endgame chapter 2 - problems - answer

8/20/2019 Endgame Chapter 2 - Problems - Answer

1/19

5. Problems

ow you can apply what you have learned to the

following problems. &n each one three possible moves aremarked A, B, and ; assume that there is nothing else worthconsidering on the board and try to figure out the bestsequence in which to play them.

>our first step should be to e!amine the moves one byone and determine how much each is worth and whether itis gote, sente, or whatnot. e!t you should e!periment withdifferent sequences and try to find the one that gives you

the most profit. Finally, in order to score yourself, identifythe largest move-not necessarily the largest in absolutevalue, but the one you should play first in the optimalsequence and the smallest move-the one that comes last ofthe three in the optimal sequence < and try to assign anumerical value < 1 points in double sente, for e!ample <to each move. %fter turning the page and reading theanswer, give yourself ten points if you correctly identified

the largest move and ten points if you correctly identifiedthe smallest move, then subtract the total amount by whichyour numerical values were off the mark. Twenty points isthus the perfect score for each problem, and there is ascoring chart at the end.

Gargest moveHHHHHHHH smallest moveHHHHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH

"+


2/19

Lr!est move8


3/19

Smllest move8 %-"I points in gote.Dia. 6. 'lack " saves a prisoner, and ne!t 'lack a would

make one point of territory.

Dia. 7. )hite " takes a prisoner, but without making anyterritory.

ombination figure. 'lack takes his two points in senteat ", then goes to +. )hite*s connection at 1 leaves 'lack 3and 5, at two points in gote, as the largest plays on theboard, so 'lack makes them and )hite gets 6. 'lack hastaken ' and , worth a total of five points. &f he had startedwith ', or + in the figure, followed by )hite " and 'lack 7,

he would have picked up only four and a half points, whichshows how two points in sente can be more valuable thanthree points in gote.

)hite 1 at 3 would give the same net result, but fromthe standpoint of not leaving ko threats, 1 is best.

Gargest move HHHHHHHH smallest move HHHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH

"3


4/19

Lr!est move8 ' < 1 points in gote.Dia. 1. $escending to " means that )hite will not have

to connect around a, and ne!t he can push out at + in sente.

&ncidentally, if )hite played " at +, 'lack could make athrow-in at ", and then )hite would have to connectaround a.

Dia. 2. 'lack " is gote, but + and 3 follow automatically.%fter mentally removing 'lack + and moving )hite 1 over,we see that )hite*s territory is three points smaller, and'lack*s one point larger, than in $ia. ".

2n" lr!est move8 %


5/19

Smllest move8 < ( points in gote.Dia. 6. &f 'lack has his eyes open he will not connect

against )hite ", but play ( and make )hite connect. )hite

has reduced 'lack*s territory by one point in gote.Dia. 7. @imilarly, 'lack can reduce )hite*s territory by

one point in gote. The total value here is two points.

Comb$nt$on %$!ure. %ll three moves are gote, so theplayers take them in order of absolute value, from largest tosmallest. The only possible variation in this sequence is that)hite could play 5 at 7, threatening 6. 'lack would defend

at 5, and then )hite could connect at ". T&$s would givehim one more point in the upper left corner, but one lesspoint in the upper right corner. Either way, )hite ends thee!change in gote.

Gargest move HHHHHHHH smallest move HHHHHHHH A:____ pts. inHHHH B:____ pts. inHHHH 8HHHH pts. inHHHH

"5


6/19

Lr!est move8 '


7/19

Smllest move8 %


8/19

Lr!est move8


9/19

Dia. 6. )hite " saves ' and captures ", which makes adifference of two points so far, and there is a further playleft at a.

Dia. 7. That play is worth three points < two at " andone at ! < but it is gote, so only half its value should beadded on. )hite " in $ia. 4, or 'lack " in $ia. 3, is worth8

(/I ! +0+I points in gote.

Comb$nt$on %$!ure. 'lack plays " in sente, then +, andanswers 1 at 5, so all )hite manages to get are the twopoints noted in $ia. 4. &f 'lack had begun at +, )hite wouldhave gotten both " and 1, gaining 1- points. )orse yet, if

'lack had begun by playing at the right of 5, )hite wouldhave gotten " and +, gaining 4- points.

Gargest moveHHHHHHHH smallest moveHHHHHHHH A________ B________ C________

("


10/19

Lr!est move8 % < 5 points in gote.Dia. 1. %ssume 'lack a and )hite b later.Dia. 2. 'lack " and + are gote, but they leave two white

stones in atari. To compute their value, first imagine that)hite connects at ". %ssuming a-b at the edge, 'lack*sterritory is two points larger than in $ia. ", and )hite*s isthree points smaller, at b, ", and (. That makes five.

Dia. 3. e!t, if 'lack captures at &, he gains another fourpoints in gote. %dding in half of this, we get8

3/I ! 105 points in gote.

2n" lr!est move8 ' < 4 points in gote.Dia. 4. @ince )hite cannot hane at a in sente, we can

assume 'lack a and )hite b. )hite has gained three pointsof territory8 two at " and one at x .

Dia. 5. 'y connecting at ", 'lack also gains three pointsof territory, so the total value is si! points.

Smllest move8 < 1 points in gote.Dia. 6. %fter )hite ", assume 'lack a and )hite b.

((


11/19

Dia. 7. 'y playing ", or a < )hite ignores either move,'lack can destroy the three points marked ! in $ia. 4.

Dia. 8. Toward the end of the game the e!change from "

to 1 is reasonable, so 'lack has augmented his own territoryat ! , bringing the total value of 'lack " in $ia. 5, or )hite "in $ia. 4, to four points.

ombination figure. :aving the first move, )hite getstwo of the three large plays. 'lack*s only gain is si! pointsfor connecting at 1. &f )hite began at 1, 'lack would take$ia. (, gaining five points, and ne!t $ias. + and 5 would be

miai, so 'lack would get one of them, bringing his total tonine points.

Gargest moveHHHHHHHHHH smallest moveHHHHHHHHHH A__________ B__________ C__________

(+


12/19

Lr!est move8 < 3 points in reverse sente.Dia. 1. 'lack " saves four points of friendly territory,

and later on 'lack can play a in sente to rob )hite of ! .

Dia. 2. )hite " to 3 are sente. 'lack cannot afford toanswer " at +, because he would be risking considerablymore than )hite in the ensuing ko fight.

2n" lr!est move' % < 6 points in gote.Dia. 3. &f 'lack played ", )hite would probably not

defend at a. which would save only three points.Dia. 4. @o 'lack could keep on in sente as shown.Dia. 5. omparing this diagram with the last, we see

that )hite " saves eight points8 two at " plus three morepairs.

(1


13/19

Smllest move8 ' < 4 - points in gote.Dia. 6. 'lack " may look bigger than it really is.Dia. 7. Even if 'lack connects at ", he only gains seven

points8 four prisoners and three points of territory.Dia. 8. &f )hite recaptures at ", 'lack*s gain drops to five

points, or four if )hite also gets to play a. 'oth $ias. 5 and 6are gote, so we8 average them to obtain 4- as the value of'lack " in $ia. 4.

Comb$nt$on %$!ure. 'y starting with the reverse sente

play, 'lack is able to take two of the three large moves for atotal gain of about eleven points. &f he had started with (,)hite would have played " in sente, then +, and 'lack*s gainwould have been only eight points.


(3


14/19

Lr!est move8 % < 1 / points in double sente.Dia. 1. )hite can play " and + in sente.Dia. 2. @imilarly, 'lack " threatens to kill the corner. The

difference between these two diagrams is the four pointsmarked x , plus a little more since in Dia. 2 )hite may haveto give up another point to avoid a seki.

2n" lr!est move8 ' < "" points in gote.Dia. 3. )hite " rescues three white stones, and if 'lack

plays elsewhere )hite can follow with +, capturing twoblack stones. &f 'lack tries to connect at a, )hite plays b.))hite + is worth si! points in gote, as compared with 'lack+ followed by 'lack c, )hite d.

Dia. 4. %ssuming 'lack a, )hite b in this diagram, thetotal difference between it and $ia. + is fourteen points8 ninepoints of black territory, three prisoners plus the x*s, and

(4


15/19

five points of white territory, two prisoners plus c in $ia.+, but since )hite + in $ia. + is gote, only half its value,three points instead of si!, should be counted. )hite or

'lack " is therefore worth "1-+0"" points in gote.Smllest move8 < "9 points in gote.Dia. 5. )hite " means five points of territory for )hite8

two for capturing " and three for the ! *s.Dia. 6. 'lack " likewise means five points, so the value

of a move by either side here is ten points.

Comb$nt$on %$!ure. )hite gains four points at " and +,then fourteen points at 3 and 5, making eighteen in all.


(5


16/19

Lr!est move8 < 4 points in gote.Dia. 1. 'lack must answer )hite ( at +, or a white

throw-in there is fatal. %fter this 'lack a, )hite b, and then)hite c, 'lack d are a fair assumption to make.

Dia. 2. @uppose )hite plays l. &f 'lack replies at (, hehas to keep on at 1, 4, and 6. )hite has erased two of thepoints marked x in $ia. " and been able to play both + and 3instead of ust one of them, so his total gain is three.

Dia. 3. &f 'lack ignores )hite ", )hite continues with +,3, and 5 in sente and 'lack loses the other three points

marked x in $ia. ", bringing the total difference between$ias. " and + to si! points in gote.

2n" lr!est move8 % < 3- points in gote.Dia. 4. 'lack " promises 'lack +.

(6


17/19

Dia. 5. )hite*s territory is now two points larger thanbefore, 'lack*s is two points smaller, and )hite hascaptured a prisoner, making a total difference of five points.

@ince 'lack may be able to recapture the prisoner, we countthis as 3


18/19

Lr!est move8 ' < 4 points in double sente.Dia. 1. )hite cannot afford to ignore 'lack ", and 'lack

+ and 3 are also sente. )hite a, 'lack b will come later.

Dia. 2. )hite could perform the same manoeuvre insente. The difference is three points of territory on each side,or si! in all.

2n" lr!est move' %-"9 points in gote.Dia. 3. 'lack has gained five points of territory8 two for

' and three others. Gater, a will be )hite*s sente.Dia. 4. )hite also gains five points of territory if he

plays first, so the total value here is ten.

Smllest move8 < ( points in double sente.Dia. 5. @ince 'lack cannot play a in sente, assume )hite

a, 'lack b, and, of course, )hite c, 'lack d.

+9


19/19

endgame chapter 2 - problems - answer

Documents