector Lines.<br><br>
307 Black can then cut these Sector Lines, but can’t forcibly break out through them.<br><br>
308 Now let’s examine why allowing W1 is usually bad for Black.<br><br>
309 <br><br>
310 </td>
311 </tr>
312 </table>
313
314 <br><br>
315
316 <table>
317 <tr>
318 <td align="left" valign="top">
319 <img src="C5D11.jpg" border="1">
320
321 </td>
322
323 <td width="10">&nbsp;</td>
324 <td valign="top" align="left">
325
326 <br><br><br>
327 <strong>Diagram 11</strong> Black can still live in the corner, if he either knows this sequence by heart or can find his way through its tactical complications unaided.<br><br>
328 But it’s dangerous because even a slight error in the sequence can easily result in the entire corner’s death! And even if Black lives, as here, White’s thickness usually gives him the better position globally.<br><br> So playing this way is usually only advisable in special circumstances.
329 <br><br>
330 </td>
331 </tr>
332 </table>
333
334 <br><br>
335
336 &nbsp;&nbsp;&nbsp;<strong>B. Defender’s Uses Of Sector Lines<br><br>
337 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1. Run into the center to escape.</strong>
338 <br><br>
339 <table>
340 <tr>
341 <td align="left" valign="top">
342
343 <img src="C5D12.jpg" border="1">
344
345 </td>
346
347 <td width="10">&nbsp;</td>
348 <td valign="top" align="left">
349 <br><br><br><br>
350 <strong>Diagram 12</strong> Black will usually be best advised to break out of the White Sector Line, most often by occupying the key point himself via B1 as shown, but sometimes by attaching at “a” or “b”instead.<br><br>
351 After B1, W2 to seize the corner is by far the most frequent continuation, and then Black will usually (sooner or later) block at either “c” or “d”, the choice depending on the global board position.<br><br>
352
353 <br><br>
354 </td>
355 </tr>
356 </table>
357 <br><br>
358 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>2. Try to connect to nearby friendly stones.</strong><br><be>
359
360 <br><br>
361
362 <table>
363
364 <tr>
365 <td align="left" valign="top">
366 <img src="C5D13.jpg" border="1">
367
368 </td>
369
370 <td width="10">&nbsp;</td>
371 <td valign="top" align="left">
372 <br><br><br><br><br>
373 <strong>Diagram 13</strong> In this game between an 8D and 6D, the marked Black stone is completely enclosed by White Sector Lines, so it appears that all of this large territory is about to become White’s.<br><br>
374
375 Living in place is difficult, but Black saw an opportunity to save this stone and neutralize much of White’s potential territory in the surrounding area if he could somehow manage to connect to the Black stones below.
376 The next diagram shows how he went about doing it.<br><br>
377
378 </td>
379 </tr>
380 </table>
381 <br><br>
382
383 <table>
384 <tr>
385
386 <td align="left" valign="top">
387 <img src="C5D14.jpg" border="1">
388
389 </td>
390
391 <td width="10">&nbsp;</td>
392 <td valign="top" align="left">
393 <br><br>
394 <strong>Diagram 14</strong> With this clever sequence, Black managed to connect underneath in the lower left and achieve life, thus neutralizing most of this formerly large White area.<br><br>
395
396 In return, White captured a part of Black’s former lower edge group, to sharply increase his own territory there.<br><br>
397 So Black’s gain was not without cost, and that’s a fairly common result of such confrontations. But on balance Black has profited a bit more, at least in part because he has emerged from this fight with Sente.<br><br>
398
399 </td>
400 </tr>
401 </table>
402 <br><br>
403
404 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>3. Make eyes.</strong><br><br>
405
406 <table>
407 <tr>
408 <td align="left" valign="top">
409 <img src="C5D15.jpg" border="1">
410
411 </td>
412
413 <td width="10">&nbsp;</td>
414 <td align="left" valign="top">
415 <img src="C5D16.jpg" border="1">
416
417
418 </td>
419
420
421 <td width="10">&nbsp;</td>
422 <td valign="top" align="left">
423
424 <b>Dia 15</b> In this game between two 7D players, when the marked Black stone was played it not only prevented White’s damaging push through-and-cut, but also completed the enclosure of the White 7-stone group on the right edge.<br><br>
425 In the absence of special circumstances Black should without fail play to enclose White as shown!
426 <br><br>
427 <b>Dia 16</b> If White now desires, his 7 stones on the right edge can live easily via W1, because then if B“a”, W”b” completes his two eyes.<br><br>
428
429 And if Black doesn’t play at “a”, it’s possible that at an appropriate later time White will be able to follow with the profitable endgame sequence of W“a”, B“c”, W“b”, B“d”.<br><br>
430
431 </td>
432 </tr>
433 </table>
434 The problem with making life by playing W1 is that Black will then happily continue with B2 to connect his corner stones out while seriously weakening the important (and presently both shapeless and eyeless) 5-stone “L” shaped White center unit immediately below!<br><br>
435 Because that was a prospect that was unacceptable to White, what he played instead of this W1 is shown next.<br><br>
436 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>4. Abandon the threatened stones (at least temporarily).</strong><br><br>
437
438 <table>
439 <tr>
440 <td align="left" valign="top">
441 <img src="C5D17.jpg" border="1">
442
443 </td>
444
445 <td width="10">&nbsp;</td>
446 <td valign="top" align="left">
447
448 <strong>Diagram 17</strong> Because the result of Dia 16 was unpalatable, White chose instead to play W1 here, to strengthen the crucial weak 5-stone center White string!<br><br>
449
450 This not only undercut the Black corner while preventing Black’s connection underneath, but also isolated the lone Black stone on the upper edge.<br><br>
451 But the severe price that White had to pay for this was B2, which more or less assures the death of the White right edge group, because now White needs both “a” and “b” to secure his two eyes, and he can only manage that by making two successive moves here.
452 (Only possible if played as a Ko threat which Black can’t afford to answer.)<br><br>
453 So after B2 White had no choice but to tenuki, and hope that circumstances would later enable him to rescue this “abandoned” 7 stone group on the right edge.<br><br>
454
455
456 </td>
457 </tr>
458 </table>
459 <br>
460
461 Here’s another example, arising in a position that’s not uncommon in both handicap and even games:<br><br>
462
463
464 <table>
465 <tr>
466 <td align="left" valign="top">
467 <img src="C5D18.jpg" border="1">
468
469 </td>
470
471 <td width="10">&nbsp;</td>
472 <td valign="top" align="left">
473 <br>
474 <strong>Diagram 18</strong> W4 is a probe intended to induce Black to fix the shape of his stones, so that White will then know how to best proceed locally at the appropriate later time.<br><br>
475 But as things stand it was too early in the game to be sure after B5 whether White will prefer to continue below, on the right, or on the 3-3 point in the corner, and W4 is enclosed within the indicated
476 close and very threatening Black Sector Lines. So for the moment W4 was correctly “abandoned”, as White played elsewhere!<br><br>
477 (From that, it might reasonably be argued that W4 was premature and should better have been deferred until a later time. But that's an issue well beyond our present focus.)<br><br>
478
479 </td>
480
481 </tr>
482 </table>
483 <br><br>
484
485 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>5. Counterattack.</strong><br><br>
486
487
488 <table>
489 <tr>
490 <td align="left" valign="top">
491
492 <img src="C5D19.jpg" border="1">
493
494 </td>
495
496 <td width="10">&nbsp;</td>
497 <td valign="top" align="left">
498 <br><br><br><br><br><br><br><br>
499 <strong>Diagram 19</strong> In this game between a 4D and a 3D, when W1 was played it seemed that White had visualized the indicated Sector Lines and the huge potential moyo that they enclose. But, although appearing logical,
500 this reasoning is actually doubly flawed!<br><br>
501 Not only are there are two Black Sector Lines running from the upper right to the lower left that intersect (and therefore neutralize) several of White’s, but, far more significant, Black can counter-attack by establishing his
502 own far more threatening Sector Lines!<br><br>
503
504 </td>
505 </tr>
506 </table>
507 <br><br>
508
509 <table>
510 <tr>
511 <td align="left" valign="top">
512 <img src="C5D20.jpg" border="1">
513
514
515 </td>
516
517 <td width="10">&nbsp;</td>
518 <td valign="top" align="left">
519 <br><br><br><br><br><br><br><br>
520 <strong>Diagram 20</strong> A strong Black response would have been as shown, not only enclosing the 4 weak White stones within the indicated close (and therefore very threatening) Sector Lines of his own, but also simultaneously
521 assuring that Black can move into the White moyo before it can be consolidated. (Note that the 8 marked Whites at the top are tightly enclosed with only 3 liberties, and are therefore effectively captured!)<br><br>
522 Although the outcome of the fight that would have followed isn’t entirely clear, it would have offered Black his best chance to win. When he failed to make this key play, White moved smoothly on to an easy victory!<br><br>
523 <br><br>
524
525 </td>
526 </tr>
527 </table>
528 <br><br>
529
530 <strong>Sector Lines As Moyo Invasion/Reduction Indicators<br><br>
531 &nbsp;&nbsp;&nbsp;&nbsp;- Playing anywhere inside the opponent’s Sector Lines will constitute an invasion.<br>
532 &nbsp;&nbsp;&nbsp;&nbsp;- A play on or just outside an opponent’s Sector Line will initiate a reduction.<br><br>
533
534 The key clues to deciding whether a reduction or invasion of an opposing moyo is the more likely to produce a satisfactory result are whether or not one or more of the following is true:<br>
535 &nbsp;&nbsp;&nbsp;&nbsp;- There is at least one long Sector Line operative.<br>
536 &nbsp;&nbsp;&nbsp;&nbsp;- One or more of the enclosing Sector Lines have significant gaps for possible ingress or egress by opposing stones, &nbsp;&nbsp;especially if<br><br>
537 &nbsp;&nbsp;&nbsp;&nbsp;- There are friendly stones fairly close outside those Sector Lines.</strong><br><br>
538
539 If any of these conditions exist, an invasion will often be feasible because there will be opportunities to either connect out or to live within the moyo by placing key eyemaking stones which also threaten to connect out.<br><br>
540
541 To the extent that these enabling conditions don’t exist, only a reduction will usually be feasible.<br><br>
542 But it’s important to remember that there are no absolutes! Although the use of Sector Lines will go a long way toward enabling you to make the right decision, your ultimate success or failure in the fighting that ensues will still depend upon your ability to find and correctly time the right threats, and on your opponent’s ability to meet them.<br><br>
543
544 The following example shows the kind of dangerous tactical complications that frequently result from invasions, and why application of the indications provided by Sector Lines must always be made with great caution and forethought.<br><br>
545
546
547 <table>
548 <tr>
549 <td align="left" valign="top">
550 <img src="C5D21.jpg" border="1">
551
552
553 </td>
554
555 <td width="10">&nbsp;</td>
556 <td valign="top" align="left">
557 <br><br><br>
558 <strong>Diagram 21</strong> This is a not uncommon situation in which Black has made a 5 point skip from a 4-stone wall based on the third line to form a small moyo, against which White will often feel compelled to act.<br><br>
559 But how? And where?<br><br>
560
561 <br><br>
562
563 </td>
564 </tr>
565 </table>
566 <br><br>
567
568 <table>
569 <tr>
570 <td align="left" valign="top">
571
572 <img src="C5D22.jpg" border="1">
573
574 </td>
575
576 <td width="10">&nbsp;</td>
577 <td valign="top" align="left">
578 <br><br>
579 <strong>Diagram 22</strong> The best try to make a live group within the Black space is to begin with this one point third line skip of W1 from the extension stone.<br><br>
580 In response, the diagonal extension of B2 is the strongest way to prevent White’s escape to the outside, forcing him to try to live in place.<br><br>
581
582 This diagram shows one possible continuation, in which the invasion dies, and the next diagram shows another with the same result.<br><br>
583
584 </td>
585 </tr>
586 </table>
587 <br><br>
588
589 <table>
590 <tr>
591
592 <td align="left" valign="top">
593 <img src="C5D23.jpg" border="1">
594
595 </td>
596
597 <td width="10">&nbsp;</td>
598 <td valign="top" align="left">
599 <br><br><br><br><br>
600 <strong>Diagram 23</strong> The problem in this position with an invasion like this W1. is that there really isn’t room enough for the invaders to live if Black defends correctly! And if White does die, as here, that allows Black to consolidate a territory of over 30 points.<br><br>
601
602 </td>
603 </tr>
604 </table>
605 <br><br>
606
607 <table>
608 <tr>
609 <td align="left" valign="top">
610 <img src="C5D24.jpg" border="1">
611
612
613 </td>
614
615 <td width="10">&nbsp;</td>
616 <td valign="top" align="left">
617 <br><br><br><br><br>
618 <strong>Diagram 24</strong> This diagram shows that if Black errs, then White can escape, with a disastrous reduction to what formerly seemed a large potential Black territory. But in at least partial compensation Black now is strong on both sides while the still eyeless Whites remain weak and vulnerable!<br><br>
619
620 </td>
621
622 </tr>
623 </table>
624 <br><br>
625
626 <table>
627 <tr>
628 <td align="left" valign="top">
629 <img src="C5D25.jpg" border="1">
630
631 </td>
632
633 <td width="10">&nbsp;</td>
634 <td valign="top" align="left">
635 <br><br><br>
636 <strong>Diagram 25</strong> From the foregoing, it’s likely that a prudent White won’t choose to invade but will instead opt for a reduction.<br><br>
637 For that purpose, W1 as shown here (just breaking the Black Sector Line) or “a” are usually the best moves, the choice between them depending upon the location of other nearby White and Black stones and the tactical considerations they engender.<br><br>
638
639
640 </td>
641 </tr>
642 </table>
643 <br><br>
644 Now let’s see how Sector Line principles were applied in a complex Moyo situation.<br><br>
645
646
647 <table>
648 <tr>
649
650 <td align="left" valign="top">
651 <img src="C5D26.jpg" border="1">
652
653 </td>
654
655 <td width="10">&nbsp;</td>
656 <td valign="top" align="left">
657
658 <strong>Diagram 26</strong> In this position from a game between two 5D players, White has created a large moyo in the upper center which Black must do something to reduce before it can be consolidated into a winning territory!<br><br>
659 As usual in such situations, the question to be answered is whether Black should invade the moyo and attempt to live within its confines, or try to reduce it by nibbling away at it from somewhere on its outer perimeter.<br><br>
660
661 This is the kind of situation in which Sector Lines can often provide the best clue as to which of these courses of action is likely to be the most productive.<br><br>
662 The major difficulty in this position is that a White Sector Line actually covers each of this moyo’s borders, so that only an invasion is really feasible if Black wants to prevent White from consolidating too much of this vast area.<br><br>
663 At the same time, we see that there are four places, marked “A”, “B”, “C”, and “D” in which the White Sector Line is long enough and/or Black stones are near enough to it to offer support to an invasion. Such potential places of ingress and/or egress are called “doors”.<br><br>
664 Here, only doors A and B offer real potential for Black as things now stand.<br><br>
665
666 </td>
667 </tr>
668
669 </table>
670 <br><br>
671
672 A complication is that the White moyo is so large that only a player of professional strength seems likely to be able to even come close to accurately visualizing all of the invasion possibilities and their likely responses in advance. So “mere mortals”, even fairly strong players
673 like the 5D protagonists in this game, necessarily have to largely rely on their “gut” instinct plus confidence in their tactical skills to guide them in making difficult decisions like this.<br><br>
674 A detailed analysis of all of the complex tactics involved in the fighting that transpired next in this game is advanced material far beyond the scope of our interest in Sector Lines. So in the discussion of the actual game resolution provided below we will focus only on the main theme of the invasion.<br><br>
675
676
677 <table>
678 <tr>
679 <td align="left" valign="top">
680 <img src="C5D27.jpg" border="1">
681
682 </td>
683
684 <td width="10">&nbsp;</td>
685 <td valign="top" align="left">
686
687 <strong>Diagram 27</strong> Because the main A and B doors capable of exploitation are both on the left side of White’s moyo, it’s clear that Black’s best invasion point must be somewhere in that vicinity, but the choice of <strong>B81</strong> as the starting point for Black’s invasion was a judgment call.<br><br>
688 <strong>W82</strong> Rather than simply trying to limit Black’s incursion, White counterattacked by threatening to continue at 83, which would both restrict the expansion of Black’s upper left corner territory while making a sizeable territory of White’s own in that area in conjunction with his stones below. In addition, it blocked Black’s access to door A.<br><br>
689
690 <strong>B83</strong> Given that door B is still open. and because a White continuation at 83 would be too good to allow, Black felt that he had no choice but to block here himself to seal off his upper left territory. So White retained Sente.<br><br>
691 <strong>W84</strong> similarly blocks off Black’s flight path to door B, leaving Black with the difficult problem of how to continue to achieve life. But now Black’s chances for success are somewhat improved, because he will be able to play a second stone inside White’s moyo before White can respond there.<br><br>
692 The details of the complex fighting that actually followed in this game are primarily tactical considerations that lie far beyond our focus on learning how to use Sector Lines, so are not presented here.<br><br>
693
694
695 </td>
696 </tr>
697 </table>
698
699
700
701 CAUTION!! As we’ve seen, with substantial amounts of maneuvering room available inside a substantial moyo, not only does the ultimate capture of any invaders become more uncertain, but the possibility of resulting external complications also increases exponentially.<br><br>
702 And even when the invaders are trapped and must be at least temporarily “abandoned”(as in Dia 23), they typically still retain considerable Aji. This may either lead to their later rescue or to an advantage elsewhere for the invader, especially if a Ko fight erupts. So both sides will have to remain alert to this potential until the situation is finally completely resolved or the game ends.<br><br>
703 As earlier noted, detailed exploration of those complications is beyond our present interest, but you might find it productive to investigate them on your own.<br><br>
704 Now let’s look at a key portion of the Fuseki/early middle game between a 5D and 4D, to see how Sector Lines provide almost unerring guidance to strong (if not necessarily perfect!) moves.<br><br>
705
706
707 <table>
708 <tr>
709
710 <td align="left" valign="top">
711 <img src="C5D28.jpg" border="1">
712
713 </td>
714
715 <td width="10">&nbsp;</td>
716 <td valign="top" align="left">
717 <br><br><br>
718 <strong>Diagram 28</strong> <strong>W1</strong> encloses the Black lower right corner stone within White Sector Lines. Then, in the absence of any more urgent play elsewhere, it’s to Black’s advantage to respond by expanding/sealing off his eyespace to ensure his life.<br><br>
719
720 The defensive attachment of B2 is an excellent, time tested way for Black to achieve safety, and begins a popular Joseki.<br><br>
721
722
723 </td>
724 </tr>
725 </table>
726 <br><br>
727 After the necessary connection of W5 Black remains enclosed, but his formation can now make eyes against any White attack! So it’s not strictly necessary (although often desirable!) to make a further submissive play like B“a” immediately, because even if W“b” is permitted the simple B“c” gives Black an unassailable live shape.<br><br>
728 So after W5 Black can afford to tenuki with sente. But because White is now threatening to build a moyo on the lower side, it’s often globally incumbent on Black to try to prevent that from becoming a reality before it’s too solid to readily counter.<br><br>
729
730 Black’s problem is that, wherever he plays on the lower side now, his stone will already be within (somewhat distant) White Sector Lines! But because the end points of the upper Sector Line are so far apart, that’s not particularly dangerous. So with B6 Black makes a “standard” kakari against the White lower left corner star-point stone.<br><br>
731 Because that doesn’t enclose the White corner stone within Black Sector Lines, White need not defend but may instead counter-attack. He does that with maximum force via the squeeze play of W7, which does enclose B6 within close (and therefore very threatening) White Sector Lines, while also making a maximum strategic extension from his W3,5 wall on the right!<br><br>
732 This leaves Black with only two viable choices - either dive into the corner and at least temporarily “abandon” B6, or run out to break the White Sector Line. Given White’s thick position in the lower right, diving into the corner would concede White too much almost secure territory on the lower side, so Black has no real option but to break White’s Sector Line! His choice to do this is
733 the “standard”one point skip of B8, although in some global positions either “d” or “e” may be preferable.<br><br>
734 B8 is Sente because it encloses the White star-point stone within Black Sector Lines! So W9 (or “f”) to break that Sector Line and sketch out some territory is also natural. Although this also establishes a new White Sector Line enclosing B6,8, in conjunction with W1 all the way across the board, once again its anchor points are so far apart that it has almost no effect.<br><br>
735 The result is that Black is free to take sente with the strong “shoulder hit” on W7 of B10, to once again establish close (and therefore very threatening) Black Sector Lines around W7. That’s the “normal” joseki continuation in this position, but in this game the circumstances in the lower right impelled Black to deviate from the “usual” sequence would normally follow, as we see in the next diagram.
736
737 Although the complex ramifications of this intensely tactical fight are well beyond our focus on the Sector Line concept itself, they’re shown below for the reader’s edification.<br><br>
738 <hr>
739
740 <center>The following material may be glossed over at the reader’s discretion.</center>
741 <hr>
742
743 <table>
744 <tr>
745 <td align="left" valign="top">
746 <img src="C5D29.jpg" border="1">
747
748 </td>
749
750 <td width="10">&nbsp;</td>
751 <td valign="top" align="left">
752 <br><br><br><br>
753 <strong>Diagram 29</strong> Instead of continuing with the “normal” Joseki move of W11 at 14 to establish a live group along the edge, with this W11 a swap occurred, with Black destroying White’s potential at the bottom in return for White’s effectively killing the 3 Blacks on the left and almost (but not quite) securing the lower left corner!<br><br>
754
755 </td>
756 </tr>
757 </table>
758
759 <br><br>
760 <strong><hr></strong>
761 <center>End of material to be glossed.</center>
762 <strong><hr></strong>
763 <br><br>
764 <strong>The Limitations of Sector Lines<br><br>
765 The action guidelines provided by Sector Lines are necessarily incomplete because:<br><br>
766
767 1. There may be several different groups affected by active Sector Lines at any given instant</strong>, so their presence alone doesn’t change the player’s overall problem of deciding which situation takes priority, and of handling any interactions between them.<br><br>
768 <strong>2. Sector Lines only provide guidance to an appropriate local strategy!</strong> Global considerations involving a nearby corner, side, the center or even the entire board may dictate that a move other than that indicated by a Sector Line analysis is best overall.<br><br>
769 &nbsp;&nbsp;&nbsp;&nbsp;<strong>A. From the defender’s perspective</strong>, this may mean that a rescue attempt should be deferred, or that a threatened weak group should be abandoned for later use as Aji, despite the fact that it could be rescued!<br><br>
770 &nbsp;&nbsp;&nbsp;&nbsp;<strong>B. From the attacker’s perspective</strong>, it will frequently mean that pressure should be applied to weak opposing stones without any real intention or expectation of capturing them (although that outcome will be welcomed if it should present itself!), in order to build up strength for use in attaining some important objective elsewhere.<br><br>
771
772 <strong>3. Sector Lines do not identify the specific move that works best in any given situation</strong> - whether a tesuji, or just the most appropriate strategic play. Correctly identifying the best global move requires a high level of tactical and strategic competence, most of whose development is outside our focus in this book.<br><br>
773
774 Despite these limitations it’s advisable in your own games to:<br><br>
775
776 <center>
777 <br><table class="txtbox">
778 <tr>
779 <td width="30">&nbsp;</td>
780
781 <td align="middle" valign="top">
782 <br>
783 <font class="txtboxbig">
784 Look First At The Relative Strength<br><br>
785 Of The Opposing Groups<br><br>
786 And Any Sector Lines They Generate<br>
787 </font>
788
789
790 <br><br>
791 </td>
792 <td width="30">&nbsp;</td>
793 </tr>
794 </table><br><br>
795 </center>
796 and<br><br>
797 <center>
798 <br><table class="txtbox">
799
800 <tr>
801 <td width="30">&nbsp;</td>
802 <td align="middle" valign="top">
803 <br>
804 <font class="txtboxbig">
805 Override Those Indications<br><br>
806 Only If There Is A Clear And Compelling<br><br>
807 Reason For Doing So<br>
808
809 </font>
810
811 <br><br>
812 </td>
813 <td width="30">&nbsp;</td>
814 </tr>
815 </table><br><br>
816 </center>
817
818 No single simplifying idea like Sector Lines can instantly transform a beginning or intermediate Go player into an expert, but in many situations it can go a long way toward suggesting reasonable lines of play that might otherwise be missed.<br><br>
819
820 Although the influence of Sector Lines is often easy to see after-the-fact, things are necessarily far less clear in the heat of battle!<br><br>
821 Reacting appropriately after you’ve recognized that an opponent’s move has enclosed one of your key groups within a dangerous Sector Line is often essentially routine because there may only be a limited number of viable options, but correctly deciding
822 what to do next when you have Sente with which to play anywhere is quite another matter! Not only is it necessary to decide whether and where you should take profit or attack, but in the latter case to also where you might <U>create</U> potentially profitable
823 new Sector Lines. And even if that hurdle is successfully surmounted, the concept still offers no automatically applicable criteria for judging which of several possible alternative Sector Lines might prove the most profitable. And then the Sector Lines in
824 and of themselves offer little help in resolving any of the inevitable tactical complications that will accompany their creation.<br><br>
825 The result is that although full understanding of the Sector Line concept may be necessary, it’s nevertheless an insufficient condition for becoming a strong player! Finding the best move in any given position still requires an entire complex of knowledge and
826 tactical skills that can only be developed over time as a result of much play and study - all of which are outside the scope of this book.<br><br>
827 Despite these caveats, <strong>mastering the simple idea of Sector Lines offers perhaps the greatest “bang per buck” for the effort expended in any beginning/intermediate player’s quest for improvement!</strong><br><br>
828 Finally, it’s also important to recognize that when implementing the Sector Line concept in your own games, you will almost necessarily make some strategic errors and even more tactical ones. And those errors will in turn result in some failures in either or
829 both attack and defense, sometimes even resulting in last minute reversals of winning games in which a long series of excellent moves is completely offset by a single egregious blunder.<br><br>
830
831 But such occurrences, however difficult they may be to accept cheerfully, are a natural part of the learning process and should not be allowed to dissuade you from making the strongest moves of which you are capable! With application of the key concepts provided
832 in this book and continued diligent study and practice, sooner or later the number and seriousness of such errors will diminish, and your playing strength will then make the quantum leap upward that your new found strategic insights justify.<br><br>
833 Now let’s try some problems to see how well you’ve mastered the Sector Line concept.<br><br>
834
835
836 <strong>Click Here To Go To</strong><a href="Ch5P.html"><font size=+1><font Color="#0033FF"><strong> Chapter 5 Problems </strong></font></a>
837 <br><br>
838 <strong>Click Here To Move On To</strong><a href="Ch6.html"><font size=+1><font Color="#0033FF"><strong> Chapter 6</strong></font></a>
839
840 <br><br>
841 <strong>Click Here To Return To</strong><a href="Improve%20Fast%20Index.html"><font size=+1><font Color="#0033FF"><strong> Table Of Contents </strong></font></a>
842 <br><br>
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844 <br><br>
845 <strong>Click Here To Email Your Comments/Suggestions To</strong><font size=+2><font color="#0033FF"><a href="mailto:bradleym@eniinternet.com?subject=Improve Fast Comments/Suggestions"> Milton N. Bradley</font></a>
846
847
848 <br><br><br><br>
849 </td>
850 <td width="100">&nbsp;</td>
851 </tr>
852 </table>
853 </body>
854
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