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author Franklin Schmidt <fschmidt@gmail.com>
date Sun, 02 Apr 2023 10:30:03 -0600
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+<!-- 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 -->
+<head>
+<title></title>
+</head>
+<body text="#000000" link="#0000ff" vlink="#551a8b" alink="#ff0000" bgcolor="#c0c0c0">
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="The Magic Of Go">
+<p><strong>The Magic Of Go</strong>
+
+<p><strong>&copy; 2002 Milton N. Bradley</a></strong>
+
+<p>Although the characteristic which places Go on a unique plane far above competitors like chess
+is its almost unbelievably profound strategy, it is the clever, incisive tactics of Go that are the
+most obvious and accessible feature which provides much of its appeal.
+
+<p>As in chess, perhaps the most startling and frequently unexpected of Go's extensive catalog of
+clever tactical ploys is the sacrifice, so this will be the focus of many of the few selected
+examples presented here.
+
+<p>Unlike chess, in which many of the best problems can be shown to be impossible to achieve in a
+real game, EVERY GO PROBLEM IS COMPLETELY REALISTIC and the vast majority of the
+best ones have actually occurred in master games! <a href="#Problem 1">
+
+<p>Problem 1</a> - Elementary <a href="#Problem 2">
+
+<p>Problem 2</a> - Elementary <a href="#Problem 3">
+
+<p>Problem 3</a> - Easy <a href="#Problem 4">
+
+<p>Problem 4</a> - Easy <a href="#Problem 5">
+
+<p>Problem 5</a> - Intermediate <a href="#Problem 6">
+
+<p>Problem 6</a> - Intermediate <a href="#Problem 7">
+
+<p>Problem 7</a> - Somewhat  Difficult <a href="#Problem 8">
+
+<p>Problem 8</a> - Somewhat Difficult <a href="#Problem 9">
+
+<p>Problem 9</a> - Moderately Difficult <a href="#Problem 10">
+
+<p>Problem 10</a> - Moderately Difficult
+
+<p>The examples presented here provide only a tiny insight into the beautiful and challenging world
+of Go problems. For a vastly greater and more advanced selection, please refer to the section
+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>
+
+<p>After you've had your fill of those brain twisters (at least for the moment) please don't forget to
+return here for the remainder of my presentation!<a href="Legend.html">
+
+<p><font color="#0033ff"><strong>Continue</strong></font></a>
+
+<p>Click Here To Return To<a href="index.html"><font color="#0033ff"><strong> Milt's Go Page</strong></font></a>
+
+<p><hr>
+<br wp="br1"><br wp="br2"><a name="Problem 1">
+<p>Problem 1</a> - Black To Play And Live
+
+<p><font color="#0000ff"><img src="img.gif" width="122" height="122" align="bottom" ></font>
+
+<p>Click here to see the <a href="#Problem 1 Solution">Solution And Explanation</a>
+
+<p><hr>
+<a name="Problem 2">
+<p>Problem 2</a> - Black To Play And Kill
+
+<p><img src="img1.gif" width="102" height="262" align="left" >
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+
+<p>Click here to see the <a href="#Problem 2 Solution">Solution And Explanation</a>
+
+<p><hr><br wp="br1"><br wp="br2"><a name="Problem 3">
+<p>Problem 3</a> - White to play and kill the Black upper left corner.
+
+<p><img src="img2.gif" width="162" height="202" align="left" ></font>
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+
+<p>Click here to see the<a href="#Problem 3 Solution"> Solution And Explanation</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 4">
+<p>Problem 4</a> - White to play and live in the upper left corner.
+
+<p><img src="img3.gif" width="202" height="222" align="left" ></font>
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 4 Solution">Solution and Explanation</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 5">
+<p>Problem 5</a> - Black to play and live despite the fact that the marked White stone has just been
+played on his key point!
+<p><img src="img4.gif" width="193" height="97" align="left" >
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 5 Solution">Solution And Explanation</a>
+
+<p><hr>
+</font>
+<br wp="br1"><br wp="br2"><a name="Problem 6">
+<p>Problem 6</a> - Black to Play For Ko
+<p><img src="img5.gif" width="122" height="142" align="left" >
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 6 Solution">Solution And Explanation</a>
+
+<p><hr>
+</font>
+<br wp="br1"><br wp="br2"><a name="Problem 7">
+<p>Problem 7</a> - Black To Play And Live (Despite the fact that the marked White stone has just been
+played.)
+
+<p><img src="img6.gif" width="142" height="182" align="left" >
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 7 Solution">Solution And Explanation</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 8">
+<p>Problem 8</a> - Black To Play And Kill
+
+<p><img src="img7.gif" width="122" height="162" align="left" >
+
+<br wp="br1"><br wp="br2">
+<p>Here, The white stones have excellent shape and a solid root in the corner,
+so killing them can only be achieved via the most precise play.
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 8 Solution">Solution And Explanation</a>
+
+<p><hr>
+</font>
+<br wp="br1"><br wp="br2"><a name="Problem 9">
+<p>Problem 9</a> - Black To Play And Live
+
+<p><img src="img8.gif" width="162" height="122" align="left" >
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 9 Solution">Solution And Explanation</a>
+
+<p><hr>
+</font>
+<br wp="br1"><br wp="br2"><a name="Problem 10">
+<p>Problem 10</a> - Black to Play And Kill
+
+<p><img src="img9.gif" width="162" height="142" align="left" >
+
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<br wp="br1"><br wp="br2">
+<p>Click here to see the <a href="#Problem 10 Solution">Solution And Explanation</a><hr>
+
+<br wp="br1"><br wp="br2">
+<p><hr>
+<a name="Problem 1 Solution">
+<p>Problem 1 Solution</a>
+
+<p><img src="img10.gif" width="122" height="122" align="left" >The "rule of thumb" which applies here is "in a symmetrical position, play
+at the middle", and with B1 the life of the Black group is assured!
+
+<p>If W2 attempts to narrow Black's eyespace B3 blocks while forming one
+eye.  Then W4 and B5 repeat the procedure on the other side, giving Black
+the 2 separate and distinct eyes needed for life and safety.
+
+<p>By symmetry, W2 and 4 may be played in either order.
+
+<p>Of course, in a game between experienced players, none of this will occur (except as Ko threats
+and responses) until the late endgame, since both sides can clearly see that after B1 it is
+impossible for White to kill directly.
+
+<p>Please note that whether or not the point "a" is filled (by either side) makes absolutely no
+difference to the life or death of these stones! Finally, after B5 White can only defend one or the
+other of W2 and 4, so Black is almost certain to be able to capture one of them.  <a href="#Problem 2">
+
+<p>Next Problem</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 2 Solution">
+<p>Problem 2 Solution</a>
+
+<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
+instead, he has 3 eyes and is alive!).
+
+<p>Since the position is symmetrical, it makes no difference if W2 is played as
+shown or at 5.
+
+<p>Because W2 threatens to continue at 3, not only making one eye but with atari
+on the 2 Blacks as well, the additional sacrifice of B3 to prevent this is
+necessary.
+
+<p>W4 is not only atari on the 3 Blacks, but also threatens to continue at 5 to form
+an eye as well, so B5 to prevent this is essential.
+
+<p>(Note that if W4 is played at 5 instead, B5 at 4 also kills! Please work this
+variation out for yourself.)
+
+<p>Finally, W6 could be played to capture the 3 trapped Blacks but this would not
+save him because 3 stones in an "L" is a "dead shape", so  B7 would be played
+back "beneath the stones" at 1 to reduce White to one eye. Therefore the White formation here is
+simply "dead as it stands"...... except that there is still a spark of life remaining! Do you see why?
+
+<p>The only chance for life is if White captures the 3 Blacks as a Ko Threat which Black cannot
+afford to answer here. Then, White will be the one who can play "beneath the stones" at the point
+of 1 to form his 2 eyes after all!
+
+<p>From this analysis, the alert reader may realize that in an actual game between two competent
+players in this situation no further moves would be made directly after B1, because White would
+"read" out the diagramed sequence mentally and recognize that it failed. So, in practice, ALL of
+the diagramed moves would be made ONLY as Ko Threats and responses thereto! (If and when
+such a remote Ko came into existence.) <a href="#Problem 3">
+
+<p>Next Problem</a><a href="#Problem 1">
+
+<p>Prior Problem</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 3 Solution">
+<p>Problem 3 Solution</a>
+
+<p><img src="img12.gif" width="182" height="202" align="left" >
+
+<br wp="br1"><br wp="br2">
+
+<p>The Black corner group already has one secure eye at "a", but in
+order for it to secure the second real eye  needed to ensure its
+absolute safety (here, at "b"), Black would have to play on the
+point now occupied by the marked White stone.
+
+<p>By playing the marked sacrifice stone on this key point himself,
+White has converted the point "b" into a FALSE EYE, and
+because the Black group cannot escape it is now DEAD AS IT
+STANDS. Because  these Black stones still have liberties they will
+remain on the board until both sides have passed and the game is
+over, but then White will simply remove all of them as his
+prisoners without further play! <a href="#Problem 2">
+
+<br wp="br1"><br wp="br2">
+
+<p>Prior</a><a href="#Problem 4">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 4 Solution">
+<p>Problem 4 Solution</a>
+
+<p><img src="img13.gif" width="202" height="202" align="top" ><img src="img14.gif" width="202" height="202" align="top" >
+
+
+<p>W1 is the key sacrifice, giving atari to 3 Black stones. 
+
+<p>At this point a competent Black would abandon these stones, because further resistance is futile!
+
+
+<p>If Black foolishly continues with B2 as shown to capture W1 (and remove it from the board), W3
+is again atari on the same 3 Blacks.
+
+<p>If B4 then mistakenly connects, after the inescapable atari of W5 he has lost 6 stones instead of
+only 3, but since he has captured W1 his true net loss is "only" 5 stones.  With either scenario
+White is assured of his necessary 2 eyes, and life in the corner.
+
+<p>This position arose in an actual game between two professional Go masters, played on the
+Internet Go Server (IGS) in Feb 1997, but with Black to move instead of White! So, of course,
+the opportunity for White to play this sacrificial sequence never occurred because Black foresaw
+it and wisely played on the point to the right of W5 to prevent it!
+
+<p>This sort of prophylactic play is quite common at the higher levels, and as a consequence most
+(but far from all) of the spectacular tactical ploys in Go occur only in the minds of the players,
+and not on the board!  <a href="#Problem 3">
+
+<p>Prior</a><a href="#Problem 5">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+<br wp="br1"><br wp="br2"><a name="Problem 5 Solution">
+<p>Problem 5 Solution</a>
+
+<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" >
+
+<p>B1 makes one eye, and then W2 gives atari to one Black.
+
+<p>B3 captures 2 White stones, and then W4 plays back on the point just vacated by W2 ("beneath
+the stones") to again atari the lone Black stone.
+
+<p>Next, if B5 is mistakenly played at the point of 6 to capture W4, the atari of W5 kills Black 
+because the eye at 4 is false!
+
+<p>So the only feasible response is the connection of B5 as shown, allowing W6 to capture 4
+Blacks!
+
+<p>But now it is Black who gets to make the play "beneath the stones" with B7, giving an
+inescapable atari to W4, 6 and thereby assuring Black's second eye with their capture!
+
+<p>The secret to success in such situations, of course, is not only being able to visualize the entire
+sequence beforehand, but also in not being greedy and attempting to save the 4 Black stones.
+
+<p>(Although I have characterized this as an "advanced" problem because it involved both sides
+playing "beneath the stones", to a strong Go player it is really quite simple and many more
+difficult situations are routinely encountered on a daily basis.)  <a href="#Problem 4">
+
+<p>Prior</a><a href="#Problem 6">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+</font>
+<br wp="br1"><br wp="br2"><a name="Problem 6 Solution">
+<p>Problem 6 Solution</a>
+
+<p><img src="img18.gif" width="122" height="142" align="left" >B1 is the key point, and after this White cannot avoid the Ko.
+
+<p>W2 is forced! If this stone is mistakenly played at 3 to form an eye, the
+clever "throw in" sacrifice of B3 at 2 sets up a SNAPBACK which captures
+4 stones and kills the entire White group outright!
+
+<p>If W2 correctly connects as shown, then the atari of B3 sets up a Ko in the
+corner when W4 makes its forced capture. This is a "flower viewing" Ko for
+Black because it has cost him nothing if he loses it (and even then he will
+almost certainly profit elsewhere as a result of the Ko threat which White
+can't afford to answer), while White risks his entire corner here (worth over 20 points!). <a href="#Problem 5">
+
+<p>Prior</a><a href="#Problem 7">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 7 Solution">
+<p>Problem 7 Solution</a>
+
+<p><img src="img19.gif" width="142" height="182" align="left" ><img src="img20.gif" width="142" height="182" align="left" >
+B1 is the only way to begin, but then W2 establishes a connection to his stones below, and it looks bad for Black!
+
+<p>But B3 is a clever sacrifice which gives atari to
+both Whites, so W4 MUST capture it.
+
+<p>Next, B5 threatens to continue at 7 with a double
+atari, so White MUST connect at either 6 or 8.
+
+<p>Then when B7 gives atari W must make the other connection, because allowing the capture
+would not only give Black his needed 2 eyes but some prisoners as well.
+
+<p>Finally, B9 forms the needed 2 eyes to give Black life and safety. <a href="#Problem 6">
+
+<p>Prior</a><a href="#Problem 8">
+
+<p>Next</a>
+
+<p>Click here to return to <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+
+<br wp="br1"><br wp="br2"><a name="Problem 8 Solution">
+<p>Problem 8 Solution</a>
+
+<p><img src="img21.gif" width="122" height="162" align="left" >The solution to this problem is provided by the Japanese Go proverb "There
+is death in the Hane".
+
+<p>B1 is the first Hane, narrowing White's eyespace and threatening to continue
+at "a".
+
+<p>W2 is atari on B1, while also preventing the killing B"a".
+
+<p>Because of the presence of the marked Black stone,  White cannot escape
+even if he captures B1, so B3 ignores the atari to make a second Hane on the
+other side, threatening to continue at "b".
+
+<p>This time W4 isn't an atari so Black has time for the clever placement of B5, but with W4 White
+is now assured of one eye in the corner..
+
+<p>Since B5 threatens to connect out at 6 to kill White's second eye, W6 is forced, but then....
+
+<p>B7 is atari on two separate White 2-stone units, assuring the capture of one or the other of them.
+
+<p>After this, W"c" seems to make 2 eyes after all, but is really futile because after Black captures 2
+Whites via B"d" or B"e", either W2 or W4 will eventually be put in atari, so the needed eye at
+either "a" or "b" will be false and White is dead! <a href="#Problem 7">
+
+<p>Prior</a><a href="#Problem 9">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><hr>
+<a name="Problem 9 Solution">
+<p>Problem 9 Solution</a>
+
+<p><img src="img22.gif" width="162" height="142" align="left" >B1 not only prevents a White atari at this same point while practically
+assuring the capture of the marked White stone, but also prepares to
+make an eye in the corner by continuing at 2, so...
+
+<p>W2 is a sacrifice on the key point to prevent the Black eye.
+
+<p>Next, B3 is a clever counter-sacrifice which does 2 key things: 
+
+<p>By threatening to capture the 2 Whites below, it forces W4 to assure
+its own capture; and until B3 IS captured White can't give atari at "a"
+to the 2 Blacks because it would be a self-atari!
+
+<p>This gives Black time to play B5, which threatens to continue at 6 to capture 2 Whites separately
+and make Black's needed 2 eyes, so....
+
+<p>W6 is yet another sacrifice to prevent this, allowing
+
+<p>B7, which makes an eye and assures Black's life. Why? Because with "c" still open W"d" can be
+met by B"e" to atari and assure the capture of the 3 Whites and make Black's second eye! <a href="#Problem 8">
+
+<p>Prior</a><a href="#Problem 10">
+
+<p>Next</a>
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+<p><hr>
+<a name="Problem 10 Solution">
+<p>Problem 10 Solution</a>
+
+<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
+play on this key eyemaking point.
+
+<p>W2 desperately tries to enlarge his eyespace, so the block of B3 is
+essential to contain this.
+
+<p>W4 threatens to continue at 5 to form one eye and assure the capture
+of 2 Blacks to assure the second, so.... 
+
+<p>The additional sacrifice of B5 to prevent this is necessary.
+
+<p>Next, W6 again threatens to make an eye by continuing at 7, so yet another sacrifice via B7 on
+this new key point is necessary. 
+
+<p>Next W8 threatens to continue at "a" to assure the capture of 4 Blacks with a "live shape" for
+White, so...
+
+<p>Yet another sacrifice via B9 is necessary to assure the death of the White group because now
+W"a" would capture 5 Blacks in a "dead shape". Why? Because after W"a"' captures the 5
+Blacks, a final Black sacrifice "beneath the stones" at 1 reduces White to 1 eye and kills. <a href="#Problem 9">
+
+<p>Prior</a><a href="Legend.html">
+
+<p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
+
+<p><strong><a href="Legend.html"><font Color="#0033FF">Continue</font></a></strong>
+
+<p>Click Here To Return To<a href="index.html"><Font Color="#0033FF"><strong> Milt's Go
+Page</strong></Font></a>
+
+<br wp="br1"><br wp="br2">
+<p><hr>
+
+</body>
+
+<!-- Mirrored from users.eniinternet.com/bradleym/Magic.html by HTTrack Website Copier/3.x [XR&CO'2014], Sun, 06 Nov 2022 06:49:33 GMT -->
+</html>