(
;
AB [cd][ce][dc][df][ef][fc][fd][ff][gf][hf][id][if][ja][jb][jc][jd]
AW [ec][ed][ee][fe][gd][ge][hd][ia][ib][ic]
LB [hi:1][ii:2][ji:3][ki:4][li:5]
C [Black moves first. What is the best result that black can guarantee? (1) Kill (2) Ko (3) Seki (4) Reduce (5) Nothing][FORCE]
(
; B [ii]; W [ii]
LB [jj:B][kj:W]
C [Is the ko advantageous for black or white?][FORCE]
(; B [jj]; W [jj]
LB [ik:1][jk:2][kk:3]
C [Last question. How many external ko threats would white need to live?][FORCE]
(
; B [ik]; W [ik] C [Then assume white has no external ko threats and kill through ko.]
(
; B [gb]; W [fb]
(
; B [fa]; W [eb]
(; B [db]; W [hb]; B [ea]; W [ga]; B [ha] C [RIGHT])
(; B [hc]; W [gc] (; B [ha]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb]))(; B [hb]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb])))
)
(; B [eb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))
(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb]))
(; B [ha]; W [gc] (; B [hc]; W [db])(; B [db]; W [hb]))
(; B [hb]; W [gc] (; B [hc]; W [db])(; B [db]; W [hc]))
(; B [gc]; W [eb])
)
(; B [eb]; W [fb] (; B [gb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))(; B [fa]; W [gb]))
(; B [fb]; W [eb])
)
(; B [jk]; W [jk] C [Then assume white has one external ko threat and kill through ko.]
(
; B [gb]; W [fb]
(
; B [fa]; W [eb]
(; B [db]; W [hb]; B [ea]; W [ga] C [With an external ko threat, white wins the ko.])
(; B [hc]; W [gc] (; B [ha]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb]))(; B [hb]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb])))
)
(; B [eb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))
(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb]))
(; B [ha]; W [gc] (; B [hc]; W [db])(; B [db]; W [hb]))
(; B [hb]; W [gc] (; B [hc]; W [db])(; B [db]; W [hc]))
(; B [gc]; W [eb])
)
(; B [eb]; W [fb] (; B [gb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))(; B [fa]; W [gb]))
(; B [fb]; W [eb]))
(; B [kk]; W [kk] C [Then assume white has two external ko threats and kill through ko.]
(
; B [gb]; W [fb]
(
; B [fa]; W [eb]
(; B [db]; W [hb]; B [ea]; W [ga] C [With an external ko threat, white wins the ko.])
(; B [hc]; W [gc] (; B [ha]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb]))(; B [hb]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb])))
)
(; B [eb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))
(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb]))
(; B [ha]; W [gc] (; B [hc]; W [db])(; B [db]; W [hb]))
(; B [hb]; W [gc] (; B [hc]; W [db])(; B [db]; W [hc]))
(; B [gc]; W [eb])
)
(; B [eb]; W [fb] (; B [gb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))(; B [fa]; W [gb]))
(; B [fb]; W [eb]))
)
(; B [kj]; W [kj] C [Black can do better than a disadvantageous ko.])
)
(; B [hi]; W [hi] C [Prove it.]
(
; B [gb]; W [fb]
(
; B [fa]; W [eb]
(; B [db]; W [hb]; B [ea]; W [ga] C [Ko.])
(; B [hc]; W [gc] (; B [ha]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb]))(; B [hb]; W [cb] (; B [db]; W [cc]; B [dd]; W [da] C [At best, a disadvantageous ko.])(; B [bc]; W [cc]; B [dd]; W [bb] C [At best, a disadvantageous ko.])(; B [cc]; W [bb])))
)
(; B [eb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))
(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb]))
(; B [ha]; W [gc] (; B [hc]; W [db])(; B [db]; W [hb]))
(; B [hb]; W [gc] (; B [hc]; W [db])(; B [db]; W [hc]))
(; B [gc]; W [eb])
)
(; B [eb]; W [fb] (; B [gb]; W [fa] (; B [ea]; W [gc]; B [fc]; W [fd]; B [ga]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [ga]; W [gc]; B [fc]; W [fd]; B [ea]; W [fc] (; B [db]; W [hb])(; B [hb]; W [db]))(; B [gc]; W [db] (; B [ga]; W [ea] (; B [hc]; W [cc])(; B [cb]; W [hc]))(; B [cb]; W [ea]))(; B [hc]; W [gc] (; B [ha]; W [db])(; B [hb]; W [db])(; B [db]; W [hb])))(; B [fa]; W [gb]))
(; B [fb]; W [eb]))
(; B [ji]; W [hi] C [Black can do better than a seki.])
(; B [ki]; W [hi] C [Black can do better than a reduction.])
(; B [li]; W [hi] C [Black can do better than nothing.])
)