Problem	17943
Created	2014-10-28
Name	Living Embrace
Source	Aristotle
Rating

Difficulty	9 dan
Average Solve Time	98 secs
User Attempts	2 / 100
Solve Ratio Rating	6 dan
	rating history

White to live. If not unconditionally at least with a favourable 2-step ko. (correction of #17910 refuted by blyx)

(;AB[ds]AB[cr]AW[dq]AW[er]AW[es]AW[fr]AB[fs]AB[gr]AB[hr]AB[gq]AB[gp]AB[fp]AB[bo]AW[ap]AW[ao]AW[an]AW[bm]AW[cn]AW[cl]AW[bl]AB[ck]AB[cj]AB[bj]AB[di]AB[dl]AB[dm]AW[dk]AW[ek]AW[el]AB[em]AB[dn]AB[do]AB[co]AW[fm]AB[fl]AB[gl]AB[fj]AB[gm]AW[fn]AW[fo]AW[eo]AW[gn]AB[hn]AB[ho]C[White need not keep all his stones alive. Also see introduction above]AP[goproblems] (;W[cq] (;B[bp]C[CHOICE] (;W[bs] (;B[dr] (;W[cs] (;B[ar]C[CHOICE] (;W[bq];B[aq] (;W[bn] (;B[al]C[CHOICE] (;W[ep] (;B[ej]C[CHOICE] (;W[dp] (;B[fq]LB[en:X]C[CHOICE] (;W[eq];B[bk]LB[en:X] (;W[cp];B[fk];W[as];B[br];W[bs];B[go];W[gs]C[];B[cs]C[Blacks last ditch effort];W[as] (;B[aq]LB[en:X]C[CHOICE]LB[cm:X] (;W[cr] (;B[ds]LB[en:X]LB[cm:X]C[CHOICE] (;W[ar]C[RIGHT]) (;W[cm]C[NOTTHIS]) (;W[en]C[NOTTHIS])) (;B[ar]LB[en:X]LB[cm:X]LB[br:X]C[CHOICE] (;W[ds]C[RIGHT]) (;W[en]C[NOTTHIS]) (;W[cm]C[NOTTHIS]) (;W[br]C[NOTTHIS]))) (;W[ar];B[cr]) (;W[en]C[NOTTHIS]) (;W[cm]C[NOTTHIS])) (;B[cr]LB[en:X]LB[cm:X]C[CHOICE] (;W[aq];B[br]LB[en:X]LB[cm:X] (;W[cs];B[dr]C[Seki is excellent for whiteRIGHT]) (;W[dr];B[cs]C[White is dead]) (;W[cm]C[NOTTHIS]) (;W[en]C[NOTTHIS])) (;W[cs];B[dr]LB[cm:X]LB[en:X] (;W[aq];B[br]C[Seki is excellent for whiteRIGHT]) (;W[en]C[NOTTHIS]) (;W[cm]C[NOTTHIS])) (;W[en]C[NOTTHIS]) (;W[cm]C[NOTTHIS]))) (;W[en]C[NOTTHIS]) (;W[br];B[dr]LB[en:X] (;W[cp];B[dj]) (;W[en]C[NOTTHIS])) (;W[as];B[br] (;W[bs];B[cm]) (;W[cp];B[bs];W[gs];B[go]))) (;W[cp];B[dj];W[eq];B[fk];W[as];B[br];W[bs];B[go];W[gs];B[en]) (;W[en]C[NOTTHIS]) (;W[gs];B[eq];W[br];B[dr])) (;B[bk]C[The computer will not play this variation];W[br];B[dr];W[fq]C[RIGHT])) (;W[eq];B[bk];W[dp];B[cm];W[br];B[dr];W[as];B[aq];W[ar];B[fk]) (;W[cp];B[dj] (;W[dp];B[fq];W[eq];B[fk];W[as];B[br];W[bs];B[go];W[gs];B[en]) (;W[eq];B[bk];W[dp];B[fk];W[as];B[br];W[bs];B[cm]))) (;B[dp]C[The computer will not play this variation];W[eq] (;B[bk];W[en];B[ej];W[cp]C[RIGHT]) (;B[ej];W[as];B[br];W[bs]C[Also easy for whiteRIGHT])) (;B[eq];W[br];B[dr];W[fq];B[dp];W[cp]LB[cm:A]LB[en:B]C[And black is killed by either A or BRIGHT])) (;W[eq];B[bk] (;W[dp];B[ep] (;W[cp];B[go];W[as];B[br]) (;W[as];B[br];W[bs];B[cm])) (;W[as];B[br] (;W[bs];B[cm]) (;W[dp];B[bs];W[cp];B[ep]))) (;W[dp];B[ep] (;W[cp];B[go]) (;W[cm];B[bk];W[br];B[dr];W[as];B[aq];W[ar];B[go])) (;W[cp];B[ep];W[dp];B[go])) (;B[eq]C[The computer will not play this variation];W[br];B[dr];W[al]C[RIGHT])) (;W[ep];B[bn];W[am];B[ej];W[dp];B[fq];W[eq];B[cm]) (;W[eq];B[bn] (;W[am];B[cm] (;W[dp];B[bk]) (;W[as];B[br];W[bs];B[bk])) (;W[cm];B[am]))) (;W[br];B[dr];W[bq];B[aq]) (;W[bn];B[bq];W[br];B[dr];W[aq];B[al])) (;B[bq]C[The computer will not play this variation];W[br];B[dr];W[ar];B[aq];W[ep]C[RIGHT]) (;B[br]C[The computer will not play this variation];W[bq];B[as];W[eq];B[aq]C[This is a good two-step ko for white];W[ar]C[This is a good 2-step ko for white, but it is probably the best overall play for blackRIGHT]) (;B[aq]C[The computer will not play this variation];W[br];B[dr];W[ar];B[bq];W[ep]C[RIGHT])) (;W[br];B[ar] (;W[bq];B[aq];W[as];B[aq]) (;W[cs];B[dr];W[bq];B[aq]) (;W[aq];B[bq])) (;W[eq];B[bq];W[br];B[ar])) (;B[bq]C[The computer will not play this variation];W[br];B[ar];W[dr] (;B[aq];W[ep]C[White always saves one of his wing formationsRIGHT]) (;B[ep];W[aq]C[White always saves one of his wing formationsRIGHT])) (;B[ar]C[The computer will not play this variation];W[dr] (;B[cs];W[bq];B[aq];W[ep]C[This is better for white than the main line; he now saves bith his wing formationsRIGHT]) (;B[bq];W[br] (;B[aq];W[ep]C[White always saves one of his wing formationsRIGHT]) (;B[ep];W[aq]C[White always saves one of his wing formationsRIGHT])))) (;W[bq];B[bs] (;W[aq];B[br]C[In the end black kills at A]LB[ar:A]) (;W[br];B[aq];W[as];B[cs]) (;W[dr];B[cs] (;W[aq];B[br]LB[ar:A]C[In the end black kills at A]) (;W[br];B[aq])) (;W[eq]LB[br:A]LB[ar:B]C[Black kills in the long run by playing A and B. No hurry.])) (;W[br];B[bs];W[dr];B[cs];W[as];B[cs];W[bq];B[aq]) (;W[dr];B[bs] (;W[cs]C[A direct ko is not good enough; see the introduction]) (;W[br];B[cs] (;W[as];B[cs];W[bq];B[aq]) (;W[bq];B[aq])))) (;B[br]C[The computer will not play this variation];W[bs] (;B[bq];W[bp] (;B[dr];W[eq];B[aq];W[as];B[cp];W[cs];B[ar];W[bs]C[RIGHT]) (;B[as];W[aq];B[cs];W[ar]C[RIGHT])) (;B[bp];W[bq];B[cs];W[ar];B[as];W[aq]C[RIGHT])) (;B[bq]C[The computer will not play this variation];W[bp] (;B[br];W[bs] (;B[dr];W[eq];B[aq];W[as];B[cp];W[cs];B[ar];W[bs]C[RIGHT]) (;B[as];W[aq];B[cs];W[ar]C[RIGHT])) (;B[bs];W[ar];B[br];W[aq];B[cp] (;W[dp];B[eq];W[dr];B[ep];W[cs]) (;W[dr];B[bn];W[am];B[bk];W[as]C[Good win for whiteRIGHT]))) (;B[bs]C[The computer will not play this variation];W[bp] (;B[br];W[ar];B[cp];W[dr];B[bn];W[bq];B[cm];W[cs]C[RIGHT]) (;B[bq];W[ar];B[br];W[aq];B[cp];W[as];B[bn];W[am];B[cm];W[dr]C[RIGHT]) (;B[ar];W[bq] (;B[br];W[dr]C[RIGHT]) (;B[dr];W[br]C[RIGHT]))) (;B[dr]C[The computer will not play this variation];W[br]C[RIGHT])) (;W[bp];B[cq];W[cp];B[dp];W[ep];B[eq];W[fq];B[gs]LB[cm:X] (;W[bn];B[dr]) (;W[br];B[dr];W[bq];B[eq];W[bs];B[ar];W[bn];B[al]) (;W[cm]C[NOTTHIS])) (;W[bq];B[cq];W[br];B[cp]) (;W[ep];B[cq]C[Easy semeai win for black by capturing the upper 3 stones];W[cp];B[bp];W[bq];B[br] (;W[aq];B[dp]C[Easy win in the semeai by capturing the upper 3 white stones]) (;W[ar];B[dp]C[Still an easy win in the semeai])))