(;SZ[19]AW[db]AW[bc]AW[cc]AW[dc]AB[eb]AB[gb]AB[ec]AB[bd]AB[cd]AB[dd]AB[ee]AB[ge]AB[bf]LB[jd:T]C[White is dead, but wants you to prove it. Please move at 'T' for tenuki to start this problem.]GM[1]FF[4]CA[UTF-8]AP[Jago:Version 4.43]ST[2]GN[Clipboard Content];B[jd]
(;W[ca]
(;B[ac];W[ab];B[bb];W[ba];B[aa]C[Deny the chance of White ko])
(;B[bb]
(;W[ba]
(;B[ab]C[
CHOICERIGHT])
(;B[ac];W[ab]C[Don't let W try to get a ko];B[aa]C[Deny the chance of White ko]))
(;W[ab]
(;B[ba]C[
No room for another White eyeCHOICERIGHT])
(;B[aa];W[ba])
(;B[ac];W[ba]C[Stop White from trying the ko in the corner];B[aa]C[Deny the chance of White ko])))
(;B[ab];W[ac]
(;B[bb]C[
There is no place for W to get another eye.CHOICERIGHT])
(;B[ba];W[bb])
(;B[aa];W[bb]))
(;B[ba];W[bb]
(;B[ac];W[ab])
(;B[ab];W[ac])
(;B[aa];W[ab])
(;B[ea];W[da]
(;B[ac];W[ab])
(;B[ab];W[ac])
(;B[aa];W[ab])))
(;B[aa]
(;W[bb]C[CHOICE]
(;B[ac];W[ab])
(;B[ab];W[ac])
(;B[ba];W[ab]))
(;W[ab]C[CHOICE]
(;B[bb];W[ba])
(;B[ba];W[bb])
(;B[ac];W[ad]
(;B[ba];W[bb])
(;B[bb];W[ba])
(;B[ae];W[ba]C[Actually, White does not even need to play this move yet.]))))
(;B[cb];W[bb]C[Self-atari does not help here.]))
(;W[bb]
(;B[da];W[ca])
(;B[cb];W[ca]C[Hello?])
(;B[ca];W[da]
(;B[ac]
(;W[ba]
(;B[ab]C[
CHOICERIGHT])
(;B[aa];W[ab]))
(;W[ab]
(;B[ba]C[
CHOICERIGHT])
(;B[aa];W[ba])))
(;B[ab];W[ac]
(;B[ba];W[cb])
(;B[aa];W[ba]))
(;B[aa];W[ba])
(;B[ba];W[ac]
(;B[aa]C[White is usually dead here; however, this is less than best, because Black must kill via 'bent-four-in-the-corner'. If White ends up with a non-removable ko threat, then this may end up alive in seki, under some rulesets. Find the more immediate path to victory.])
(;B[ab];W[cb])
(;B[cb];W[aa])))
(;B[ba];W[ca]
(;B[ac];W[ab])
(;B[ab];W[ac])
(;B[aa];W[ab])
(;B[ea];W[da]
(;B[ac];W[ab])
(;B[ab];W[ac])
(;B[aa];W[ab])))
(;B[aa];W[ba])
(;B[ab];W[ac]
(;B[da];W[ca])
(;B[ca];W[da]
(;B[cb];W[ba])
(;B[ba];W[cb])
(;B[aa];W[ba])
(;B[ea];W[ba])
(;B[ad];W[aa]))
(;B[ba];W[ca])
(;B[aa];W[da])
(;B[ea];W[da]))
(;B[ac];W[ab]
(;B[da];W[ca])
(;B[ba];W[ca])
(;B[cb];W[ca])
(;B[aa];W[da])
(;B[ca];W[da]
(;B[aa];W[ba])
(;B[ba]C[
CHOICERIGHT])
(;B[cb];W[ba])
(;B[ea];W[ba]))))
(;W[ba]
(;B[da];W[ab]
(;B[ca];W[cb]C[White lives -- an eye at 'A' and an eye at 'B'. White just needs to connect at 'C' when Black plays 'D' or (to start ko) 'E'. Try again, Black...]LB[aa:a]LB[bb:b]LB[ac:c]LB[ad:d]LB[ae:e])
(;B[cb];W[ca])
(;B[ac];W[ca]))
(;B[ab];W[ac]
(;B[aa];W[da])
(;B[ca];W[da])
(;B[da]
(;W[ca]
(;B[bb]C[
White eyespace is ruinedCHOICERIGHT])
(;B[ea];W[bb])
(;B[aa];W[bb]))
(;W[bb]
(;B[ca]C[
White has only one eye.CHOICERIGHT])
(;B[ea];W[ca])
(;B[cb];W[ca])))
(;B[bb]
(;W[da];B[cb]C[ CHOICERIGHT])
(;W[cb];B[da]C[ CHOICERIGHT]))
(;B[cb];W[bb]))
(;B[cb];W[bb])
(;B[ca];W[da]
(;B[ab];W[ac])
(;B[bb];W[cb])
(;B[aa];W[bb]))
(;B[bb];W[ab]))
(;W[ab]
(;B[aa];W[ba])
(;B[bb];W[ba])
(;B[cb];W[ca])
(;B[ca];W[ba]
(;B[da];W[cb]LB[aa:A]LB[bb:B]C[White lives with eyes at A and B.])
(;B[bb];W[cb])
(;B[cb];W[da]))
(;B[ac];W[ba])
(;B[ba]
(;W[ca];B[bb]C[
CHOICERIGHT])
(;W[bb]
(;B[ca]C[
CHOICERIGHT])
(;B[da];W[ca]C[Stop W from getting a ko -- there are better ways to kill.])
(;B[aa];W[ca]))))
(;W[ac]
(;B[da];W[ca]
(;B[bb]C[
Bulky five diesCHOICERIGHT])
(;B[ea];W[bb])
(;B[ba];W[bb]C[
Stop White from trying for ko. Kill more surely.CHOICE])
(;B[ab];W[bb])
(;B[aa]
(;W[bb]C[CHOICE])
(;W[ba]
(;B[ab];W[bb]C[CHOICE])
(;B[bb];W[ab]C[CHOICE])
(;B[cb];W[ab])))
(;B[cb];W[bb]))
(;B[ba];W[bb]
(;B[da];W[ca]C[Deny White a chance at ko.])
(;B[ca];W[da]
(;B[ab];W[cb])
(;B[aa]C[This kills via 'bent-four in the corner'. If White develops an unremovable ko threat, then Black may find that White lives in seki, under some rulesets. There is a better way to kill this.]))
(;B[aa];W[ca])
(;B[ab];W[ca])
(;B[cb];W[ca])
(;B[ad];W[ca])
(;B[ea];W[ca]))
(;B[ca];W[da]
(;B[bb];W[ba]
(;B[aa]
(;W[cb]
(;B[ea];W[ba]C[Don't let W try for a ko.])
(;B[ab];W[ba])
(;B[ad];W[ba]C[Don't let White try for ko])
(;B[ba];W[ab];B[ba]C[
This works, but I think it's inferior because... what if White does not play A18 right now, but saves it for a ko threat? Black can kill without giving White such a chance.CHOICERIGHT]))
(;W[ab]
(;B[cb];W[ba])
(;B[ea];W[ba]C[Don't let White get a ko])
(;B[ad];W[ba]C[Don't let W try a ko])
(;B[ba];W[cb];B[ba]C[
This works, but I dislike it. Suppose W does not capture with C18 right away, but saves it for a threat in a ko fight. Black has better ways to kill.CHOICERIGHT])))
(;B[cb];W[ab])
(;B[ab];W[cb])
(;B[ea];W[cb])
(;B[ad];W[cb]))
(;B[ba];W[bb]
(;B[ab];W[aa]C[Stop W from trying a ko])
(;B[cb];W[aa])
(;B[aa]C[This sets up 'Bent-four in the corner', which is almost always dead. However, if W comes up with an unremovable ko threat, then White may live in seki, under some rulesets. Find a more direct way.]))
(;B[cb];W[bb])
(;B[aa];W[ba]
(;B[cb];W[bb])
(;B[ab];W[cb])
(;B[bb];W[cb]
(;B[ab];W[ba])
(;B[ba];W[ab];B[ba]C[
This seems to work, but I dislike giving White a ko threat (suppose W does not capture with A18 right now; then Wh. at A18 will be good in a ko fight). There is a simpler way.CHOICERIGHT])))
(;B[ab]
(;W[bb]C[CHOICE]
(;B[cb];W[ba])
(;B[ba];W[cb])
(;B[aa];W[ba])
(;B[ea];W[ba])
(;B[ad];W[aa]))
(;W[ba]C[CHOICE])))
(;B[aa];W[ba]
(;B[ab];W[bb])
(;B[bb];W[ab])
(;B[cb]
(;W[ca]C[CHOICE])
(;W[bb]C[CHOICE]))
(;B[ca];W[ab]
(;B[da];W[cb])
(;B[cb];W[da])
(;B[bb];W[cb]))
(;B[da];W[ab]))
(;B[cb]
(;W[bb]C[CHOICE]
(;B[ca];W[da])
(;B[ba];W[ca])
(;B[da];W[ca]))
(;W[ba]
(;B[ca];W[da])
(;B[bb];W[ab])
(;B[da];W[ca])))
(;B[bb];W[ba]
(;B[aa];W[ab])
(;B[ca];W[ab]C[Don't let White try for a ko. There is a better way to kill.])
(;B[cb];W[ab])
(;B[ab]
(;W[da]
(;B[ca];W[cb])
(;B[cb]C[ CHOICERIGHT]))
(;W[cb];B[da]C[ CHOICERIGHT]))
(;B[da];W[ab]))
(;B[ab];W[bb]
(;B[ba];W[ca])
(;B[aa];W[da])
(;B[ca];W[da]
(;B[aa];W[ba])
(;B[ba];W[cb])))))