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3 <!-- Mirrored from users.eniinternet.com/bradleym/Magic.html by HTTrack Website Copier/3.x [XR&CO'2014], Sun, 06 Nov 2022 06:49:09 GMT -->
4 <head>
5 <title></title>
6 </head>
7 <body text="#000000" link="#0000ff" vlink="#551a8b" alink="#ff0000" bgcolor="#c0c0c0">
8
9 <p><hr>
10
11 <br wp="br1"><br wp="br2"><a name="The Magic Of Go">
12 <p><strong>The Magic Of Go</strong>
13
14 <p><strong>&copy; 2002 Milton N. Bradley</a></strong>
15
16 <p>Although the characteristic which places Go on a unique plane far above competitors like chess
17 is its almost unbelievably profound strategy, it is the clever, incisive tactics of Go that are the
18 most obvious and accessible feature which provides much of its appeal.
19
20 <p>As in chess, perhaps the most startling and frequently unexpected of Go's extensive catalog of
21 clever tactical ploys is the sacrifice, so this will be the focus of many of the few selected
22 examples presented here.
23
24 <p>Unlike chess, in which many of the best problems can be shown to be impossible to achieve in a
25 real game, EVERY GO PROBLEM IS COMPLETELY REALISTIC and the vast majority of the
26 best ones have actually occurred in master games! <a href="#Problem 1">
27
28 <p>Problem 1</a> - Elementary <a href="#Problem 2">
29
30 <p>Problem 2</a> - Elementary <a href="#Problem 3">
31
32 <p>Problem 3</a> - Easy <a href="#Problem 4">
33
34 <p>Problem 4</a> - Easy <a href="#Problem 5">
35
36 <p>Problem 5</a> - Intermediate <a href="#Problem 6">
37
38 <p>Problem 6</a> - Intermediate <a href="#Problem 7">
39
40 <p>Problem 7</a> - Somewhat Difficult <a href="#Problem 8">
41
42 <p>Problem 8</a> - Somewhat Difficult <a href="#Problem 9">
43
44 <p>Problem 9</a> - Moderately Difficult <a href="#Problem 10">
45
46 <p>Problem 10</a> - Moderately Difficult
47
48 <p>The examples presented here provide only a tiny insight into the beautiful and challenging world
49 of Go problems. For a vastly greater and more advanced selection, please refer to the section
50 entitled "Problems" in the wonderful <a href="http://nngs.cosmic.org/hmkw/golinks.html"></font><font color="#0033ff"><strong>The Web Go Page Index</strong></font><font color="#0000ff"></a></font>
51
52 <p>After you've had your fill of those brain twisters (at least for the moment) please don't forget to
53 return here for the remainder of my presentation!<a href="Legend.html">
54
55 <p><font color="#0033ff"><strong>Continue</strong></font></a>
56
57 <p>Click Here To Return To<a href="index.html"><font color="#0033ff"><strong> Milt's Go Page</strong></font></a>
58
59 <p><hr>
60 <br wp="br1"><br wp="br2"><a name="Problem 1">
61 <p>Problem 1</a> - Black To Play And Live
62
63 <p><font color="#0000ff"><img src="img.gif" width="122" height="122" align="bottom" ></font>
64
65 <p>Click here to see the <a href="#Problem 1 Solution">Solution And Explanation</a>
66
67 <p><hr>
68 <a name="Problem 2">
69 <p>Problem 2</a> - Black To Play And Kill
70
71 <p><img src="img1.gif" width="102" height="262" align="left" >
72 <br wp="br1"><br wp="br2">
73 <br wp="br1"><br wp="br2">
74 <br wp="br1"><br wp="br2">
75 <br wp="br1"><br wp="br2">
76 <br wp="br1"><br wp="br2">
77 <br wp="br1"><br wp="br2">
78 <br wp="br1"><br wp="br2">
79 <br wp="br1"><br wp="br2">
80
81 <p>Click here to see the <a href="#Problem 2 Solution">Solution And Explanation</a>
82
83 <p><hr><br wp="br1"><br wp="br2"><a name="Problem 3">
84 <p>Problem 3</a> - White to play and kill the Black upper left corner.
85
86 <p><img src="img2.gif" width="162" height="202" align="left" ></font>
87 <br wp="br1"><br wp="br2">
88 <br wp="br1"><br wp="br2">
89 <br wp="br1"><br wp="br2">
90 <br wp="br1"><br wp="br2">
91 <br wp="br1"><br wp="br2">
92 <br wp="br1"><br wp="br2">
93
94 <p>Click here to see the<a href="#Problem 3 Solution"> Solution And Explanation</a>
95
96 <p><hr>
97
98 <br wp="br1"><br wp="br2"><a name="Problem 4">
99 <p>Problem 4</a> - White to play and live in the upper left corner.
100
101 <p><img src="img3.gif" width="202" height="222" align="left" ></font>
102 <br wp="br1"><br wp="br2">
103 <br wp="br1"><br wp="br2">
104 <br wp="br1"><br wp="br2">
105 <br wp="br1"><br wp="br2">
106 <br wp="br1"><br wp="br2">
107 <br wp="br1"><br wp="br2">
108 <p>Click here to see the <a href="#Problem 4 Solution">Solution and Explanation</a>
109
110 <p><hr>
111
112 <br wp="br1"><br wp="br2"><a name="Problem 5">
113 <p>Problem 5</a> - Black to play and live despite the fact that the marked White stone has just been
114 played on his key point!
115 <p><img src="img4.gif" width="193" height="97" align="left" >
116
117 <br wp="br1"><br wp="br2">
118 <br wp="br1"><br wp="br2">
119 <br wp="br1"><br wp="br2">
120 <p>Click here to see the <a href="#Problem 5 Solution">Solution And Explanation</a>
121
122 <p><hr>
123 </font>
124 <br wp="br1"><br wp="br2"><a name="Problem 6">
125 <p>Problem 6</a> - Black to Play For Ko
126 <p><img src="img5.gif" width="122" height="142" align="left" >
127
128 <br wp="br1"><br wp="br2">
129 <br wp="br1"><br wp="br2">
130 <br wp="br1"><br wp="br2">
131 <br wp="br1"><br wp="br2">
132 <br wp="br1"><br wp="br2">
133 <p>Click here to see the <a href="#Problem 6 Solution">Solution And Explanation</a>
134
135 <p><hr>
136 </font>
137 <br wp="br1"><br wp="br2"><a name="Problem 7">
138 <p>Problem 7</a> - Black To Play And Live (Despite the fact that the marked White stone has just been
139 played.)
140
141 <p><img src="img6.gif" width="142" height="182" align="left" >
142
143 <br wp="br1"><br wp="br2">
144 <br wp="br1"><br wp="br2">
145 <br wp="br1"><br wp="br2">
146 <br wp="br1"><br wp="br2">
147 <br wp="br1"><br wp="br2">
148 <br wp="br1"><br wp="br2">
149 <p>Click here to see the <a href="#Problem 7 Solution">Solution And Explanation</a>
150
151 <p><hr>
152
153 <br wp="br1"><br wp="br2"><a name="Problem 8">
154 <p>Problem 8</a> - Black To Play And Kill
155
156 <p><img src="img7.gif" width="122" height="162" align="left" >
157
158 <br wp="br1"><br wp="br2">
159 <p>Here, The white stones have excellent shape and a solid root in the corner,
160 so killing them can only be achieved via the most precise play.
161
162 <br wp="br1"><br wp="br2">
163 <br wp="br1"><br wp="br2">
164 <br wp="br1"><br wp="br2">
165 <p>Click here to see the <a href="#Problem 8 Solution">Solution And Explanation</a>
166
167 <p><hr>
168 </font>
169 <br wp="br1"><br wp="br2"><a name="Problem 9">
170 <p>Problem 9</a> - Black To Play And Live
171
172 <p><img src="img8.gif" width="162" height="122" align="left" >
173
174 <br wp="br1"><br wp="br2">
175 <br wp="br1"><br wp="br2">
176 <br wp="br1"><br wp="br2">
177 <br wp="br1"><br wp="br2">
178 <p>Click here to see the <a href="#Problem 9 Solution">Solution And Explanation</a>
179
180 <p><hr>
181 </font>
182 <br wp="br1"><br wp="br2"><a name="Problem 10">
183 <p>Problem 10</a> - Black to Play And Kill
184
185 <p><img src="img9.gif" width="162" height="142" align="left" >
186
187 <br wp="br1"><br wp="br2">
188 <br wp="br1"><br wp="br2">
189 <br wp="br1"><br wp="br2">
190 <br wp="br1"><br wp="br2">
191 <br wp="br1"><br wp="br2">
192 <p>Click here to see the <a href="#Problem 10 Solution">Solution And Explanation</a><hr>
193
194 <br wp="br1"><br wp="br2">
195 <p><hr>
196 <a name="Problem 1 Solution">
197 <p>Problem 1 Solution</a>
198
199 <p><img src="img10.gif" width="122" height="122" align="left" >The "rule of thumb" which applies here is "in a symmetrical position, play
200 at the middle", and with B1 the life of the Black group is assured!
201
202 <p>If W2 attempts to narrow Black's eyespace B3 blocks while forming one
203 eye. Then W4 and B5 repeat the procedure on the other side, giving Black
204 the 2 separate and distinct eyes needed for life and safety.
205
206 <p>By symmetry, W2 and 4 may be played in either order.
207
208 <p>Of course, in a game between experienced players, none of this will occur (except as Ko threats
209 and responses) until the late endgame, since both sides can clearly see that after B1 it is
210 impossible for White to kill directly.
211
212 <p>Please note that whether or not the point "a" is filled (by either side) makes absolutely no
213 difference to the life or death of these stones! Finally, after B5 White can only defend one or the
214 other of W2 and 4, so Black is almost certain to be able to capture one of them. <a href="#Problem 2">
215
216 <p>Next Problem</a>
217
218 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
219
220 <p><hr>
221
222 <br wp="br1"><br wp="br2"><a name="Problem 2 Solution">
223 <p>Problem 2 Solution</a>
224
225 <p><img src="img11.gif" width="102" height="262" align="left" >B1 is the key initial play, on White's eye-making point (if White plays here
226 instead, he has 3 eyes and is alive!).
227
228 <p>Since the position is symmetrical, it makes no difference if W2 is played as
229 shown or at 5.
230
231 <p>Because W2 threatens to continue at 3, not only making one eye but with atari
232 on the 2 Blacks as well, the additional sacrifice of B3 to prevent this is
233 necessary.
234
235 <p>W4 is not only atari on the 3 Blacks, but also threatens to continue at 5 to form
236 an eye as well, so B5 to prevent this is essential.
237
238 <p>(Note that if W4 is played at 5 instead, B5 at 4 also kills! Please work this
239 variation out for yourself.)
240
241 <p>Finally, W6 could be played to capture the 3 trapped Blacks but this would not
242 save him because 3 stones in an "L" is a "dead shape", so B7 would be played
243 back "beneath the stones" at 1 to reduce White to one eye. Therefore the White formation here is
244 simply "dead as it stands"...... except that there is still a spark of life remaining! Do you see why?
245
246 <p>The only chance for life is if White captures the 3 Blacks as a Ko Threat which Black cannot
247 afford to answer here. Then, White will be the one who can play "beneath the stones" at the point
248 of 1 to form his 2 eyes after all!
249
250 <p>From this analysis, the alert reader may realize that in an actual game between two competent
251 players in this situation no further moves would be made directly after B1, because White would
252 "read" out the diagramed sequence mentally and recognize that it failed. So, in practice, ALL of
253 the diagramed moves would be made ONLY as Ko Threats and responses thereto! (If and when
254 such a remote Ko came into existence.) <a href="#Problem 3">
255
256 <p>Next Problem</a><a href="#Problem 1">
257
258 <p>Prior Problem</a>
259
260 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
261
262 <p><hr>
263
264 <br wp="br1"><br wp="br2"><a name="Problem 3 Solution">
265 <p>Problem 3 Solution</a>
266
267 <p><img src="img12.gif" width="182" height="202" align="left" >
268
269 <br wp="br1"><br wp="br2">
270
271 <p>The Black corner group already has one secure eye at "a", but in
272 order for it to secure the second real eye needed to ensure its
273 absolute safety (here, at "b"), Black would have to play on the
274 point now occupied by the marked White stone.
275
276 <p>By playing the marked sacrifice stone on this key point himself,
277 White has converted the point "b" into a FALSE EYE, and
278 because the Black group cannot escape it is now DEAD AS IT
279 STANDS. Because these Black stones still have liberties they will
280 remain on the board until both sides have passed and the game is
281 over, but then White will simply remove all of them as his
282 prisoners without further play! <a href="#Problem 2">
283
284 <br wp="br1"><br wp="br2">
285
286 <p>Prior</a><a href="#Problem 4">
287
288 <p>Next</a>
289
290 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
291
292 <p><hr>
293
294 <br wp="br1"><br wp="br2"><a name="Problem 4 Solution">
295 <p>Problem 4 Solution</a>
296
297 <p><img src="img13.gif" width="202" height="202" align="top" ><img src="img14.gif" width="202" height="202" align="top" >
298
299
300 <p>W1 is the key sacrifice, giving atari to 3 Black stones.
301
302 <p>At this point a competent Black would abandon these stones, because further resistance is futile!
303
304
305 <p>If Black foolishly continues with B2 as shown to capture W1 (and remove it from the board), W3
306 is again atari on the same 3 Blacks.
307
308 <p>If B4 then mistakenly connects, after the inescapable atari of W5 he has lost 6 stones instead of
309 only 3, but since he has captured W1 his true net loss is "only" 5 stones. With either scenario
310 White is assured of his necessary 2 eyes, and life in the corner.
311
312 <p>This position arose in an actual game between two professional Go masters, played on the
313 Internet Go Server (IGS) in Feb 1997, but with Black to move instead of White! So, of course,
314 the opportunity for White to play this sacrificial sequence never occurred because Black foresaw
315 it and wisely played on the point to the right of W5 to prevent it!
316
317 <p>This sort of prophylactic play is quite common at the higher levels, and as a consequence most
318 (but far from all) of the spectacular tactical ploys in Go occur only in the minds of the players,
319 and not on the board! <a href="#Problem 3">
320
321 <p>Prior</a><a href="#Problem 5">
322
323 <p>Next</a>
324
325 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
326
327 <p><hr>
328 <br wp="br1"><br wp="br2"><a name="Problem 5 Solution">
329 <p>Problem 5 Solution</a>
330
331 <p><img src="img15.gif" width="193" height="97" align="bottom" > <img src="img16.gif" width="193" height="97" align="bottom" > <img src="img17.gif" width="193" height="97" align="bottom" >
332
333 <p>B1 makes one eye, and then W2 gives atari to one Black.
334
335 <p>B3 captures 2 White stones, and then W4 plays back on the point just vacated by W2 ("beneath
336 the stones") to again atari the lone Black stone.
337
338 <p>Next, if B5 is mistakenly played at the point of 6 to capture W4, the atari of W5 kills Black
339 because the eye at 4 is false!
340
341 <p>So the only feasible response is the connection of B5 as shown, allowing W6 to capture 4
342 Blacks!
343
344 <p>But now it is Black who gets to make the play "beneath the stones" with B7, giving an
345 inescapable atari to W4, 6 and thereby assuring Black's second eye with their capture!
346
347 <p>The secret to success in such situations, of course, is not only being able to visualize the entire
348 sequence beforehand, but also in not being greedy and attempting to save the 4 Black stones.
349
350 <p>(Although I have characterized this as an "advanced" problem because it involved both sides
351 playing "beneath the stones", to a strong Go player it is really quite simple and many more
352 difficult situations are routinely encountered on a daily basis.) <a href="#Problem 4">
353
354 <p>Prior</a><a href="#Problem 6">
355
356 <p>Next</a>
357
358 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
359
360 <p><hr>
361 </font>
362 <br wp="br1"><br wp="br2"><a name="Problem 6 Solution">
363 <p>Problem 6 Solution</a>
364
365 <p><img src="img18.gif" width="122" height="142" align="left" >B1 is the key point, and after this White cannot avoid the Ko.
366
367 <p>W2 is forced! If this stone is mistakenly played at 3 to form an eye, the
368 clever "throw in" sacrifice of B3 at 2 sets up a SNAPBACK which captures
369 4 stones and kills the entire White group outright!
370
371 <p>If W2 correctly connects as shown, then the atari of B3 sets up a Ko in the
372 corner when W4 makes its forced capture. This is a "flower viewing" Ko for
373 Black because it has cost him nothing if he loses it (and even then he will
374 almost certainly profit elsewhere as a result of the Ko threat which White
375 can't afford to answer), while White risks his entire corner here (worth over 20 points!). <a href="#Problem 5">
376
377 <p>Prior</a><a href="#Problem 7">
378
379 <p>Next</a>
380
381 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
382
383 <p><hr>
384
385 <br wp="br1"><br wp="br2"><a name="Problem 7 Solution">
386 <p>Problem 7 Solution</a>
387
388 <p><img src="img19.gif" width="142" height="182" align="left" ><img src="img20.gif" width="142" height="182" align="left" >
389 B1 is the only way to begin, but then W2 establishes a connection to his stones below, and it looks bad for Black!
390
391 <p>But B3 is a clever sacrifice which gives atari to
392 both Whites, so W4 MUST capture it.
393
394 <p>Next, B5 threatens to continue at 7 with a double
395 atari, so White MUST connect at either 6 or 8.
396
397 <p>Then when B7 gives atari W must make the other connection, because allowing the capture
398 would not only give Black his needed 2 eyes but some prisoners as well.
399
400 <p>Finally, B9 forms the needed 2 eyes to give Black life and safety. <a href="#Problem 6">
401
402 <p>Prior</a><a href="#Problem 8">
403
404 <p>Next</a>
405
406 <p>Click here to return to <a href="#The Magic Of Go">The Magic Of Go</a>
407
408 <p><hr>
409
410 <br wp="br1"><br wp="br2"><a name="Problem 8 Solution">
411 <p>Problem 8 Solution</a>
412
413 <p><img src="img21.gif" width="122" height="162" align="left" >The solution to this problem is provided by the Japanese Go proverb "There
414 is death in the Hane".
415
416 <p>B1 is the first Hane, narrowing White's eyespace and threatening to continue
417 at "a".
418
419 <p>W2 is atari on B1, while also preventing the killing B"a".
420
421 <p>Because of the presence of the marked Black stone, White cannot escape
422 even if he captures B1, so B3 ignores the atari to make a second Hane on the
423 other side, threatening to continue at "b".
424
425 <p>This time W4 isn't an atari so Black has time for the clever placement of B5, but with W4 White
426 is now assured of one eye in the corner..
427
428 <p>Since B5 threatens to connect out at 6 to kill White's second eye, W6 is forced, but then....
429
430 <p>B7 is atari on two separate White 2-stone units, assuring the capture of one or the other of them.
431
432 <p>After this, W"c" seems to make 2 eyes after all, but is really futile because after Black captures 2
433 Whites via B"d" or B"e", either W2 or W4 will eventually be put in atari, so the needed eye at
434 either "a" or "b" will be false and White is dead! <a href="#Problem 7">
435
436 <p>Prior</a><a href="#Problem 9">
437
438 <p>Next</a>
439
440 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
441
442 <p><hr>
443 <a name="Problem 9 Solution">
444 <p>Problem 9 Solution</a>
445
446 <p><img src="img22.gif" width="162" height="142" align="left" >B1 not only prevents a White atari at this same point while practically
447 assuring the capture of the marked White stone, but also prepares to
448 make an eye in the corner by continuing at 2, so...
449
450 <p>W2 is a sacrifice on the key point to prevent the Black eye.
451
452 <p>Next, B3 is a clever counter-sacrifice which does 2 key things:
453
454 <p>By threatening to capture the 2 Whites below, it forces W4 to assure
455 its own capture; and until B3 IS captured White can't give atari at "a"
456 to the 2 Blacks because it would be a self-atari!
457
458 <p>This gives Black time to play B5, which threatens to continue at 6 to capture 2 Whites separately
459 and make Black's needed 2 eyes, so....
460
461 <p>W6 is yet another sacrifice to prevent this, allowing
462
463 <p>B7, which makes an eye and assures Black's life. Why? Because with "c" still open W"d" can be
464 met by B"e" to atari and assure the capture of the 3 Whites and make Black's second eye! <a href="#Problem 8">
465
466 <p>Prior</a><a href="#Problem 10">
467
468 <p>Next</a>
469
470 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
471 <p><hr>
472 <a name="Problem 10 Solution">
473 <p>Problem 10 Solution</a>
474
475 <p><img src="img23.gif" width="162" height="142" align="left" >The key to the solution is the sacrifice of B1 to prevent White's own
476 play on this key eyemaking point.
477
478 <p>W2 desperately tries to enlarge his eyespace, so the block of B3 is
479 essential to contain this.
480
481 <p>W4 threatens to continue at 5 to form one eye and assure the capture
482 of 2 Blacks to assure the second, so....
483
484 <p>The additional sacrifice of B5 to prevent this is necessary.
485
486 <p>Next, W6 again threatens to make an eye by continuing at 7, so yet another sacrifice via B7 on
487 this new key point is necessary.
488
489 <p>Next W8 threatens to continue at "a" to assure the capture of 4 Blacks with a "live shape" for
490 White, so...
491
492 <p>Yet another sacrifice via B9 is necessary to assure the death of the White group because now
493 W"a" would capture 5 Blacks in a "dead shape". Why? Because after W"a"' captures the 5
494 Blacks, a final Black sacrifice "beneath the stones" at 1 reduces White to 1 eye and kills. <a href="#Problem 9">
495
496 <p>Prior</a><a href="Legend.html">
497
498 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
499
500 <p><strong><a href="Legend.html"><font Color="#0033FF">Continue</font></a></strong>
501
502 <p>Click Here To Return To<a href="index.html"><Font Color="#0033FF"><strong> Milt's Go
503 Page</strong></Font></a>
504
505 <br wp="br1"><br wp="br2">
506 <p><hr>
507
508 </body>
509
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