Learn to Play Go Volume 4

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    Volume IV:Wattle Strategies

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    The KoreanGoAssociation's

    Learn to Play GorVolume IV:Wattle StrategiesJanice Kim 1 dan

    Jeong Soo-hyun 9 dan

    Drawings by Brian D'Amato

    GoodMove Press

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    Published byGoodMove PressPO Box 6984

    Denver,CO 80206www.samarkand.net

    1997 Janice KimAll rights reserved. This book or any part or parts hereof may not be reproduced in anyformwithout written permission from Good Move Press.

    ISBN 0-9644796-4-8

    Printed in Canada

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    Preface & AcknowledgementsEdward Lasker, the well-known chess player, once said "If there are aliens, they

    play Go." Others have gone so far as to postulate that not only do aliens play Go, butthat Go itself is a message from the aliens to us. One might wonder in that case whatthe aliens are trying to say.So far inmy research I've been noticing recurring patterns in Go that Ispeculatehold the key to the aliens' code.Many of these patterns are documented here for thefirst time. I've taken the liberty of naming some of them, although this was an agonizing task, as in the case of the "Alien Symbol" (the "Poodle" being a close-runningsecond choice). Throughout the text, "I" refers to Janice Kim,who is fully responsible

    for errors, omissions, and mistranslations of the extraterrestrial signals Ihave beenreceiving. As a way of making the "great pronoun debate" work for us, I've adoptedthe convention that Black is male andWhite is female.Volume IV, the continuation of the Learn to PlayGo series, assumes knowledge ofbasic ideas and terms covered in the first three volumes, including dual life, eyes and

    eye shapes,basic capturing techniques, haengma or the six basic relationships betweenstones, basic opening theory, and counting and scoring the game. Knowledge of Goterminology is de-emphasized, although the terms hane, sente, and atari are used frequently and should be familiar to the reader. Key terms to know are in boldface anddescribed within the main body of the text, or in notes below the text when a fullerdescriptionwould break the flow. .

    This volume is designed so that any player who has read the first three volumesshould have no inordinate difficulty understanding and using the information presented with the exception of the "Extra for Experts" sections, which may requiredeeper study to grasp fully. However,Istrongly believe that even muchmore experienced or higher-ranking players can benefit from studying the often-overlooked fundamentals which this book endeavors to cover.Thanks to my family, Michael J. Simon,BrianD'Amato and the D'Amato family,David Mechner, John Lee, and Barbara London. More thanks to Liz Shura, ValerieBlum,and the extraordinary Jonathan Englander and Bruce Price.

    Janice KimSeptember 1, 1997

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    Par t

    TheMiddleGameManypeoplefeel lost in the middle game.It's true that it's hard to know ifyou aremakingmistakes in the opening, so it mayseem easier.And there are morestones onthe board in the middlegame, so itmayappear more complex.But actually thereare fewer places to play in the middle gamethan in the opening, andyou areplayingwith more information, so don't let themiddle game throw you.

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    Invasionand Reductioni. The Difference

    Knowing the techniques of invasion and reduction, and the differencebetween them, is crucial in middle-game fighting. Both techniques are usedto neutralize your opponent's potential territory, but there is a big difference.In an invasion,you operate inside a hostile area to prevent it from becomingterritory. A reduction works from the outside to prevent your opponent'sarea from getting any bigger. Invasions can be dangerous there's a chanceyour stones may be killedwhen they are deep in your opponent's sphere ofinfluence.Reduction is a safer way of playing.However, if an invasion succeeds, it has a greater effect than a reduction.

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    INVASIONAND REDUCTION o 3

    -

    r>-cS r A g1ra J %LJ #A\

    1 1 grs ' 1S WJrsJ -A\

    Diagram1

    Diagram 1:Black wants to preventWhite from converting the area on the left side into territory.

    Hemight consider the invasion at A or the reduction at B. Let's look at how they differ.

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    4 O the middle game

    Diagram 2:If Black invades at I,White attacks at 2

    and there's a big possibility that Black'sstoneswill be trapped. This is a dangerousposition, since it's difficult to live in thisnarrow space. However, if Black does live,White doesn't make territory in this area.

    Diagram3:Black can reduce at 1, staying a safe

    distance away while preventing this areafrom getting bigger,but thenWhite canmake some territory with 2. Conclusion:the reduction is safer, but it has a less ofan effect.

    r > KrJ

    rs ?cJ-c w i

    rk>

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    INVASIONAND REDUCTION o 5

    2. Safety FirstWhen invading, the first thing you need to think about is whether or not your invading

    stones can live.

    1cS 9JgA 'A3J r" 41g rs 919 LJ 9

    Diagram4Diagram4:

    Black invades at 1. IfWhite attacks at 2, can Black live?

    ||rs 9LJgr.K 1v.j r\ g|9:

    A R9

    H1 D1Diagram5

    Diagram5:Black can make a basewith the two-point extension at 3, so this invasion is not veryhazardous. (Notice Black has the option of attaching at A or B, a standard way of securinglife in this kindof position.)

    extension: generic term for a move along the side away from one of your stones, to make a base or territory.

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    6 o THE MIDDLEGAME

    Diagram 6Diagram6:

    What ifWhite plays 1, taking away Black's potential base? Black can jump out at 2. NextifWhite A, Black can keep his head out by jumping at B, so the invasion is reasonable.

    Diagram7Diagram 7:

    What if Black invades at 1,where there is one more stone atWhite on the right andan ironpillar (the two marked stones) on the left? ThenWhite will probably cap at 2.This time Black can't jump out, and he'll have difficulty making a secure base right upagainstWhite's wall of iron. In this case, the invasion is an overplay, or a move that triesto accomplish too much a mistake if your opponent respondswell.ironpillar: two solidly-connected stones on thethird and fourth lines.

    cap: an opposing stone with a one-point jump relationship to a stone closer to the edge (usually onthe third line).

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    INVASIONAND REDUCTION o 7

    3. Use BackupIt's a good idea to have backup before you invade.

    Diagram 8:The invasion at 1 is a sharp move.Because of BlackQ>White can't catchthe invader.

    Diagram 8

    Diagram 9:White has no choice but to play at 2

    and let Black connect in the sequence to7. In this invasion, not only did BlackdestroyWhite's area, but he gained someterritory as well.

    Diagram 9

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    8 o THEMIDDLEGAME

    Diagram10:If Black doesn't have backup,White

    can engulf the invader with the diagonalat 2. When Black pushes up at 3,Whiteblocks at 4. IfBlack cuts at 5,White cutsat 6, and Black can't escape.

    Diagram10

    Diagramu:White's all-or-nothing moves in theprevious diagram are overplays whenthere's a backup stone at Black . Oneway for Black to escape is the clever

    move at 5 now Black can connectunderneath at A or B.

    4W- 4 k%W

    >11

    Diagramu

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    INVASIONAND REDUCTION o 9

    Diagram 12:The backup stone at BlackQ makes for an easy invasion at 1.

    4

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    10 O THEMIDDLEGAME

    4. When InvadingLooks Grim,ReduceWhen you feel it's dangerous to invade, reducing is a better choice.

    Diagram 14:What shouldWhite do about Black'sframework, or large potential territory?

    rsJ

    kw

    ?

    bDiagram 14

    Diagram 15:IfWhite neglects this area, Black canenlarge it with amove at 1or A. It's difficult for White to break into this area now,

    but she can't allow Black to make territoryof this size.White needs to do somethingbefore Black plays 1.

    sJ

    1.~.f 1 nMW_ I' i 1b

    Diagram 15

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    INVASIONAND REDUCTION o 11

    Diagram16:What ifWhite invades at 1 in thisposition? The diagonal at 2 is a goodsurrounding move. IfWhite pushes out

    at 3,when Black plays the hane on topat 4,White has trouble getting out. Sheneeds to make two eyes inside,but thatlooks difficult.And even ifWhite succeeds, itwill probably give Black influence that would dominate the rest ofthe board.

    Diagram17:What about an invasion at 1on thisside? Again, Black can sealWhite inwith2 and 4. Making two eyes inside is not

    easy. This is probably a good area tothink about a reduction.

    rS.LJ

    Diagram17

    Diagram16

    Black 1 is called turning:

    ftBlack 1here is a hane, a "quick turn"leaving a cut at A:

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    12 O THEMIDDLEGAME

    The cap and the shoulder hit are the moves used most frequently for reduction.Diagram18:

    White caps at 1.Although Blackwillstillmake territory, this move preventsBlack's area from getting bigger.White 1is probably not going to get caught sinceit is out in the center.

    > r pj\x 1A> ig1'h

    Diagram18

    Diagram19:If Black plays at 2,White can attach at3. If Black responds at 4,White can jump

    at 5, further reducing Black's area andstrengtheningWhite's stones. (With 4, ifBlack plays the hane at A,White can justextend at B,waiting for a chance to usethese stones as backup to exploit weaknesses in Black's position later.)

    rsJ1MU

    gA*iDiagram 19

    shoulder hit: a play one line higher (usually the fourth line) with a diagonal relationship to an opposing stone.

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    INVASIONAND REDUCTION o 13

    Diagram 20:What should Black do aboutWhite's area on the upper side?

    As A>-iJ \1Pg11PAsJ

    Diagram20

    Diagram 21:An invasion at 1here is not good. Black only has room to make a narrow extension.

    White can attack severely at 2 and 4.__1 g As A> % A 9 yj yA yy AK 1pyy g1p

    AsJDiagram 21

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    14 o THE MIDDLE GAME

    Diagram22:In this case, a shoulder hit at Black 1 is appropriate.When a stone is on the third line,pressing it downwith a cap or a shoulder hit is often a good idea.

    rs r>-AiY LsJ \ \ iX 1 11

    rs.JDiagram22

    Diagram23:IfWhite pushes at 2, Black extends at 3. IfWhite continues, Black keeps extending.

    Up to Black 11 ,White takes territory, and Black gets thickness that is, a strong, influential group of stones. This result is good for Black, because his thickness is actuallyworth more than White's territory.

    r> 4o)| Ui1 11 kt rsJ

    Diagram 23

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    INVASIONAND REDUCTION o 15

    Diagram 24:Pushing once at 2 and then turning at 4 is a standardway of dealingwith the shoulderhit. If Black 5,White prevents Black from making the tiger'smouthwith 6> and Black makesa knight'smove connection at 7.Black hasn't made thickness,but he has preventedWhite'sarea from expanding. (Youmay have seen inVolume Ihat the knight's move connection hasthe most scope for getting out into the center. In this case, Black 7 isn't really a connectionWhite can cutwithWhite A, Black B,White C but Black can afford to give up a small parof his group in exchange for thickness if he does ge t cut, so Black's not worried.)

    Diagram24Middle Game Tip:When the opponent's area is sketched out with a stone on the thirdline, it's often better to reduce/That's because these areas usually aren't big enough to make

    an invasion worthwhile, and invading stones may have trouble livingwith the prime base-making real estate already taken. On the other hand, if the stone is on the fourth line,youmightwant to consider an invasion, because the potential territory is uncomfortably largeand it's a bit easier for invaders to live underneath stones on the fourth line.In a related vein, the third line is sometimes called the territory line, because if you playthere, it's probable your opponent will reduce and you'll end upwith territory. The fourthline is called the power line,because if you play there, your opponent will probably invade,and you'll gain influence by attacking.

    Three stones of the same color in psna "V" shape is the tiger'smouth: [1X1 Black 1,protecting against a cut at Awith a knight's move relationship toeach of the marked stones that maybe

    cut is the knight'smove connection:

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    16 o THEMIDDLEGAME

    5. Reducing LargeAreasDiagram 25:Both Black andWhite have built large frameworks. These areas are so big and imposing, it's hard to know what to do. It'sWhite's turn where's a good place to play?

    rsY rs LJ 4A LJ \*4wrs 4%LJ 9

    4k\9

    4k4 *f4 9 i9 %wDiagram25

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    INVASIONAND REDUCTION o 17

    Diagram 26:A deep invasion atWhite 1 is not good.You can ge t into trouble by invading anddestroying only one part of a large framework. Capping at 2 makes center influencefor Black.White can make a base and liveinside,but Black can sealWhite in at 4.Black's still got a huge area, and now it'seven harder to dealwith.What Whiteneeds in this case is a move that reducesthe most potential territory.

    rArs LJ g\J 9llg1%9

    gb\9

    Diagram27:It's better to reduce from a high (thatis, further from the edge) position atWhite 1. If Black 2,White can jump at 3.If Black continues to make territory with

    4,White can jump out lightly at 5. Thisreduction successfully prevents a bigpartof Black's area from turning into territory.

    rsrs LJ gbCJ11

    gb%9gbr, \9k:y

    Diagram27

    Diagram 26

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    18 o THEMIDDLEGAME

    Diagram 28:Here, Black has four corners andWhite has influence. Blackwants to preventWhitefrom turning all her area into territory. Invading either side will make the other side

    stronger.How should Black approach this situation? A move that reduces all ofWhite'sarea would be ideal.

    4rs 4LJ 1

    rsJ

    Diagram28

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    INVASIONAND REDUCTION o 19

    Diagram 29:Black 1, right on the center star point, is good here. (Neat translation moment: the

    center star point is called tengen in Japanese,meaning roughly "Axis of Heaven") IfWhiteattacks at 2, Black escapes at 3. IfWhite chases at 4, Black can even jump in the otherdirection at 5. Since the center is wide open, Blackwill probably not die.A white play atA is not that big, because Black can still jump in the area on the upper left at B.

    Diagram29

    When your opponent has a really large framework, keep your eye on the whole boardand aim for maximum reduction.

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    BattleStrategiesIn this chapter, we'll be focusing on battles between armies on the march, asopposed to those typically arisingfrom invasions.

    Diagram 1:at at 2 and makes a:e pushes at 6 and 8 andf Black's stones. Blacke right and Black'sthree-stone group arenot yet alive and are onthe run. This kindoffight is referred to as arunningbattle.

    pincer: move on the thirdor fourth line, taking awaythe potentialbase of a stoneusually one, two, or threepoints away.

    When Black plays the pincer at 1,White jumpscounterpincer at 4.When Black jumps out at 5,Whthen turns her wheel sharply at 10, cutting in frontswerves to the side at 11 .Both the white group on t

    fs rLh . , J r *P % 9 |% W 1PDiagraml

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    BATTLE STRATEGIES o 21

    Diagram 2:There are also con

    tact battles, as in thisposition. As youmightimagine, in contact battles stones are playednext to each other oneach other's liberties(the lines that emergefrom a stone).

    i>

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    22 o THE MIDDLE GAME

    i. Identifying Key StonesSome stones are currently performing a function, and others have already served their

    purpose. The former are called key stones and the latter are expendables. In battle, it'scrucial to distinguish between the two and save the key stones.

    Diagram 3

    Diagram 3:On the left, ifWhiteplays at A, six black

    stones can be pinned that is, Black can'tconnect all the weakpoints, so White cancapture.On the right,BlackQ is in atari.Which side shouldBlack save?

    Diagram 4

    Diagram 4:If Black connects at1and saves the six

    stones, thenWhitemakes a death star at 2,capturing a key stone.This is an error injudgement by Black.Connecting at 1 savessix stones,but has noeffect onWhite's group.

    The death star (ponnuki in Japanese and bbangdaerim in Korean) is the immensely powerful four-stonediamond shape that results from the capture of a key stone. (Note that a great deal of its power stems fromthe fact that you have captured a stonewith the minimal number of moves just going around the boardmaking this shape, or spending five or six moves to capture a stone, is not the same.) One experiment is toplay a game where you startwith a death star right smack in the center of the board.Your opponent gets allfour corner star points,which should be worth at least thirty points.Findout for yourself if the Go proverb"the death star is worth thirty points" is true or not.

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    BATTLE STRATEGIES o 23

    Diagram5:Black should extend

    at 1. Black@ is onlyone stone, but it's a keystone, keepingWhitesplit into two groups.Both groups fall underattack when Black savesthe cutting stone, so itis very valuable.

    Diagram5

    > 1 -i -i t4k J 4k* *i 4kw 9 . 1WDiagram6:

    Let's look at anotherexample.White cancatch the two markedblack stones on the leftor the two on the right.Black can only rescueone side.Which sideshould Black save?

    Diagram 6

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    24 o THEMIDDLE GAME

    Diagram 7:Saving the stones on the left at 1 is correct. These two stones are serving an importantfunction, namely,cutting off the marked stones fromWhite's corner group. If Black saves

    the cutting stones,White will have a hard time looking after her two isolated stones floating in the center.

    g -iJ) j k

    |

    Diagram7

    Diagram8:Saving the stones on the rightwith 1 is misguided.When White catches the two keyblack stones at 2, allWhite's stones on the left are now connected. Black 1doesn't haveany effect onWhite's group on the right,which is already connected by the marked stone.

    JAAA

    r,r>Diagram8

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    BATTLE STRATEGIES o 25

    2. Don'tSeparate Living GroupsTo maintain an attack on a weak group, you have to keep it from connectingwith a

    strong one.But separating two living groups is a little like trying to take over Newcastleby denying it coal.Diagram 9:

    Here,Black can cutWhite in two.

    Diagram9Diagram 10:

    Black 1 is a powerfulmove.Next,Black can seal in three stones at A or twostones at B. This type of cut,which makesyour opponent struggle to tke care oftwo weak forces, is very worthwhile.

    Diagram 11:This case is different. Even after Blackcuts at 1,bothWhite groups have a base,so White doesn't have anything to worryabout. On the contrary, Black can beseverely counterattackedwithWhite 2.

    f

    rL

    Diagram10 Diagram 11

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    26 O the middle game

    3. GoodDefenseIn running battles, the strongest offense is a good defense.Put another way: you can'tpunch very hardwhen you're standing on only one foot.

    Diagram 12:The battle is on in the upper right Black jumps at 1,chasingWhite's two stones,White jumps at 2, and Black pushes out at 3. But then Black isn't happy whenWhiteplays the hane at 4. The Black 1-White 2 exchange actually weakened Black's group.Youdon't want to put your own stones in jeopardy when attacking.

    rsJrs g , gLJ 9 19 9g\%\ 4k. w

    Diagram 12

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    BATTLE STRATEGIES o 27

    rsJ.-J 1

    fs dIJ 9g%9

    gf\1-4J 9Diagram 13

    Diagram13:In this case, it's better to jump at 1here, putting pressure onWhite's stones while giving the black group some scope in the center. IfWhite comes out at 2, Black pushes at 3and 5, forcingWhite along while further strengthening Black's stones. Finally Black

    secures the right side with 7, andWhite is still saddledwith a weak group. By looking outfor your own stones like this you can create a favorable attacking position.

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    28 o THE MIDDLEGAME

    4. Watch Your Connections CarefullyIn a running battle,you can blow the whole game by playingmoves that give your

    opponent a chance to cut.

    Diagram 14:In this complicated battle, the two large marked groups have run out into the center.

    Diagram 14

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    BATTLE STRATEGIES o 29

    Diagram 15:Black pushes at 1and 3 and jumps to the

    sidewith 5.But Blackisn't being carefulenough about hisconnections he'shelped create a weakpoint in his own group.

    Diagram15

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    30 O THE middle game

    Diagram16:In the sequence to 7,White is able to cut theblack group in two.Black has no way ofconnecting,since A and

    B reflect that is , ifBlack plays A,White cancut at B,and if Black B,White cutswith A.Black has sustained somuch damage he can'tfight on any longer. Diagram 16

    Diagram 17

    Diagram 17:Going back to theoriginalposition,we

    can see where the disaster started. Blackexchanged BlackA forWhite B.OnceWhitegot a stone at B, the cutwas possible.Blackshould have played at 1instead, securing hisconnection whilethreatening to catch thethree marked stones.

    A moment's carelessness about connections can cost you the game. Try to avoidunnecessary pushing and shoving, even if it forces your opponent to respond.

    Two points are said to reflect (miai in Japanese and matbogi in Korean) when if one side plays one, the otherside plays the other.

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    BATTLE STRATEGIES o 31

    5. Don'tFear The BogusAttackWisdom from the East: Unless you have no choice, don't try to live in a very smallarea. In Go, this means don't get scared in the middle of a battle and hunker down whenthe board is wide open. If you can, get out into the center and fight.

    Diagram 18:In six- to nine-stone handicap games,after approaching at 1and 3,White often

    caps at 5, threatening the black side starpoint stone. The weak mentality is to getscared and struggle to live inside, likeraising the drawbridge and rationingthe water when you see a lone knight onthe horizon.

    g\ gkf 9 9AsJAp--i: 9

    AKygg %9\9

    Diagram 19:In the moves to 12,Black is busy making a base.This negative way of playinggivesWhite thickness on the outside andthe opportunity to start new operations

    at 13 .

    A31aVA rSy \r5

    |%f

    gkg %919

    Diagram19

    Diagram 18

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    32 o THEMIDDLE GAME

    Diagram20:After the cap, Black should come out

    at 2, keepingWhite's stones separated. IfWhite pushes at 3 and 5, Black cancounterattack with 4 and 6. Because hehas a lot of stones around, this fight isgood for Black.

    ML X 11

    A>-ij wAs.jtgg 11w

    Diagram 21:Black could also come out on theother side at 2. IfWhite jumps at 3,Blackpushes into the center with 4.

    Diagram 20

    Asj

    gg 1%

    Diagram 21

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    BATTLE STRATEGIES o 33

    6. FightWithPurposeDon't chase groups without a specific goal in mind.

    Diagram 22:Black attacks the twowhite stones by capping

    at 1.White plays 2 and 4to stabilize them.Whatshould Black do now?

    Diagram22

    c -c rsfcSJ I 9 9%9 919

    r\9 LJ

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    34 o THEMIDDLE GAME

    Diagram 23:What if Black attacks at 5? White pushes at 6 and 8, then jumps at 10 . If Black tries toblockWhite's path to the center at 11and 13,White pushes at 14,Black saves one stone

    at 15,andWhite leaks out at 16. In this fight Black may feel that he is accomplishingsomething. In fact, he is he'sweakening his own group in the upper left.

    cVs cV rs\Ah |SJ gg\ 1\ 9 1919 9-(14)-pnIQQJ-

    g rsLJDiagram 23

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    BATTLE STRATEGIES o 35

    Diagram24:In this case, Black should push at 5 and attackwith the knight's move at 7.WhenWhite jumps out, Black can secure a large area in the lower left at 9.

    r r rskSJ 44 4 9 \ 9%9 %9gI

    rsX LJDiagram24

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    36 O the middle game

    7. PlayAggressively Where YouAre ThickIn places where you are weak, it's wise to avoid fights and try to settle things peacefully.

    When you have thickness, be aggressive.Diagram 25:

    White tries to surround Black in the corner at 1.Black has a lot of stones around here he's very thick on the left and has the marked stone on the right helping out as well. Inthis case, Black should play strong, aggressivemoves.

    cs4 T J g* %9 i A 91 uj Js1 9 JJ g fc95

    *

    rs rsLjDiagram 25

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    BATTLE STRATEGIES o 37

    Diagram 26:Pushing and cuttingwith 2 and 4 is a

    strongway of playing.WhenWhite extendsat 5, Black extends at6, attacking the topwhite group. Black isin control of this fightWhite will have tostruggle to settle bothgroups.

    Diagram 27:White 7 and 9 aresente that is,Blackwill have to answerthese moves.NextWhite probably plays amove around 11 .Butwhen Black calmlymakes life in the cornerat 12, so far, neitherwhite group is alive.

    Diagram26

    J

    1 g%9 1sid1 1 U9

    Diagram 27

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    38 o THEMIDDLE GAME

    Diagram28:What happens if, after White 1,Black submissively tries to live inside at 2? SinceWhite's 3 and 5 are sente, she can settle her group nicely with the tiger's mouth at 7. Themarked stones haven't been utilized effectively, and Black has lost a good chance to takecontrol of the game by playing aggressively in his sphere of influence.

    pidkk gk ft7?'

    gy* kdh ft9wrL g%ft9

    Diagram28Diagram29:

    What if the position looks like this, andWhite plays at 1? Now pushingand cutting at 2and 4 are too aggressive. SinceWhite has a lot of stones around here, this fight is disadvantageous for Black.After White extends at 5

    gb

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    BATTLESTRATEGIES o 39

    Diagram30:If Black extends at 6,White makes the sente moves at 7 and 9, then connects the

    stones on top with the one-point jump at 11.Black has to live in the cornerwith 12,and the tables turn nowWhite goes on the attack at 13.

    Diagram30

    Diagram31:In this case, it's a good idea for Black to secure life in the cornerwith 2,waiting for

    an opportunity to use this stone as backup to invade around A later.

    Diagram31Whether you live quietly and wait or cut and fight depends a great deal on thesurroundings. Try to make your plans based on your resources.

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    40 O the middle game

    8. At Times,ExchangeIt's important to have the flexibility to make exchanges.

    isDiagram 32

    Diagram32:Black cuts at 1,severing one white

    stone from the main force. How shouldWhite respond?

    Diagram33:IfWhite extends at 1 to save the one

    stone, Black extends at 2. NowWhite'sgroup on top is sealed in. IfWhite playsat 3 to live,Black comes out at 4. IfWhitejumps out at 5, Black can continuewith 6on a pivot often the point that compromises a group's shape, leading to allsorts of nastyproblems.White's handsare full trying to save both sides.

    Diagram33

    A black stone at any of the points markedA would make a tiger's mouth.A white stone atany of the points markedA would be on the pivot.Watch for pivots, as a play on your opponent's pivot can be enormously effective, and an opposing stone on your pivot can be a realthorn in your side.

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    BATTLE STRATEGIES o 41

    Diagram34:In this case, it's better to give up one side.White plays atari at 1and then connects with thetiger's mouth at 3. If Black catches the marked

    stone with 4,White engulfs a stonewith 5. Makingthis exchange is much better than trying to saveone expendable stone.

    Diagram34

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    How to AttackTo attack means to harass stones that are not aliveyet, i.e., those without a

    base for making two eyes. Perhaps the most important basic concept in attackingis to attack with a reasonablegoal in mind.

    rs r>-A1LJ rs WLJg%w t

    4 rgn %9 Lnnr* iNfefv WLJ-rsJ Yscs Lj 4 kJ \W X -A.JV

    Diagram 1:On the right side,Black is on the attack.Black peeps at 1,mak

    ingWhite's groupheavy, or unwieldy anddifficult to maneuver.Next Black caps at 3.NowWhite's groupdoesn't have a base or agood way of advancinginto the center, so she'sin danger.

    Black 1 is apeep: a threatto cut a one-point jump.Diagraml

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    HOW TOATTACK o 43

    Making a group heavy before attacking it is a good idea it's a lot easier to catch agang of escaping prisoners if they are all chained together.A heavy group is all stucktogether in a mass, so a small part cannot be sacrificed in order to get away.

    Diagram 2:White tries to

    escape at 4. IfBlackgives chase at 5,Whitejumps at 6, but afterBlack 7,White has noway to get out into thecenter. IfWhite can'tmake two eyes,Blackcan kill this group.

    Diagram 2

    But forcing White to run into Black's area to make two eyes is a very dangerous strategy. If Black fails to killhe may fall short in territory, as Black pushedWhite right intohis area. It's unlikely that Blackwill kill in fact, ifWhite plays at A, Black may findhimself struggling to live. Rather than such an all-or-nothing attack

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    44 o THEMIDDLEGAME

    DiagramyThis attack is more realistic.After White 2, Black chasesWhite at 3 while making territory on the right side. IfWhite pushes at 4, even though Black can't sealWhite in as in

    Diagram 2, he can loosely attackWhite's group at 5.White 6 is about the only thingWhite can do, so Black builds thickness in the sequence to 9. Note that White is still notcompletely out of the woods.

    -< A -Q4iviI- -Q~ --UCr V"Vr-0

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    HOW TO ATTACK o 45

    i. TakeAway the BaseSince you can't successfully attack a group that has a base,you need to take away thegroup's base before you can attack it.

    Diagram4:How should Blackattack White's lone

    stone on the lowerside?

    K>gAs ILJ

    g'H

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    46 o THEMIDDLEGAME

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    HOW TO ATTACK o 47

    Diagram 8:If Black caps at 1,White can make abase by sliding at 2, settling herselfwhile

    gouging out Black's territory. This is idealfor White.

    Diagram 8

    Diagram 9:The iron pillar at Black 1, taking awayWhite's potential base, is the rightway toattack. Black 1also secures territory onthe lower right side. IfWhite jumps out

    at 2, Black can attack while surroundingarea on the upper side with 3.

    4 4%\9 M

    41w g

    54l1Diagram9_Black 1 is a slide: a base-makingplay (usually on the second line)one point under an opposing stone.

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    48 o THE MIDDLE GAME

    2. MakeProfitWhileAttackingIt seems like the idea of attacking is to kill,but this is misguided. Trying to kill groupsrarely succeeds unless your opponent makes bigerrors (a dangerous assumption) andoften puts your own groups or territory at risk.You should attack in a way that makessufficient profit to make attackingworthwhile, even if you killnothing.

    fsr J rs rsLJ Jcss \.J 1g\

    gk1 7gN sg \ fr k

    Diagram10

    Diagram 10:The group in the lower right doesn't have a base, so White jumps out at 1.

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    HOW TO ATTACK o 49

    rsry iJ rs rsJ LJ LJ srs sJ 19gk g\9 \ 9

    g\9Mg19

    Diagram 11Diagramu:

    It seems like a severe attack to cap at 2 and chaseWhite's group with 4 and 6. Blackcan preventWhite from escaping into the center at 8, but Black's own stones come underattack whenWhite is forced to try to live inside starting withWhite 11 . IfWhite lives (agood assumption, given Black's problemswith the four marked stones on the lower side)Black's area is destroyed.

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    50 O themiddle game

    Diagram12:Black must make sure to gain sufficient profit to make the attack worthwhile. Black

    can simply enlarge the left side by attackingwith 2, 4, and 6.Next, ifWhite plays at A,Black can play B, creating a huge framework.

    rSrksJ rs rsJ LJ LJr

    rs \?LJ 1 t ft%911> 4g\ 9%9

    4 fc9g%9 .

    Diagram 12

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    HOW TO ATTACK o 51

    3. Use the Knight'sMoveThe speed, stability and directed force of the knight's movemake it a natural fo r

    attacking.

    Diagram 13:The two black stones on the left are

    not alive yet.How canWhite attack thisgroup and gain some profit?

    rVJ

    . ? :

    rs AKJ rsJ.Diagram 13

    Diagram14:The knight's move atWhite 1 is ideal.If Black runs at 2, thenWhite can play

    another knight'smove at 3. This type ofknight's move attack is like a fan opening, enlargingWhite's area in the lowerleft one linewith every move.

    rs.Jf.Vy

    tr-

    rs ALJ rsDiagram14

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    52 o THEMIDDLE GAME

    Diagram 15

    4. Drive Towards Your ThicknessThickness is not the same thing as potential territory. You shouldn't drive your oppo

    nent towards your potential territory those areas you've sketched outwith a fewstones. However, thickness a strong, influentialwall of many stones is most effective when it is used for attack.

    White jumps out at1.How should Blackattack this group?

    Diagram 15:

    Diagram 16

    Diagram 16:If Black pushes at

    2,White extends at 3.After White jumps at5, it's hard to attackthis group. Blackgained a little on theleftwith 2 and 4, butnot as much as Blackcould have gained byusing his thicknessmore effectively.

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    HOW TO ATTACK o 53

    Diagram 17:In this case, forcingWhite to run towards

    Black's thickness byattacking at 2 is good.IfWhite runs at 3,Black continues at 4. IfWhite jumps at 5,Black can play solidlyat 6. Next

    Diagram 17

    Diagram 18:IfWhite runswiththe diagonals at 7 and

    9, Black sealsWhite inwith 8 and 10.Whitecan't escape to the center, and since Black isso thick, it looks difficult forWhite to maketwo eyes inside.

    Diagram18

    Sometimes it maybe difficult to tell whether you are pushing a weak group towardsthickness, or towards your potential territory. One way to tell is that if you don't have tokill to benefit from the attack, you are on the right track. InDiagram 18,Black is completely safe, and can just sit back and watchWhite spend move after move struggling tomake two eyes. In the meantime Black has built a tremendous wall of power in the center. This power can be used for attack, framework building, or just preventingWhitefrom making any significant territory on the rest of the board.

    Itmay seem odd at first,but give the "drive towards your thickness" concept a try. Ifyou just use your thickness to make territory directly,you may often fall behind in theterritorial balance. That's because it's unlikely you'll make as much territorywith yourthickness than if you had simply sketched some territory out, and you've most likelygiven territory to your opponent to make the thickness in the first place. This is also agood reason why you don't want to give your opponent thickness for nothing thenanything they make is pure profit.

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    54 o THE MIDDLEGAME

    5. Protect Your OwnWeaknessesIt's a common mistake to neglect your own weaknesses when you are attacking (and

    as a result, for your position to fall apart if your opponent counterattacks).While attacking, remember to keep your stones secure.Diagram 19:

    This position is taken from a professional game.White's group on the rightside is in danger, so White tries theweird-looking attachment at 1.Actuallythis move is a trap.

    gIgk

    4 %9%9

    Diagram 20:Suppose Black cuts off the whiteattachment stone in the sequence to 6.White is sealed in, so will this group die?

    Diagram 19

    Diagram 20

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    HOW TO ATTACK o 55

    Diagram 21:In his hurry to sealWhite in, Black leftbehind a big weakness.WhenWhite counterattacks with the cut at 7, Black's moves

    up to 12 are necessary to save the twomarked stones. FinallyWhite plays atari at13 and Black has no good response.A andB reflect if Black saves the one stone inthe center at B,White catches two stones atA, and if Black saves the two stones at A,White makes a death star at B. Black's failure was the result of attacking withoutregard to his own safety.

    Diagram22:A more reasonable plan is to protectthe cutting point at Black 2 whenWhiteattaches.When White connectswith abamboo joint at 3 and 5, now Black cansafely attack the whole group at 6.

    < f Digigk 1w1P

    Diagram22

    Diagram21

    Bamboo joint: four stones in this configuration haveflexibility while maintaining a strong connection:

    fcid1*4*41mm

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    Howto Take Careof Your Stonesi. Makea Base

    Often the best way to secure stones under attack is to make a base. If youhave two eyes, you can't be chased around.

    Diagram 1:i 1wrsJ g gIli1

    gI P w%w Jk gIw LJ 1wIn response toWhite's invasion onthe right side, Black

    capped at 1.How canWhite protect thisstone?

    Diagram 1

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    HOW TO TAKE CARE OF YOUR STONES o 57

    Diagram 2:Making a base bysliding at 2 is best.Black 3 is about theonly way to block,butthenWhite can make

    lifewith 4 and 6 asuccessful invasion forWhite.

    \ rsJ g g%

    \ g 1t9 9 rk (T gI1 * k J 0 \ w

    Diagram 2

    Diagram 3:Here, the two marked black stones aresurrounded. They can't escape, but they

    can make a base inside and live.

    Diagram4:Black 1 threatens to connect to the

    corner group, so White needs to block at2. Next Black can push up at 3 andWhiteneeds to block at 4, this time to preventBlack from poking out.

    rK 1JA

    Diagram2 Diagram 2

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    58 o THE MIDDLE GAME

    Diagram5:Next,when Black plays at 5,White must answer

    at 6 to prevent Black from playing here and slicingthroughWhite's stones. Finally Black can make lifewith the tiger's mouth at 7. IfWhite plays 8, Blackmakes two guaranteed eyes with 9.

    Diagram 5

    -i> a*[\ >LJ \?JkLJ4's ckLJ JyA

    Diagram 6:In a slightly more difficult example, let's look athow to secure Black's lone stone on the right side.

    Diagram 6

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    HOW TO TAKE CARE OF YOUR STONES o 59

    Diagram7:Black can escape with the one-pointjump at 1,but whenWhite peeps at 2 and

    takes Black's potential base away at 4,Black doesn't have even one eye. Thesestones are going to ge t chased around.

    (

    Y XDiagram7

    Diagram 8:In this case,making a one-pointextension at 1 is best.WhenWhite blocks

    at 2, Black pushes up at 3. IfWhiteextends at 4, now the one-point jump at5 is looking better than inDiagram 7.Black has made one eye and can livewithonemoremove at A.

    1

    Diagram8

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    60 THE MIDDLE GAME

    Diagram9:IfWhite pushes at 2, Blackmakes thetiger's mouth at 3. This shape has a lot ofpotential for making eyes. IfWhite blocks

    at 4, Black makes an eye by extending at 5.White doesn't have a good attack nowbecause Black can either escape into thecenter or make life on the side.

    (

    Diagram9

    There's a big difference between a group with one eye and a group with no eyes.Youneed two eyes to live, but to paraphrase Erasmus, in the landof the blind, the one-eyedgroup is truly king.

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    HOW TO TAKE CARE OF YOUR STONES o 61

    2. MakeEye SpaceIt's hard for stones in the center to live,because all four walls of their base, or eye

    space,must be constructed from scratch. That's why in the center it's especially important to make volume-enhancing moves like contact plays, and shapeswith lots of eye-making potential like the tiger's mouth.

    Diagram 10 Diagram 11

    Diagram 11:Here's a group that is difficult toattack because it has the potential tomake eyes for example,White can

    make an eye at A or surround a smallarea by playing at B.

    Diagram 10:This stringy Black group doesn't have

    an eye, or even the potential to make aneye. Since groups like this can be easilyattacked, it's best to not make them.

    Just as it can be difficult to tell "thick" and "heavy" apart, it's sometimes hard to tell ifyour group is like a lightning bolt blazing through a poorly-wired house, or like a helpless vegetable in a rabbit's cage. The difference: the latter (whichIefer to as a StringBeanArmy) doesn't have eye space or eye-making potential, and is surrounded bysecured enemy stones.

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    62 o THE MIDDLE GAME

    Diagram 12:How can Black's group on the rightside make eye space?

    g19 9

    sJ

    Diagram 12

    Diagram 13:Black attaches at 1.Contact plays likethis attachment are a good way to makeeye space.WhenWhite plays the hane at2, Black extends at 3. When Whiteextends at 4, Black blocks at 5, makingtwo tiger's mouths.Now these stones canmake an eye by playing at A or at B, soBlack doesn't have any worries.

    -49y4>>

    -M jQ1

    1i

    A

    csJ

    Diagram 13

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    HOW TO TAKE CARE OF YOUR STONES o 63

    Diagram 14:Let's look at an example from a gamebetween Jeong Soo-hyun 9 dan and Suh

    Bong-soo 9 dan.WhenWhite played areducingmove at 1,Suh 9 dan attackedfrom above at 2. How canWhite protecthis stone?

    i1gh-Qs **j

    Diagram15:White played right up against Black'sside star point stonewith 1and 3.WhenBlack extended at 4,White played aknight's move at 5, Black followed at 6,andWhite blew a little air into his eye-

    space balloonwith 7. In this situation,White has already made one eye and hasmoves at A or B to make another, so hisgroup is almost settled.

    \ r-Kg> \ y IDtji

    J

    -M

    gh%w X JVDiagram 15Diagram14

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    64 o THEMIDDLE GAME

    3. Tread Lightly inYour Opponent's AreaWhen you can't live inside your opponent's area, you have to run. In this case you

    should try to tread lightly.Diagram16:White's three stones on the right don'thave a base or any eye-making potential.How canWhite settle these stones?

    --i> 141

    4

    Diagram 17:What ifWhite plays at 1? Blackwillimmediately try to swallow this groupwhole with 2. In this situation, slow-and-steady moves l ike White 1 can be easilyoutflanked, causing serious problems.Afaster and lighter move is required.

    Diagram16

    --

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    HOW TO TAKE CARE OF YOUR STONES o 65

    Diagram 18:How about the one-point jump at 1?This is better than the diagonal inDiagram 17, but it's still too slowBlackcan still attack at 2.White can jump further out and retain connectivity. NoticeWhite A is sente (Black should answer, inthis case at B) so after the A-B exchange,White will have three stones in a row.Generally from a wall of three stones youcan jump at least two points without anyworries that your stones can be cut.

    -rib *-PD AJ wb-< !>A>m1

    Diagram 19:White 1 is best. In your opponent's

    area, it's a good idea to "float like a butterfly"with fast and light haengma like thistwo-point jump. Black can't find a goodmove to harass these stones now if hecaps at A,White can jump at B, and if hechasesWhite at B,White can jump at A.

    --C> 4b

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    66 O the middle game

    4. TakeAdvantage o f KoKo can be your friend, especially when settling weak stones.

    Diagram20

    Diagram 21

    gI gkcs gk ! \ f0j r J w ! m iL 1 w1nrsJ

    r t-O-A-M X>T 1L

    fs

    Diagram 20:In the lower right,White's four marked

    stones are in great dangeHow canWhite savethem?

    Diagram 21:Trying to make a baseby extending at 1gets th

    group killedwhen Blackplays the hane at 2. IfWhite pushes at 3 Blackextends at 4. IfWhite A,Black can connect at B,making C a false eye looks like an eye,butWhite's stones aren't allconnected. Ordinarymoves like White 1won'take care of the problem

    Diagram 22:The hane atWhite 1 ibest. If Black plays atari a2,White makes a ko at 3.If you can't secure unconditional life for yourstones, you should try atleast to make a ko.

    Diagram 22

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    HOW TO TAKE CARE OF YOUR STONES o 67

    Diagram 23:If Black takes the

    ko at 4,White can playthe hane at 5, threatening to connect to thegroup on the left.Black blocks at 6 andWhite takes the koback at 7.

    rSJ 3 j

    Diagram 23

    Diagram24:Next ifWhiteignores a ko threat andcaptures a stone at A,winning the ko,Whiteis alive. Black's notthrilledwith this ko,since if he loses it, healso loses a lot of corner territory.Furthermore,Whitehas some handy kothreats at B and C.

    *sJE AiTf A T

    Diagram 24

    Diagram 25:WhenWhite playsthe hane at 1,whathappens if Black

    extends at 2 to avoidthe ko?White canmake lifewith thetiger's mouth at 3.

    rYLJ

    Diagram 25Ko-making is a difficult art to master for now, just try to look fo r ways to make ako out of situations where your stones look like they've had it.

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    68 O THE MIDDLEGAME

    5. Give UpHopeless StonesThere are times when an attack is so powerful that you cannot save your stones.Logically,you should just give up stones which have no hope of survival or escape.Emotionally this can be difficult, but trying to save mortallywounded soldiers oftenresults in heavier losses.

    Diagram26:WithWhite , Black's invading force

    on the left side is in trouble.White'snearby thickness makes escape look verydifficult.What is the best plan for Black?

    sr JT

    rsJ

    Diagram27:Even if one suspects these stones can'tescape, it's very tempting to just try to

    pull them out. In the sequence to 8, Blackgets completely sealed in. Black has a little breathing room,but it would take amiracle for him to make two eyes.

    Diagram 26

    Diagram27

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    HOW TO TAKE CARE OF YOUR STONES o 69

    Diagram 28:In this case, it's a good idea to give up the

    stones on the leftwith Black 1. Then whenWhitecuts them off at 2, Black pushes at 3, neutralizingWhite's influence in the center.

    If you realize they are beyond help, it's best togive up stones that havewithered on the vine andtry to get something from the "sacrifice."Icall thisthe "Iplanned that three months ago" attitude.

    Diagram 28

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    Part II:

    Lifeand DeathDeterminingwhich groups arealive andwhich are dead is one ofthe most important components ofthe game. The ability to read, or toanticipatemove sequences, is thekey to life and death. Butfirst,there are some basic conceptsabout eye shapes and techniquesfor making and destroying eyes tolearn, so you'll know what to lookfor when you're reading.

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    0-earchingfor Lifei. Eye Shapes

    If a group's eye shape cannot be reduced to fewer than seven points, it'sprobably more accurate to say the group has territory, rather than an eyeshape.Another way of looking at it is that eye shapes of seven points ormore are alive you can make two eyes, or at least dual life, in spaces thislarge. (Keep inmind,however, that you always need to be on the lookout ifyour stones are not all solidly connected a space-reducing, potentiallylethal atari may be in your future).All eye shapes boil down to ten basic formations: straight three, bentthree, straight four, three kinds of bent fours (the "L", the "T",and the "Z"),square four, radial five, flower six, and rectangular six. It may seem like a lot

    to remember at first, but if you are conversant with these basic formations,you are well on your way to being a master at life and death.

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    SEARCHING FOR LIFE 73

    Diagram 1:The black group's eye shape on the left is the L bent four, on the right, the straightfour, and in the middle, the Z bent four.All these groups are alive just as they are,

    becauseWhite can't prevent Black from making two eyes even if it's her turn.

    aM 2mWW"A7i-A .vSl A AA a~AAA-A..AAJ 7V7A 77rj777

    Ifnfa *21fa7A7 77i7r11 77Diagram1

    Diagram 2: 'In the upper left is a bent three, in the upper right a straight three, and in the middle

    a T bent four. In all these cases, Black needs to play a stone in the center of each eyeshape to live. (If the marked stone is pushed out to give an extra point inside the T, theresulting shape is what Icall the "Maltese five" Black needs a stone in the center to livehere too.)

    Diagram 2

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    74 LIFEAND DEATHDiagram3:With both the radial five on the left and the flower six on the right, Black needs toplay at A to live.A is also the vital point forWhite to kill.

    Diagram3Diagram4:

    The square four on the left is dead even if it's Black's turn to play.On the right,rectangular six is alive. It's better to think of these groups as "alive" or "dead", ratherthan thinking if you could play twice, you could live with the square four, or kill therectangular six. It's not very useful to speculate how you or your opponent might getin two moves in a row, since that would be relying on one player's having a seizure inthe middle of the game.

    Diagram4The upshot: The status of three-point eye shapes is undetermined.Of the four-

    point eye shapes, all are alive except the T bent four (undetermined) and the squarefour (dead).All five-point eye shapes are alive, except the radial five and the Maltesefive (both undetermined).All six-point eye shapes are alive, except the flower six(undetermined).All eye shapes with seven points or more are alive. Remember, an eyeshape is eye space that is completely surrounded, by stones that are all connected.Specialnote:We have been calling the vital point the point that determines life and death of agroup if it is not already alive or dead as it stands the "center" or the "center of symmetry." There's alsoan interestingway of looking at it in terms of pivots. The pivot,you may recall, is an opposing stone onthe unoccupied "jaw" of a just-about-to-be-formed tiger's mouth. The vital point of an eye shape is alwayson a pivot. For example, the vital point of the radial five inDiagram3 is on two pivots.Icall the shape

    that results when there is a killingstone on this pivot the "blown-out radial."

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    SEARCHING FOR LIFE 752. How to Live

    There are two techniques for livingwhen your group is surrounded and needs tomake two eyes: enlarging the base, and playing at the vitalpoint.Diagram 5:

    Try to save this white group.Diagram 6:

    The hane at 1and descent to 3enlarges the base to itsmaximum size.Making the rectangular six eye shape isthe only sure way to live here.

    Diagram5 Diagram 6

    Diagram 7:The rectangular six is alive because ithas two "center" points that reflect; ifBlack 4,White plays 5, and if Black 5,White 4. Reading further, if Black plays at

    A here,White plays B,and if Black playsB,White plays A.

    Diagram7

    Note:As youmay have seen inVolume II ,if all the stones in an otherwiseliving eye shape are not all solidly connected to each other, you need to makesure no lethal atari is coming up.For example,here when Black plays at 1andWhite plays 2, after Black cuts at 3,White can't play at A to make the secondeye, because that would be putting her own group in atari. The marked stoneis blocking a liberty that turns the living group inDiagram 7 into a killablegroup here.

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    76 LIFEAND DEATHDiagram 8:

    How doesWhite live here? SinceWhite's small living room can't beexpandedmuch further, she needs to puta stone in a strategic spot to make thisarea livable.

    Diagram 9:IfWhite had tried to enlarge the basewith 1,Black could play the hane at 2.White can't block at A (do you see why?)and a play at 3 makes the radial five,which can be killedby playing on thepivot at 4.

    Diagram 8 Diagram9Diagram 10:

    In this case,White needs to play at 1first to live.

    % fk

    Diagram 11:What if Black attacks at 2? Whiteblocks at 3, and if Black 4,White lives byconnecting at 5.

    Diagram10 Diagram 11

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    SEARCHING FOR LIFE 773. The Tiger'sMouth

    The tiger's mouth has a kindof built-in eye structure, so it's often very useful in life-and-death situations.

    Diagram 12:How can Black live?

    ---C XL1T LJDiagram 12

    Diagram 13:If Black tries enlarging his base at 1,White can killby playing on the pivot at2. (Try to confirm for yourself that A and

    B reflect and Black is dead.)

    Diagram 13Diagram 14:

    Since maximizing the size of Black'sbase doesn'twork, he should play thetiger'smouth to make two eyes. (Formental exercise, try to figure out howWhite can kill if Black plays the othertiger'smouthat A.)

    Diagram 15:IfWhite plays the hane at 2, Blacklives by playing at 3.

    Diagram 14 Diagram15

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    78 LIFEAND DEATHDiagram16:

    This group needs to make another eyeon the edge.

    Diagram17:If Black connects at 1,White playsatari at 2. Black's only chance then is toplay at A and try to live by ko.

    Diagram 16 Diagram17Diagram18:

    Black can live herewith the tiger'smouth at 1. (Notice the tiger's mouth atA also works here.) IfWhite 2, Black connects at 3, forming the second eye.

    Diagram 19:IfWhite tries to catch a stone at 1,Black can descend at 2. Because of Black , ifWhite then plays atari at A, Black

    can link up on the first line at B.

    Diagram18 Diagram19

    Imagine Black starts a ko for life by blocking at A as in Diagram 17. After Whitetakes the ko , suppose Black plays a ko threat,White answers the threat, and Black takesback the ko .Next,White can connect at B as an internalko threat that is, a threatassociatedwith the ko itself, that must be answered or fighting the ko becomes meaningless. Black has to respond to this threat by playing C to try to make the second eye,so White can then take back the ko .

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    SEARCHING FOR LIFE 794. The Throw-In

    The throw-in, discussed in previous volumes, is one of the most commonly used capturing techniques in life-and-death situations.Diagram20:

    Blackmust useWhite's weaknesseshere to live.Diagram 21:

    If Black plays atari at 1,White simplyconnects at 2.

    Diagram 20 Diagram21

    Diagram22: Diagram23:With the throw- in at 1,Black can live. In this position, how can Black live?WhenWhite takes at 2, the atari at Black He'llneed to utilize the throw-in.3 pins two white stones.

    Diagram22 Diagram23

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    80 LIFEAND DEATHDiagram24:If Black plays atari at 1,White con

    nects at 2 and Black only has one eye.Diagram25:

    The throw-in at Black 1 is the key.WhenWhite takes at 2, Black can playatari at 3,pinning two stones.

    Diagram25iagram 24

    5. Util izingNo-ParkingZonesDiagram 26:

    Can the black group in the cornermake two eyes?Diagram27:If Black plays atari at 1,Black dieswithWhite 2.

    Diagram26 Diagram27

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    SEARCHING FOR LIFE 81Diagram28:

    Again, Black should play the throw-in.(It's a throw-in because Black 1 is actuallyin atari.) IfWhite takes at 2, it looks likea ko,but

    Diagram 29:When Black plays atari at 3,Whitecan't connect, because that would be

    playing on a point with no liberties without capturing (one of the few prohibitions on where you can park yourstones). Therefore Black is alive.

    Diagram 28 Diagram29

    Diagram 30:If Blackwants to live in the cornerhere, he must use the sarnie technique ofcreating aNewYork-style no-parkingzone to preventWhite from taking thevital spot.

    Diagram 31:If Black 1,White can killat 2. (To takeBlack's stones off the board,White canblock all the outside liberties, then playatari at A. If Black captures, the resultingposition is the radial five eye shapewithWhite's turn to play White kills byplaying on the pivot.)

    Diagram 30 Diagram 31

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    82 LIFEAND DEATHDiagram 32:

    Black needs to play the throw-in at 1first.WhenWhite takes at 2Diagram33:

    Black plays atari at 3.White is notallowed to make a move at A, so Black isalive.

    Diagram33iagram32

    In an alternate rule system proposed by the lateMr. IngChang-ki,one may play "self-removal" anillegal move in other rule systems by playing on a pointwith no liberties without capturing. For example,White could play at A inDiagram 33 and take her own stones off. This doesn't change the life-and-death status of the black group, though, because self-removal counts as a whole turn.After White playsA andremoves her stones, Black can then live by playing at the center of the resulting radial five.What's the difference, then?When there's a situationwhere a no-parking zone has been utilized to live in a small space, self-removal can be used as a ko threat.

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    SEARCHING FOR LIFE 836. DualLife

    The situation in which groups co-exist without two eyes is dual life (seki in Japaneseand beek in Korean), discussed in previous volumes.

    Diagram34:Black can't make two eyes. But hemake dual life.

    Diagram34

    Diagram36:IfWhite tries to kill at 2, Black cap

    tures at 3,making the L bent four.

    Diagram35:Black 1 is the key.

    Diagram35

    Diagram37:This is the result after Black captures.This shape is alive, so after Diagram 35,the bestWhite can do is dual life.

    Diagram36 Diagram 37

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    84 LIFEAND DEATHDiagram38:

    It looks like Black has a bigbase towork with, but actually it's not easy forhim to live.

    Diagram39:If Black tries to enlarge the base at 1,

    White can killby playing the hane at 2and then the pivot at 4.

    Diagram38 Diagram39

    Diagram40:Black can make dual life by making

    two tiger's mouth formations at 1.Diagram 41:IfWhite tries to kill, the sequence to 6makes dual life.Neither side has any territory here, but.Black survives.

    Diagram40 Diagram41

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    SEARCHING FOR LIFE 857. Ko

    When you're surrounded and can't make two eyes or dual life, try to make a ko.Diagram 42:

    This shape occurs frequently in realgames. How shouldWhite play?

    Diagram 42

    Diagram43:Connecting at 1getsWhite killedwhen Black plays the hane at 2.

    Diagram 43

    Diagram 44:The sequence of the hane at 1andtiger's mouth at 3 doesn't work either ifBlack attaches at 4.

    \J~

    Diagram 44

    Diagram45:Starting a ko with the atari at 1 isWhite's only hope.

    4 4wDiagram 45

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    86 LIFEAND DEATH

    -0

    Diagram46

    Diagram46:If Black gives in by connecting at 2,Whiteliveswith the hane and connection at 3 and 5.

    (T) elsewhere

    Diagram47 .

    Diagram47:If Black takes the ko with 2,White can play

    a ko threat elsewhere on the boardwith 3. IfBlack ignoresWhite's threat and wins the koby capturing at 4,White can be compensatedfor the loss of the corner by following up onthe threat, a significant improvement from justdying fo r nothing as inDiagram 43.

    Diagram 48

    Diagram48:If Black loses this ko, the capture atWhite secures life for the corner,andBlack's position on the left side is compromised by the White group streaming throughthe hole on the edge.

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    SEARCHING FOR LIFE 87Diagram 49:

    The group in the corner looks nearly dead,but Black can make a ko.

    Diagram49

    Diagram 50:If Black plays atari at 1,White simply con

    nects at 2. It's the end of the line for Black.

    Diagram50

    Diagram 51:Black can start a kowith the throw-in at 1.Even ifWhite wins the ko,Black should beable to get some compensation.

    Diagram51

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    88 LIFEAND DEATH8. Playing Under The Stones To Live

    This is an interesting sacrifice technique involving a bit of reading.

    Diagram 52

    Diagram53

    Diagram52:It looks like Black has two eyes, but there is

    a small problem.

    Diagram53:IfWhite plays the throw- in at 1and Black

    takes at 2

    Diagram54

    Diagram54:White can play the throw-in at 3 again.

    How would you play?

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    SEARCHING FOR LIFE 89Diagram55 :

    Blackmust connect at 4 to live. (If Blackcaptures at 5 instead,White at 4 makes Black'ssecond potential eye false.) White 5 capturesfour stones,but

    Diagram55

    Diagram 56:Black 6, playing under the stones, capturesWhite's two stones.With this Black is alive.

    Diagram56

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    0Death by Designi. How toKil l

    Just as there are two main techniques fo r living, there are also two corresponding killing techniques: reducing a group's base, and playing on agroup's vital point.Diagram 1:

    If Black plays first, he can kill the corner group.

    Diagram1Diagram2:

    The hane at 1, reducing the base, is a goodexample of the Go proverb "There is death in thehane".White is prettymuch limited to answeringat 2. Then Black plays the other hane at 3. IfWhiteblocks at 4, Black killsby playing the vital pointat 5.

    Diagram2

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    DEATHBYDESIGN 91Diagramy

    When Black plays the hane at 1,what ifWhite tries playing the vital point herself at 2instead of blocking? Black can stillkillby playing at 3, then pushing in at 5 and preventingthe second eye with 7. IfWhite takes at A, thisonly makes a false eye when Black plays thethrow-in at 1.

    Diagram3

    Diagram4:IfBlack plays at 1 to take the vital pointfirst,White can play at 2. Then if Black pushesin at 3,White can give up two stones and livewith the main group by playing at 4 (if Black

    A,White B,and if Black B,White A, so Whitecan make two eyes).'

    Diagram4

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    92 LIFEAND DEATHDiagram5:

    Try to kill this white group.

    Diagram 5

    Diagram7:Here,Black needs to take the vital

    point at 1 first. White doesn't have anway to live.'

    Diagram 7

    Diagram6:In this case, if Black plays the hane at1 to reduce the base,White liveswith 2.

    Diagram 6

    Diagram8:IfWhite 2, Black can killby just block

    ing at 3 White's dead because Black hasa clever way of capturing the two markedstones with a throw-in at A, and aWhiteconnection at A doesn't give her two eyes.(In fact,White 4 at A would be a tragicwaste, since her group would stillbe dead,without Black having to do anything.)

    PXO

    Diagram8

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    DEATHBYDESIGN 932. ThePivot

    The pivot, an opposing stone on one of the "jaws" of a just-about-to-be-formedtiger's mouth, is often key in the prevention of two eyes.Diagram 9: Diagram 10:

    It may look difficult to kill the corner If Black just captures a stone at 1,group, but if Black plays on the pivot, White liveswith 2 and 4.White is helpless.

    Diagram 9 Diagram 10

    Diagram 11:The killingplay is the pivot at Black 1.When White connects at 2, Black extends

    at 3 to destroy a potential eye. Next

    Diagram 12:IfWhite connects at 4, Black plays thehane at 5 to reduce the base. IfWhiteplays the hane at 6, Black 7 kills (try toconfirm this for yourself).

    Diagram 11 Diagram12

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    94 LIFEAND DEATHDiagram13:

    Try to killWhite by playing on apivot.

    Diagram 13

    Diagram 14:If Black just plays atari at 1,Whitelives at 2. If Black takesWhite's two

    stones,White takes one stone back andlives. (This isn't a ko whenWhite takesone stone back, her capturing stone is notthen in atari.)

    Diagram 15:Here,Black 1 is on the pivot.With this

    move,White is dead. SinceA and Breflect (ifWhite playsA, then Black playsB,and ifWhite B,BlackA),White can'tmake two eyes.

    Diagram 14 Diagram 15

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    _3. TheAlien Symbol

    Some aliens contactedme, and toldme about this.Diagram16:

    Diagram 17:Here's an example.White is cut and doesn'thave a base on either side. It looks pretty grim,but ifWhite knows the Alien Symbol, she can

    connect her groups by capturing Black's twomarked stones.

    Diagram18:The four marked stones have started to formthe Alien Symbol. There remain two unplayed

    points at A and B, so White should have a lookat these moves. IfWhite plays at A

    These black and white stones form the basicAlien Symbol. The marked stone occupies thecrucial point preventing the formation of thebamboo joint. The other two white stones complete the key that unlocks a door to a secretarmory of magicalweapons.

    DEATHBYDESIGN 95

    4 sr*sJDiagram16

    Diagram 17

    _A 1 !

    Diagram 18

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    96 LIFEAND DEATHDiagram 19:

    Black is in atari, so he comes out at 2.NextWhite can play double atari at 3,and Black can't save both sides. But whenyou play double atari, your opponentgets to choose which side to save. In thiscase, Blackwill save the two key stonesseparatingWhite's groups.

    Diagram 19

    Diagram 20:White A didn't work to capture the

    two black stones, so what about thestrange-looking move at B, preventingthe bamboo joint?

    Diagram 21:Black sees thatWhitewill catch the

    two stones for certain if nextWhite playsat 2, so he could try playing there first.But thenWhite can cut at 3 and all fourof Black's stones are trapped.

    Diagram21iagram 20

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    DEATHBYDESIGN 97Diagram 22:

    What if Black tries to escape by playing at 2?White blocks at 3, pinning three Black stones.

    Diagram 22Diagram 23:

    Last ditch effort Black plays the hane at 2.HereWhite just cuts at 3 and pins two stones.Black is helpless he can't save his stones afterWhite prevents the bamboo joint.

    Diagram 23

    Philosophicalspeculation: In manyways, the Alien Symbol is a structural representation of the creative conflict that is the hallmark of Go (and perhaps of life as well). Stones that are connected are strong, and stonesthat are cut are weak as E.M. Forster says, only connect. The bamboo joint and the tiger's mouth are thetwin icons of connection.You can take out an opposing force of any size with almost nothing, if you aim forthe connections and the incomplete links of the chain spoiling the bamboo joint as in the case of the AlienSymbol, or playing on the pivot as in the case of the tiger's mouth.

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    98 LIFEAND DEATH4. The Snapback

    The snapback, a capturing technique involving a sacrifice, is discussed in previousvolumes. Let's look at an advanced example.Diagram 30:

    If Black cuts at 1,where would youplay?

    Diagram30Diagram32:

    In a snapback,when you capture thesacrificial throw-in you block one of yourown liberties,puttingyourself in atari.For example, ifWhite takes one stone at3, she's put her own twelve stones in atari.

    Diagram31:White 1 looks natural, but if Blackplays at 2, no matter which stoneWhite

    captures, she is caught in a snapback.

    Diagram31Diagram33:

    So after Black 1, isWhite dead? Not ifshe is on the lookout for a snapback.White can avoid it by playing at 2.

    Diagram 32 Diagram33

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    DEATHBYDESIGN 995. The Strange Property of the 2-1Point

    The corner of the board has strange properties. If a stone is on the I-1point you cancapture it with only two moves and you can make a "tigersmouth"with only onemove on the 2-1 point. Since life and death often involves making an eye quickly, the 2-1point is often the vital point.Diagram24:

    How can Black kill this group?

    Diagram 24Diagram 25:

    Black 1, the 2-1 point, is the killingmove.(The term 2-1 point could refer to either ofthe points immediately adjacent to the 1-1point.)

    Diagram 26:IfWhite plays at 2, Black can just block at3. IfWhite connects at 4 to prevent Black fromcatching two stones in a snapback,White diesin gote that is,White's dead even afterspending a move to defend.

    Diagram 25

    Diagram 26

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    100 LIFEAND DEATH

    Diagram27

    Diagram 27:Let's look at another example of thestrange property of the 2-1 point.White

    looks safe,but Black canmake a ko.

    Diagram28:The first step is Black 1at the 2-1point.

    Diagram 28Diagram 29:

    White needs to connect at 2 to avoid asnapback. (Do you see it?) Black thenthrows in at 3,making a ko.

    Diagram 29

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    DEATHBYDESIGN 1016. Playing Under the Stones to KillDiagram34: Diagram35:

    Black looks alive, because if he cap- IfWhite gives up another stone at 1,tures he'll have two eyes, and ifWhite and Black captures four stones at 2plays at A and Black captures at B, theresulting position looks like a Z bentfour. However

    Diagram34 Diagram35

    Diagram 36:White can cut at 3, putting Black's five

    stones in atari. Black is helpless.Just as when you're trying to live it'simportant to make sure there are no cutting points in your eye space where your

    stones can be put in atari, it's often fruitful to check if there might be any flaws inyour opponent's eye space.

    Diagram36

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    102 LIFEAND DEATH7. DEADL

    The L bent four is alive without playing, except in one case. If a group is forced into anLwith all the points of the eye space on the first line,because of the strange property of the2-1 point, there's a ko . If the group can be forced into this shape at any time, and the stonessurrounding the group are alive, the group is dead as it stands. Here's how it works:Diagram37:

    All the points of this L bent four areon the first line. Ordinarily the L is alive,but here, Black needs another move at Aor B to live.Otherwise,White can play atA, setting up a ko if Black plays B totry to make two eyes,White can take at C.

    Diagram38:If a group may be forced into thisshape at any time, it is dead as it stands.Let's look at an example of how this can

    come up.To save the corner group, whereshould Black play?

    Diagram37 Diagram38Diagram39:If Black plays at 1,he lives.

    Diagram40:But Black dies if he tries to enlarge hisbase at 1.White 2 and 4 lead to the dead L.

    Diagram40iagram39

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    DEATHBYDESIGN 103Diagram 41: Diagram 42:

    Let's see why Black is dead. IfWhite White can play atari at 1. If Blackwanted to take out this group, after all takes at 2the outside liberties are blocked andWhite connects with the marked stone

    Diagram 42iagram 41Diagram43:

    This is the resulting shape after Blacktakes off the four stones. Black has beenforced into the L bent four with all thepoints on the first line.Notice thatWhitecan force Black into this shape at any time as long asWhite's surrounding stonesare in no danger, it's up to her when toplay the atari at 1 inDiagram 42 .

    Diagram43

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    104 LIFEAND DEATHI(j

    Diagram44

    Diagram44:Next,White plays at 1. If Black plays at 2, hoping

    to start a ko

    Diagram45:White takes the ko at 3.Now Blackmust play ako threat. But what if Black doesn't have any kothreats? Black's group is in atari andWhite can takeoff all the black stones at A.

    Diagram 45

    Diagram46

    Diagram46:This is the shape beforeWhite starts the ko. Sinceher surrounding stones are fine,White doesn't have

    to start trying to take Black off the board. It's completely up to White when to play at A and start theko Black doesn't have any way of living even if it'shis turn. That meansWhite can ge t rid of all kothreats first and then play at A.With no threats,Blackwill lose the ko and thus will be captured.

    Most rule systems, reasoning that White canwin the ko if it's up to her when to start it,treat this black group like any dead group White can just remove it from the board atthe end of the game, without getting rid ofall ko threats first.Of course, like any other deadgroup, if the surrounding stones killing the group get into trouble, it may have somepotential of rising from the grave White may have to start the ko before the end of thegame, in order to remove it from the board to save her own stones.And, of course, ifWhite starts the ko by mistake, she'll just have to fight it out like any other ko.

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    DEATHBYDESIGN 105Diagram47:

    CanWhite make the dead L here?

    Diagram 47

    Diagram48:IfWhite plays the hane at 1,Black lives at 2. (IfWhite A, Black B.)

    Diagram 48

    Diagram 49:White 1on the pivot kills. If Black 2,Whiteextends at 3. If Black 4,White 5 makes the dead L.rvTA'sL'J

    Diagram 49

    Note:According to most rule systems in use today, the dead L (also known as "bent-four-in-the-corner")is just removed at the end of the game. There may be something a bit elitist about this, since it assumes it'sunnecessary to play out, because the best possible moveswill be played. It is also making a somewhat arbitrary ruling based on aesthetics, that it's inelegant to potentially have to play inside your own territory at theend, losingpoints and possibly the game, in order to remove ko threats to take off stones of otherwise undetermined status. In Ing's rule system,your opponent may insist that you play to take out dead stones at theend of the game. Since in the Ing counting system it makes no difference whether you play in your own territory or not at the end of the game, the result is the same as with other rule systems, with one exception: ifthere are so-called "non-removable ko threats" as can occur in dual life, then the ko fight in dead L starts forreal. So, in the unlikely event you are playingby Ing rules and have a dual life and the dead L, try to play itout (or just throw a party, it's a one-in-a-million game).

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    oCaptur ing RacesYou may remember from previous volumes that a capturing race is a fight

    between opposinggroups, each ofwhich needs to capture the other first in orderto survive. Since capturing races are by their nature somethingwe humans cananalyze in a quantitative way, much of the material in this chapter is mathematical. So, while some of the information may be difficult, at leastyou knowthat when you've got it, you've got it. The capturing race is perhaps unique inthat ofall the situations that arise in Go, we canplay this oneperfectly. You canabsorb and use the information in this chapter and then play this part of thegame as well as any world champion.i. BlockOutside LibertiesFirstIn the context of capturing races, liberties come in two flavors: inside andoutside. Inside liberties are those that are shared by both groups. Outsideliberties belong to only one side. If you're blocking liberties, you'll want toblock those that belong to your opponent alone first, and then block theones that you share since when you block an inside liberty you block yourown liberty as well as your opponent's.

    Diagram1:It's Black's turn in this capturing race.Which liberties should he block first?

    Diagram1

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    CAPTURING RACES 107Diagram2:

    First,notice Black has three outsideliberties.White also has three outside liberties.Both sides have three inside liberties, markedwith an X.

    Diagram3:Black 1here, or on any of the insideliberties, doesn't work. IfWhite blocks an

    outside liberty at 2, Black can blockanother liberty at 3 but gets captured firstwhenWhite plays at 4.

    Diagram4:Black should block one of the outsidelibertieswith 1. Then ifWhite 2, Blackblocks another outside liberty with 3.

    Next

    Diagram5:White blocks at 4 and Black blocksWhite's last outside liberty at 5. Theresult in the sequence to 8,with eachside playing the bestmoves possible, isdual life.

    Diagram2 Diagram3

    Diagram4 Diagram5

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    108 LIFEAND DEATH2. Counting Liberties

    To find out what the result of a capturing race will be, count the liberties. If there areno inside liberties and no eyes, the winner will be the one with more liberties or if thenumber of liberties is the same, the side whose turn it is to play wins.When there areinside liberties, the resultwill sometimes be dual life.Diagram 6:

    The first capturing race we lookedis an example of a position resulting indual life. Ifboth sides have the samenumber of outside liberties, neither sid

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    CAPTURING RACES 109Diagram8:

    What will be the result of this capturing race?We know it can never be dua l lifebecause if there are no eyes, you need atleast two inside liberties. It may appearthat since Black andWhite each have threeoutside liberties,whoever's turn it is toplaywillwin. But here, Black's outside liberty at A is a bit more than it seems.

    Diagram9:SupposeWhite begins this race.Whitecan't block Black's final outside liberty at

    A, because playing there would be playinginto atari.A is called an approach-moveliberty.When there are inside liberties,anapproach-move liberty counts double,since it takes two moves to block it.

    Diagram8 Diagram9Diagram10:

    How about this case? Here, there areno inside liberties, and A is an approach-move liberty. In the sequence up to 3,White puts Black into atari as usual.Withno inside liberties,having one approachmove liberty has no effect on the race.

    Diagram 11:But where there are no inside libertiesand two approach-move liberties, thishas the effect of giving you an extra liberty. Try to confirm this fo r yourselfusing this example.

    Diagram 10 Diagram 11

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    110 LIFEAND DEATH

    3. Eye vs.No EyeThere's a Go proverb: "Eye vs. no eye is not a fight."What does this mean?

    Diagram 12:In this capturing race,where shouldBlack play?

    Diagram13:Blocking a liberty at Black 1 results indual life whenWhite plays at 2.

    Diagram 12 Diagram13

    Diagram 14:Insteadof blocking a liberty,making

    an eye at Black 1 is correct.With thismove,White can be captured.

    Diagram15:Next, ifWhite blocks a libertywith 2,Black blocks an outside liberty at 3. IfWhite 4, Black 5.White can't play at A, soBlack wins the race.

    Diagram14 Diagram 15

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    CAPTURING RACES 111Why did this happen? An eye is worth more than an ordinary outside liberty.Whenthere's a possibility of making an eye ...

    Diagram16:Back to the original position.White has sixliberties (four outside and two inside) and Blackhas four (two outside and two inside). It seems asthough Black can'twin this race, but, as we saw,Black can make an eye.

    Diagram17:When Black makes an eye,White still has sixliberties, three outside and three inside. Black hasfour liberties, in this case three inside and oneoutside (an eye is an outside liberty,because itbelongs to only one side). But now,because hehas an eye, he can add the number of inside liberties again to his total. For practical counting purposes Black's eyed group has seven liberties, soBlackwins this race by one liberty.

    Diagram 17

    Since you can't block an outside liberty that is also an eye without first blocking allthe inside liberties, the effect of making an eye is to add the number of inside liberties toyour total of outside liberties.Don't worry if you don't ge t all the hows and whys fornow: the important conclusion from all this is that making,or preventing your opponentfrom making an eye, is a good idea in capturing races.

    Diagram16

    SpecialNote:To convey profound understanding, next time you're in one of these capturing races with aJapanese friend, just shrug and say mean menashi ("eye vs . no eye," the shrug indicating either quiet acceptance of defeat or sympathy for the opponent's bit of bad luck).

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    112 LIFEAND DEATHExtra for Experts O Yout +1 = dual life.

    Diagram 1:Here's an example. In this race, there are seven inside

    liberties and neither side has an eye.White has ten outside liberties; Black has six. Plugging inWhite as X, Iasseven, and Black as Y in our formula, 10+7>6+1, andwith Black as X, 6+7 > 10+1,so we know the resultwillbe dual life. (If Xout + I= Yout +1, the result is dual lifeif the smaller of Xout or Yout plays first.) The formulamust hold true for both cases,White as X and Black as X.But since we can see that we'll reach equality sooner withBlack as X, we'll just examine that case.

    Diagram2:IfWhite blocks a liberty at 1, then it's 5+7 > 10, so the result is still dual life. IfWhite blocks another libertywith 3, then it's 4+7 >10, still dual life.Next, ifWhiteblocks another liberty, it will be 3 + 7,which is notgreater than 10 so Blackwill die if he doesn't blockone ofWhite's outside libertieswith 4. In order to maintain dual life,you only have to playwhen the left side ofthe formula is one greater than the right side.

    Diagram 2Converting knowledge to power:We knowWhite wasted amove at 1 Blackcould ignore it and play a usefulmovewith 2. We know that if Black fills an insidelibertywith 2, he's killinghimself: 5+6 >10,but next whenWhite 3 blocks an outside liberty, it'llbe 4+6,which is not greater than 10 .Finally,we know thatWhite

    can wait until all her outside liberties are blocked before she has to play (0 + 7 > 6).Imagine a fifty-move capturing race sequence where, after your opponent painfullydeliberates the next play,you smile and play elsewhere.

    Diagram 1

    -3 o &, 0 0 0 O 0 0 0 0

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    CAPTURING RACES 1134 3-3> 4-5> 5-8, 6-12

    Suppose your stones have a big eye that is , an eye of two points or more.Howshould you count the liberties of a big eye? Since opposing stones played inside an eyecan be captured, playing a capturing race with a big eye is not as simple as just blockingliberties.You'll have to play moves inside the big eye, letting your stones be captured,and play inside again. Each time your stones are captured, the big eye gets smaller, untilfinally it is just a single point and the group is in atari. In the pairs of numbers above,the first number is the size of the big eye, and the second number is the number of ordinary outside liberties the big eye is equivalent to. For instance, a four-point eye shape isworth five ordinary outside liberties.

    This only holds true if a group can't make two eyes, of course you can't captureliving groups. Some eye shapes are just dead, and some require a move on the pivot tokill them. In the latter case we have to include the killingmove in the total number ofequivalent ordinary outside liberties. Let's see how this works.

    Diagram 18Diagram18:

    The Black group in the upper right corner has a three-point eye shapewith a killingstone on the pivot. This shape is equivalent to three liberties, less the killing stone for atotal of two. The group in the upper left has a four-point eye shape, so according to theguide, this is equivalent to five ordinary outside liberties.The blown-out radial five eyeshape in the middle has the equivalent of eight liberties,minus the killingmove for atotal of seven.

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    114 LIFEAND DEATHDiagram19:

    When Black plays on the pivot at 1, thecapturing race is on. Black has six liberties. The white group has a five-point eyeshape,which has the equivalent of eightliberties. Black's already played the firstmove at 1,so nowWhite has seven.Whitewillwin this race.

    Diagram 19

    Diagram20:White can even play elsewhere andstillwin. Suppose she does, and Blackcontinues with 3. Now it's six to six in

    the liberty fight. If Black could play againhe could capture,but it'sWhite's turn. SoWhite just blocks a libertywith 4.(T) elsewhere

    Diagram21:There's no point for Black to continue

    now,but if he blindly continues to fill inWhite's eye space,White just keepsblocking liberties. Black 7 is atari, soWhite takes at 8. Next

    Diagram20 Diagram21