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date | Sun, 02 Apr 2023 10:30:03 -0600 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Magic.html Sun Apr 02 10:30:03 2023 -0600 @@ -0,0 +1,511 @@ +<html> + +<!-- 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>© 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>