kendfrey · July 5, 2025 18:37
diff --git a/snakebite_solution.sgf b/snakebite_solution.sgf
 (;GM[1]FF[4]CA[UTF-8]AP[Sabaki:0.52.2]SZ[19]DT[2025-07-01]AB[bq][bo][fq][fp][fo][ir][iq][ip][jp][ko][lp][lq][mo][mn][nn][oo][op][pq][qr][ll][lk][kk][kj][jj][ij][hk][gm][lh][lg][mg][nh][pk][qb][eb][df][fh][jg][ke][kc][jb][ia][lb][ma]AW[cp][dq][kp][kq][jq][jr][js][ks][mp][mq][nq][ms][nr][or][os][sr][po][sm][om][ol][lo][jn][ho][an][dl][dj][gj][ii][ih][hh][ki][li][mh][pi][dg][ag][ac][ab][da][ea][fb][sc][sb][ra][qa][pb][ib][jc][lc][mb][pe][kg]GN[Snakebite]AN[Kendall Frey]GC[Can black kill the white group on the lower side?]C[Black's simple move is at A to capture the cutting stone. But then white can play B to live.]LB[ln:A][lr:B];B[lr]C[Black's only option is to play the vital point.
 Locally the situation is clear. Black has three liberties on the inside. If white can find enough liberties with the cutting stone, white can capture three stones to make a second eye.]TE[1];W[ln];B[kn];W[lm];B[km];W[mm];B[nm];W[ml];B[nl];W[mk]HO[1]LB[mi:C][mj:A][nj:B]C[Since black has three liberties, the ladder is not the only option. A net or loose ladder may also be successful.](;B[mj];W[nk];B[ok];W[nj]HO[1](;B[oi]TE[1]C[This is the crucial net.](;W[mi];B[ni];W[lj](;B[oj];W[mj];B[ji];W[kh];B[jh];W[kf]HO[1]C[The ladder resumes, but now black is faced with a fork in the road.]LB[jf:A][lf:B](;B[lf]TE[1];W[jf];B[if];W[je];B[jd];W[ie];B[he];W[id];B[ic];W[hd];B[gd];W[hc];B[hb];W[gc];B[fc];W[gb];B[fa];W[ga];B[ha];W[fa];B[db];W[ca];B[cb];W[ba];B[bb];W[aa]HO[1]C[Another decision point. Black must continue the ladder in one of two directions. The net is now impossible because of the weak laddering stones.]LB[ad:A][bc:B]TR[fc][gd][he][if](;B[ad]TE[1];W[bc](;B[bd];W[cc](;B[cd];W[dc];B[ec];W[dd](;B[de];W[ed];B[fd];W[ee](;B[ef];W[fe];B[ge];W[ff](;B[fg];W[gf];B[hf];W[gg];B[gh];W[hg];B[ig];W[hi]C[Black's ladder has repaired itself. The net is once again a possibility.](;B[gi];W[hj](;B[fj];W[gk](;B[fk];W[gl](;B[hl];W[fl];B[el];W[fm];B[em];W[fn];B[gn];W[en];B[dn];W[eo](;B[do];W[ep](;B[dp];W[eq];B[cq]HO[1];W[cr](;B[ds]TE[1];W[fr](;B[es]TE[1]C[The tanuki deals the killing blow.
 https://senseis.xmp.net/?TanukiNoHaraTsuzumi
 White is no longer in atari, and so is free to play many threatening moves, but none of them quite work.]GB[1]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os](;W[dr];B[br];W[er];B[gr];W[fs];B[gs];W[cs];B[bs];W[ls];B[es]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[er];B[gr];W[dr];B[br];W[cs];B[bs];W[fs];B[gs];W[ls];B[es]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[cs](;B[gr];W[er];B[fs];W[dr];B[gs];W[ls];B[br]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[br]C[This move does work, but it's more complicated.];W[fs](;B[bs];W[gr];B[dr];W[er];B[gq];W[hr];B[hq];W[is];B[hs]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][gr][hc][hd][hg][hh][hi][hj][hr][id][ie][ih][ii][is][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[gr]BM[1];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.]))(;B[bs];W[fs];B[br]C[This reverts to the previous variation.]))(;W[fs];B[gr];W[cs](;B[gs];W[br];B[er];W[dr];B[ar]MA[aa][ab][ac][ba][bc][br][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[br]BM[1];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.]))(;W[br];B[dr];W[er];B[gr]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[gr];B[er];W[dr];B[br]MA[aa][ab][ac][ba][bc][ca][cc][cr][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[on];B[no];W[pp];B[oq];W[qq];B[pr];W[rr](;B[qs])(;B[er]BM[1]C[Black does not need to hurry to finish the capturing race.];W[qs];B[qp];W[rq](;B[qo];W[pn](;B[qn];W[ps];B[dr];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[rn];W[ps];B[dr];W[rp];B[ro];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])(;B[ro];W[ps];B[dr];W[rp];B[sp];W[qn]MA[qo][qp][ro][sp]))(;B[ro];W[ps];B[dr];W[rp];B[qo];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])))(;W[no](;B[on]C[Connecting is the correct move.])(;B[np]C[Capturing is the instinctual move, but leaves black with a lack of liberties.]BM[1];W[on];B[no];W[pp];B[oq];W[qq];B[pr];W[rr];B[er];W[qs];B[dr];W[ps];B[qp];W[rq](;B[qo];W[pn](;B[qn];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[rn];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[ro];W[rp];B[sp];W[qn]MA[qo][qp][ro][sp]))(;B[ro];W[rp];B[qo];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])))(;W[ek];B[dm];W[ej];B[fi])(;W[dm];B[ek])(;W[le];B[kd];W[ng];B[mf](;W[nf];B[me](;W[ne];B[md])(;W[md];B[ld];W[ne];B[le]))(;W[me];B[nf](;W[ne];B[og];W[of];B[ng])(;W[of];B[og];W[ne];B[ng]))(;W[ne];B[nf];W[of];B[og];W[me];B[ng])))(;B[gr]BM[1];W[dr];B[br];W[es];B[gs];W[cs];B[bs];W[ls]MA[lp][lq][lr])(;B[er]BM[1];W[dr];B[fs];W[es]C[Black has no way to fight this ko.])(;B[fs]BM[1];W[gr];B[er];W[dr];B[br];W[es]C[Black has no way to fight this ko.])(;B[dr]BM[1];W[er];B[gr];W[cs]MA[dr][ds][lp][lq][lr]))(;B[br]BM[1];W[fr](;B[gr];W[ls];B[er];W[dr];B[fs];W[mr]MA[lp][lq][lr])(;B[es];W[er];B[gr];W[ds];B[gs];W[fs];B[bs];W[ls]MA[lp][lq][lr]))(;B[er]BM[1];W[dr](;B[ds];W[fr];B[fs];W[es]C[Black has no way to fight this ko.])(;B[br];W[fr];B[gr];W[es];B[cs];W[ls]MA[lp][lq][lr]))(;B[dr]BM[1];W[er];B[fr];W[ds];B[fs];W[es](;B[br];W[ls]MA[lp][lq][lr])(;B[bs];W[br];B[ar];W[ls]MA[lp][lq][lr]))(;B[cs]BM[1];W[br];B[dr];W[er];B[es];W[ds]C[Black has no way to fight this ko.])(;B[fr]BM[1];W[dr];B[br];W[ls]MA[lp][lq][lr])(;B[es]BM[1];W[dr];B[br];W[ls]MA[lp][lq][lr]))(;B[eq]BM[1];W[dp];B[dr];W[ls]MA[lp][lq][lr]))(;B[dp]BM[1];W[dm];B[ek];W[do]))(;B[fl]BM[1]C[Is there a net somewhere in here?];W[hl](;B[im];W[il];B[jl];W[ik];B[hm];W[jm]TE[1];B[jo];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.])(;B[hm];W[il];B[jl];W[ik];B[im];W[jm]TE[1];B[jo];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.])(;B[il];W[hm];B[hn];W[im](;B[in];W[ik];B[jl];W[gn])(;B[jm];W[ik];B[jl];W[gn]))))(;B[gl]BM[1]C[This is a very similar-looking ladder, but it loses a crucial liberty.];W[fk];B[ek];W[fl];B[el];W[fm](;B[em];W[fn];B[gn];W[en];B[dn];W[eo];B[do];W[ep];B[dp];W[eq];B[cq];W[ej];B[fi];W[dm]MA[ek][el][em][lp][lq][lr])(;B[fn];W[em];B[dm];W[en];B[dn];W[eo];B[do];W[ep];B[dp];W[eq];B[cq];W[ej]MA[ek][el][lp][lq][lr])(;B[en];W[ej];B[fi];W[em]MA[ek][el][lp][lq][lr]))(;B[fl]BM[1]C[This net looks promising.];W[hl](;B[gl];W[ik];B[fk];W[hk](;B[hm];W[jl]TE[1];B[kl];W[jo]MA[bb][cb][db][eb][ec][fc][fd][gd][ge][he][hf][if][ig][ij][jg][jh][ji][jj][kj][kk][kl][km][kn][ko][lk][ll][lp][lq][lr])(;B[im];W[ls]MA[lp][lq][lr]))(;B[ik];W[gl];B[hm];W[il](;B[jl];W[im];B[in];W[hn](;B[io];W[fm];B[gn];W[fk])(;B[fk];W[io];B[jm];W[in];B[gn];W[ls]MA[lp][lq][lr]))(;B[im];W[jl];B[kl];W[jm];B[jo];W[in];B[fk];W[ls]MA[lp][lq][lr]))))(;B[fk]BM[1];W[fj];B[ej];W[ei]))(;B[fj]IT[]C[This is a valid order of moves.];W[gk];B[fk];W[gl];B[hl];W[fl](;B[gi]C[Black must come back to take the atari before continuing.];W[hj];B[el]C[Now this reverts to the main variation.])(;B[el]BM[1];W[gi]TE[1](;B[fm];W[ek];B[em];W[fi]MA[fj][fk][lp][lq][lr])(;B[fi];W[em])(;B[em];W[ls]MA[lp][lq][lr]))))(;B[gf]BM[1];W[fg];B[eg];W[gg];B[hf];W[ig]MA[bb][cb][db][eb][ec][fc][fd][gd][ge][gf][he][hf][if][lp][lq][lr]))(;B[fe]BM[1];W[ef];B[eg];W[ff];B[ge];W[hf]MA[bb][cb][db][eb][ec][fc][fd][fe][gd][ge][he][lp][lq][lr]))(;B[ed]BM[1];W[de](;B[ee];W[ce];B[cf];W[be]MA[ad][bd][cd][lp][lq][lr])(;B[ce];W[ee];B[fd];W[ge]MA[bb][cb][db][eb][ec][ed][fc][fd][gd][lp][lq][lr])))(;B[dc]BM[1];W[cd];B[ce];W[dd];B[ec];W[fd]MA[bb][cb][db][dc][eb][ec][fc][lp][lq][lr]))(;B[cc]BM[1];W[bd];B[be];W[cd];B[dd];W[ce];B[cf];W[ae]))(;B[bc]BM[1];W[ad];B[ae]IT[]C[The ladder looks broken, but black can use the stone on the fourth line to fill a liberty.];W[bd];B[cd];W[be];B[bf];W[ce];B[de];W[af];B[cf];W[ae];B[bg];W[ah];B[bh];W[ai];B[bi];W[aj];B[bj];W[ak];B[bk];W[al];B[bl];W[am];B[bn];W[ge]))(;B[jf]BM[1];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa]C[The net is now impossible because of the weak laddering stones.]TR[ne][od][pc](;B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk]IT[]C[The ladder looks broken, but black can use the stone on the fourth line to fill a liberty.];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[rn];W[so](;B[ro];W[sp];B[rp];W[sq];B[rq];W[oe])(;B[sp]IT[];W[ro];B[qo];W[rp];B[rq];W[qp](;B[qn];W[oe])(;B[pp];W[qn];B[qq];W[sq])))(;B[sd];W[rc];B[qc];W[rd];B[re];W[qd];B[pd];W[oe])))(;B[ji]C[This is a valid order of moves, but doesn't change anything about the life of the white group compared to the simple atari.]))(;W[on];B[no]C[White is free to play one forcing move before continuing.];W[pp];B[oq]C[However, this exchange creates a problem for white, allowing black an easier solution.](;W[qq];B[pr]C[This exchange doesn't fix the problem, only changes it slightly.](;W[rr];B[qs]C[The final exchange, however, solves the problem, and black must find the main variation once again.])(;W[mi];B[ni];W[lj];B[oj];W[mj];B[ji];W[kh];B[jh];W[kf];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[rn];W[so];B[sp];W[ro];B[qo];W[rp];B[rq]TR[qq]C[This time it's the other stone that's a problem for white.];W[sq];B[qp]MA[jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lj][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][nj][nk][nq][nr][oa][ob][oc][or][os][pa][pb][qa][ra][rj][rk][ro][rp][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn][so]))(;W[mi];B[ni];W[lj];B[oj];W[mj];B[ji];W[kh];B[jh];W[kf];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[so];W[rn];B[qn];W[ro];B[rp];W[qo];B[pn]TR[pp]C[The extra white stone turns out to be a liability.];W[sp];B[qp]MA[jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lj][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][nj][nk][nq][nr][oa][ob][oc][or][os][pa][pb][po][pp][qa][qo][ra][rj][rk][rn][ro][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn])))(;B[oj]BM[1];W[ni];B[oi];W[mi];B[ji];W[kh];B[jh]C[This is similar to the earlier net variation where white also has an extra liberty. This fails for the same reasons (and also some new ones).]SQ[lj])(;B[ni]BM[1];W[oj]C[This ladder is broken immediately.]))(;B[nj]BM[1];W[mj];B[mi];W[lj];B[ji];W[kh];B[jh];W[kf]C[This looks almost like a ladder, except white has an extra liberty.]LB[jf:A][lf:B]SQ[nk](;B[jf];W[lf]LB[le:A][me:C][mf:B](;B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[oe]C[The extra liberty prevents this ladder from working.])(;B[le];W[mf];B[nf];W[me];B[md];W[ne];B[oe];W[nd];B[nc];W[od]C[This ladder wouldn't even work normally.])(;B[me];W[ls]C[White has too many liberties for the net to work.]MA[lp][lq][lr]))(;B[lf];W[jf];B[if];W[je];B[jd];W[ie];B[he];W[hf]C[The extra liberty prevents this ladder from working.]))(;B[mi]BM[1](;W[mj](;B[nj]C[This reverts to the previous variation.])(;B[lj];W[ni](;B[nj];W[mh]C[Choosing this ko is very aggressive by black. Black's ko threats aren't forceful enough, and white will have the chance to fight back.];B[is]C[Black can threaten to capture part of the group.](;W[nk]C[White can afford to sacrifice.](;B[ok];W[mi];B[ls];W[on];B[no];W[qp](;B[pn];W[pm](;B[rp];W[qq](;B[pr];W[pp](;B[oq];W[rq];B[qn];W[qm]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pn][pq][pr][qn][qr][rp])(;B[rq];W[qn];B[oq];W[rr](;B[rs];W[ro]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr][rp][rq][rs])(;B[ro];W[qs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr])))(;B[qn];W[pr](;B[rq];W[rr];B[qs];W[rs];B[qo];W[ps]C[White has two eyes and is alive.]SQ[ns][ss])(;B[rr];W[rq];B[pp];W[rs]MA[qr][rr])(;B[pp];W[rq];B[qo];W[qs]MA[qr]))(;B[rq];W[qn];B[pr];W[pp];B[oq];W[rr](;B[rs];W[ro]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr][rp][rq][rs])(;B[ro];W[qs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr])))(;B[qn];W[pp];B[oq];W[qq];B[pr];W[rr](;B[qs];W[qm]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pn][pq][pr][qn][qr][qs])(;B[qm];W[qs];B[pl];W[ps];B[ro];W[rs]SQ[ns][ss]C[White has two eyes and is alive.]))(;B[qq];W[rp];B[oq];W[mr];B[kr];W[rq];B[ps];W[pp];B[np];W[rr]MA[mn][mo][nl][nm][nn][no][np][oo][op][oq][pq][ps][qq][qr])(;B[rq];W[pp];B[oq];W[qq];B[pr];W[rp];B[rr];W[sq];B[ps];W[rs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][ps][qr][rq][rr]))(;B[pp];W[qn];B[qm];W[pn];B[rp];W[qq];B[rq];W[qo];B[rn];W[ro];B[so];W[rm];B[pr];W[rr]MA[mn][mo][nl][nm][nn][no][oo][op][pp][pq][pr][qr][rn][rp][rq][so]))(;B[ls];W[on];B[no];W[qp];B[ok];W[mi]C[This reverts to the previous variation.]))(;W[mi]BM[1]C[This is black's dream. White secures the cutting stone, but the inside group will die anyway.];B[ls](;W[nk];B[on];W[pn];B[qp]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][or][os]C[Because the stones inside are now safe, black merely needs to win the capturing race against the remaining white stones.])(;W[on];B[nk];W[no];B[np];W[ok];B[oj];W[pj];B[no];W[pp];B[oq](;W[qq];B[pr];W[rr]C[Black is running very short on liberties, but this is an overplay by white.];B[oi]TE[1];W[oh];B[ph];W[og];B[qi];W[qj];B[rj];W[qk];B[ql];W[rk];B[rl];W[sk];B[sl];W[pl];B[sj];W[pk];B[pn]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][ok][ol][om][on][or][os][pi][pj][pk][pl][qj][qk][rk][sk])(;W[qk];B[qp]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][or][os]))))(;B[nk];W[nj];B[oi];W[oj];B[ok];W[pj])))(;W[nj]BM[1];B[oj]TE[1](;W[mj];B[lj];W[ni];B[oi];W[mh];B[ji]C[In this version of the ko, black can use normal laddering moves as local ko threats, making this impossible to win for white.];W[kh];B[mi];W[is];B[gr]C[Black can freely answer even the most minor of ko threats.];W[mh];B[jh];W[kf];B[mi];W[pp]C[This looks like a ko threat, but actually it is a failure for white.];B[oq];W[mh];B[nk];W[mi];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[so];W[rn];B[qn];W[ro];B[rp];W[qo];B[pn]TR[pp]C[White's ko threat filled its own liberty, allowing black to resolve the ko and capture in a ladder.];W[sp];B[qp]MA[is][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][ni][nj][nq][nr][oa][ob][oc][or][os][pa][pb][po][pp][qa][qo][ra][rj][rk][rn][ro][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn])(;W[ni];B[nk];W[mj];B[oi];W[mh];B[ji]C[As in the previous variation, black's laddering moves work as local ko threats.];W[kh];B[mi];W[is];B[gr];W[mh]C[White can continue to fight the ko as in the previous variation, equally unsuccessfully.];B[jh];W[kf];B[mi];W[lj]C[White also has the option to connect and resume the ladder.];B[jf];W[lf];B[me]C[Black is now strong enough to play the net.]MA[is][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][lf][li][lj][lm][ln][lo][mj][mk][ml][mm][mp][mq][ms][ni][nj][nq][nr][or][os]))))
	(;GM[1]FF[4]CA[UTF-8]AP[Sabaki:0.52.2]SZ[19]DT[2025-07-01]AB[bq][bo][fq][fp][fo][ir][iq][ip][jp][ko][lp][lq][mo][mn][nn][oo][op][pq][qr][ll][lk][kk][kj][jj][ij][hk][gm][lh][lg][mg][nh][pk][qb][eb][df][fh][jg][ke][kc][jb][ia][lb][ma]AW[cp][dq][kp][kq][jq][jr][js][ks][mp][mq][nq][ms][nr][or][os][sr][po][sm][om][ol][lo][jn][ho][an][dl][dj][gj][ii][ih][hh][ki][li][mh][pi][dg][ag][ac][ab][da][ea][fb][sc][sb][ra][qa][pb][ib][jc][lc][mb][pe][kg]GN[Snakebite]AN[Kendall Frey]GC[Can black kill the white group on the lower side?]C[Black's simple move is at A to capture the cutting stone. But then white can play B to live.]LB[ln:A][lr:B];B[lr]C[Black's only option is to play the vital point.
	Locally the situation is clear. Black has three liberties on the inside. If white can find enough liberties with the cutting stone, white can capture three stones to make a second eye.]TE[1];W[ln];B[kn];W[lm];B[km];W[mm];B[nm];W[ml];B[nl];W[mk]HO[1]LB[mi:C][mj:A][nj:B]C[Since black has three liberties, the ladder is not the only option. A net or loose ladder may also be successful.](;B[mj];W[nk];B[ok];W[nj]HO[1](;B[oi]TE[1]C[This is the crucial net.](;W[mi];B[ni];W[lj](;B[oj];W[mj];B[ji];W[kh];B[jh];W[kf]HO[1]C[The ladder resumes, but now black is faced with a fork in the road.]LB[jf:A][lf:B](;B[lf]TE[1];W[jf];B[if];W[je];B[jd];W[ie];B[he];W[id];B[ic];W[hd];B[gd];W[hc];B[hb];W[gc];B[fc];W[gb];B[fa];W[ga];B[ha];W[fa];B[db];W[ca];B[cb];W[ba];B[bb];W[aa]HO[1]C[Another decision point. Black must continue the ladder in one of two directions. The net is now impossible because of the weak laddering stones.]LB[ad:A][bc:B]TR[fc][gd][he][if](;B[ad]TE[1];W[bc](;B[bd];W[cc](;B[cd];W[dc];B[ec];W[dd](;B[de];W[ed];B[fd];W[ee](;B[ef];W[fe];B[ge];W[ff](;B[fg];W[gf];B[hf];W[gg];B[gh];W[hg];B[ig];W[hi]C[Black's ladder has repaired itself. The net is once again a possibility.](;B[gi];W[hj](;B[fj];W[gk](;B[fk];W[gl](;B[hl];W[fl];B[el];W[fm];B[em];W[fn];B[gn];W[en];B[dn];W[eo](;B[do];W[ep](;B[dp];W[eq];B[cq]HO[1];W[cr](;B[ds]TE[1];W[fr](;B[es]TE[1]C[The tanuki deals the killing blow.
	https://senseis.xmp.net/?TanukiNoHaraTsuzumi
	White is no longer in atari, and so is free to play many threatening moves, but none of them quite work.]GB[1]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os](;W[dr];B[br];W[er];B[gr];W[fs];B[gs];W[cs];B[bs];W[ls];B[es]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[er];B[gr];W[dr];B[br];W[cs];B[bs];W[fs];B[gs];W[ls];B[es]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[cs](;B[gr];W[er];B[fs];W[dr];B[gs];W[ls];B[br]MA[aa][ab][ac][ba][bc][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][ls][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[br]C[This move does work, but it's more complicated.];W[fs](;B[bs];W[gr];B[dr];W[er];B[gq];W[hr];B[hq];W[is];B[hs]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][fs][ga][gb][gc][gf][gg][gj][gk][gl][gr][hc][hd][hg][hh][hi][hj][hr][id][ie][ih][ii][is][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[gr]BM[1];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.]))(;B[bs];W[fs];B[br]C[This reverts to the previous variation.]))(;W[fs];B[gr];W[cs](;B[gs];W[br];B[er];W[dr];B[ar]MA[aa][ab][ac][ba][bc][br][ca][cc][cr][cs][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;B[br]BM[1];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.]))(;W[br];B[dr];W[er];B[gr]MA[aa][ab][ac][ba][bc][ca][cc][da][dc][dd][dq][ea][ed][ee][en][eo][ep][eq][er][fa][fb][fe][ff][fl][fm][fn][fr][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[gr];B[er];W[dr];B[br]MA[aa][ab][ac][ba][bc][ca][cc][cr][da][dc][dd][dq][dr][ea][ed][ee][en][eo][ep][eq][fa][fb][fe][ff][fl][fm][fn][ga][gb][gc][gf][gg][gj][gk][gl][hc][hd][hg][hh][hi][hj][id][ie][ih][ii][je][jf][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][li][lj][lm][ln][lo][mh][mi][mj][mk][ml][mm][mp][mq][ms][nj][nk][nq][nr][or][os])(;W[on];B[no];W[pp];B[oq];W[qq];B[pr];W[rr](;B[qs])(;B[er]BM[1]C[Black does not need to hurry to finish the capturing race.];W[qs];B[qp];W[rq](;B[qo];W[pn](;B[qn];W[ps];B[dr];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[rn];W[ps];B[dr];W[rp];B[ro];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])(;B[ro];W[ps];B[dr];W[rp];B[sp];W[qn]MA[qo][qp][ro][sp]))(;B[ro];W[ps];B[dr];W[rp];B[qo];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])))(;W[no](;B[on]C[Connecting is the correct move.])(;B[np]C[Capturing is the instinctual move, but leaves black with a lack of liberties.]BM[1];W[on];B[no];W[pp];B[oq];W[qq];B[pr];W[rr];B[er];W[qs];B[dr];W[ps];B[qp];W[rq](;B[qo];W[pn](;B[qn];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[rn];W[rp];B[ro];W[sp]LB[mr:A][rs:B]C[A and B are miai. White has two eyes.])(;B[ro];W[rp];B[sp];W[qn]MA[qo][qp][ro][sp]))(;B[ro];W[rp];B[qo];W[sp]C[A and B are miai. White has two eyes.]LB[mr:A][rs:B])))(;W[ek];B[dm];W[ej];B[fi])(;W[dm];B[ek])(;W[le];B[kd];W[ng];B[mf](;W[nf];B[me](;W[ne];B[md])(;W[md];B[ld];W[ne];B[le]))(;W[me];B[nf](;W[ne];B[og];W[of];B[ng])(;W[of];B[og];W[ne];B[ng]))(;W[ne];B[nf];W[of];B[og];W[me];B[ng])))(;B[gr]BM[1];W[dr];B[br];W[es];B[gs];W[cs];B[bs];W[ls]MA[lp][lq][lr])(;B[er]BM[1];W[dr];B[fs];W[es]C[Black has no way to fight this ko.])(;B[fs]BM[1];W[gr];B[er];W[dr];B[br];W[es]C[Black has no way to fight this ko.])(;B[dr]BM[1];W[er];B[gr];W[cs]MA[dr][ds][lp][lq][lr]))(;B[br]BM[1];W[fr](;B[gr];W[ls];B[er];W[dr];B[fs];W[mr]MA[lp][lq][lr])(;B[es];W[er];B[gr];W[ds];B[gs];W[fs];B[bs];W[ls]MA[lp][lq][lr]))(;B[er]BM[1];W[dr](;B[ds];W[fr];B[fs];W[es]C[Black has no way to fight this ko.])(;B[br];W[fr];B[gr];W[es];B[cs];W[ls]MA[lp][lq][lr]))(;B[dr]BM[1];W[er];B[fr];W[ds];B[fs];W[es](;B[br];W[ls]MA[lp][lq][lr])(;B[bs];W[br];B[ar];W[ls]MA[lp][lq][lr]))(;B[cs]BM[1];W[br];B[dr];W[er];B[es];W[ds]C[Black has no way to fight this ko.])(;B[fr]BM[1];W[dr];B[br];W[ls]MA[lp][lq][lr])(;B[es]BM[1];W[dr];B[br];W[ls]MA[lp][lq][lr]))(;B[eq]BM[1];W[dp];B[dr];W[ls]MA[lp][lq][lr]))(;B[dp]BM[1];W[dm];B[ek];W[do]))(;B[fl]BM[1]C[Is there a net somewhere in here?];W[hl](;B[im];W[il];B[jl];W[ik];B[hm];W[jm]TE[1];B[jo];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.])(;B[hm];W[il];B[jl];W[ik];B[im];W[jm]TE[1];B[jo];W[ls]MA[lp][lq][lr]C[Black cannot fill a liberty.])(;B[il];W[hm];B[hn];W[im](;B[in];W[ik];B[jl];W[gn])(;B[jm];W[ik];B[jl];W[gn]))))(;B[gl]BM[1]C[This is a very similar-looking ladder, but it loses a crucial liberty.];W[fk];B[ek];W[fl];B[el];W[fm](;B[em];W[fn];B[gn];W[en];B[dn];W[eo];B[do];W[ep];B[dp];W[eq];B[cq];W[ej];B[fi];W[dm]MA[ek][el][em][lp][lq][lr])(;B[fn];W[em];B[dm];W[en];B[dn];W[eo];B[do];W[ep];B[dp];W[eq];B[cq];W[ej]MA[ek][el][lp][lq][lr])(;B[en];W[ej];B[fi];W[em]MA[ek][el][lp][lq][lr]))(;B[fl]BM[1]C[This net looks promising.];W[hl](;B[gl];W[ik];B[fk];W[hk](;B[hm];W[jl]TE[1];B[kl];W[jo]MA[bb][cb][db][eb][ec][fc][fd][gd][ge][he][hf][if][ig][ij][jg][jh][ji][jj][kj][kk][kl][km][kn][ko][lk][ll][lp][lq][lr])(;B[im];W[ls]MA[lp][lq][lr]))(;B[ik];W[gl];B[hm];W[il](;B[jl];W[im];B[in];W[hn](;B[io];W[fm];B[gn];W[fk])(;B[fk];W[io];B[jm];W[in];B[gn];W[ls]MA[lp][lq][lr]))(;B[im];W[jl];B[kl];W[jm];B[jo];W[in];B[fk];W[ls]MA[lp][lq][lr]))))(;B[fk]BM[1];W[fj];B[ej];W[ei]))(;B[fj]IT[]C[This is a valid order of moves.];W[gk];B[fk];W[gl];B[hl];W[fl](;B[gi]C[Black must come back to take the atari before continuing.];W[hj];B[el]C[Now this reverts to the main variation.])(;B[el]BM[1];W[gi]TE[1](;B[fm];W[ek];B[em];W[fi]MA[fj][fk][lp][lq][lr])(;B[fi];W[em])(;B[em];W[ls]MA[lp][lq][lr]))))(;B[gf]BM[1];W[fg];B[eg];W[gg];B[hf];W[ig]MA[bb][cb][db][eb][ec][fc][fd][gd][ge][gf][he][hf][if][lp][lq][lr]))(;B[fe]BM[1];W[ef];B[eg];W[ff];B[ge];W[hf]MA[bb][cb][db][eb][ec][fc][fd][fe][gd][ge][he][lp][lq][lr]))(;B[ed]BM[1];W[de](;B[ee];W[ce];B[cf];W[be]MA[ad][bd][cd][lp][lq][lr])(;B[ce];W[ee];B[fd];W[ge]MA[bb][cb][db][eb][ec][ed][fc][fd][gd][lp][lq][lr])))(;B[dc]BM[1];W[cd];B[ce];W[dd];B[ec];W[fd]MA[bb][cb][db][dc][eb][ec][fc][lp][lq][lr]))(;B[cc]BM[1];W[bd];B[be];W[cd];B[dd];W[ce];B[cf];W[ae]))(;B[bc]BM[1];W[ad];B[ae]IT[]C[The ladder looks broken, but black can use the stone on the fourth line to fill a liberty.];W[bd];B[cd];W[be];B[bf];W[ce];B[de];W[af];B[cf];W[ae];B[bg];W[ah];B[bh];W[ai];B[bi];W[aj];B[bj];W[ak];B[bk];W[al];B[bl];W[am];B[bn];W[ge]))(;B[jf]BM[1];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa]C[The net is now impossible because of the weak laddering stones.]TR[ne][od][pc](;B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk]IT[]C[The ladder looks broken, but black can use the stone on the fourth line to fill a liberty.];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[rn];W[so](;B[ro];W[sp];B[rp];W[sq];B[rq];W[oe])(;B[sp]IT[];W[ro];B[qo];W[rp];B[rq];W[qp](;B[qn];W[oe])(;B[pp];W[qn];B[qq];W[sq])))(;B[sd];W[rc];B[qc];W[rd];B[re];W[qd];B[pd];W[oe])))(;B[ji]C[This is a valid order of moves, but doesn't change anything about the life of the white group compared to the simple atari.]))(;W[on];B[no]C[White is free to play one forcing move before continuing.];W[pp];B[oq]C[However, this exchange creates a problem for white, allowing black an easier solution.](;W[qq];B[pr]C[This exchange doesn't fix the problem, only changes it slightly.](;W[rr];B[qs]C[The final exchange, however, solves the problem, and black must find the main variation once again.])(;W[mi];B[ni];W[lj];B[oj];W[mj];B[ji];W[kh];B[jh];W[kf];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[rn];W[so];B[sp];W[ro];B[qo];W[rp];B[rq]TR[qq]C[This time it's the other stone that's a problem for white.];W[sq];B[qp]MA[jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lj][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][nj][nk][nq][nr][oa][ob][oc][or][os][pa][pb][qa][ra][rj][rk][ro][rp][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn][so]))(;W[mi];B[ni];W[lj];B[oj];W[mj];B[ji];W[kh];B[jh];W[kf];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[so];W[rn];B[qn];W[ro];B[rp];W[qo];B[pn]TR[pp]C[The extra white stone turns out to be a liability.];W[sp];B[qp]MA[jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lj][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][nj][nk][nq][nr][oa][ob][oc][or][os][pa][pb][po][pp][qa][qo][ra][rj][rk][rn][ro][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn])))(;B[oj]BM[1];W[ni];B[oi];W[mi];B[ji];W[kh];B[jh]C[This is similar to the earlier net variation where white also has an extra liberty. This fails for the same reasons (and also some new ones).]SQ[lj])(;B[ni]BM[1];W[oj]C[This ladder is broken immediately.]))(;B[nj]BM[1];W[mj];B[mi];W[lj];B[ji];W[kh];B[jh];W[kf]C[This looks almost like a ladder, except white has an extra liberty.]LB[jf:A][lf:B]SQ[nk](;B[jf];W[lf]LB[le:A][me:C][mf:B](;B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[oe]C[The extra liberty prevents this ladder from working.])(;B[le];W[mf];B[nf];W[me];B[md];W[ne];B[oe];W[nd];B[nc];W[od]C[This ladder wouldn't even work normally.])(;B[me];W[ls]C[White has too many liberties for the net to work.]MA[lp][lq][lr]))(;B[lf];W[jf];B[if];W[je];B[jd];W[ie];B[he];W[hf]C[The extra liberty prevents this ladder from working.]))(;B[mi]BM[1](;W[mj](;B[nj]C[This reverts to the previous variation.])(;B[lj];W[ni](;B[nj];W[mh]C[Choosing this ko is very aggressive by black. Black's ko threats aren't forceful enough, and white will have the chance to fight back.];B[is]C[Black can threaten to capture part of the group.](;W[nk]C[White can afford to sacrifice.](;B[ok];W[mi];B[ls];W[on];B[no];W[qp](;B[pn];W[pm](;B[rp];W[qq](;B[pr];W[pp](;B[oq];W[rq];B[qn];W[qm]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pn][pq][pr][qn][qr][rp])(;B[rq];W[qn];B[oq];W[rr](;B[rs];W[ro]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr][rp][rq][rs])(;B[ro];W[qs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr])))(;B[qn];W[pr](;B[rq];W[rr];B[qs];W[rs];B[qo];W[ps]C[White has two eyes and is alive.]SQ[ns][ss])(;B[rr];W[rq];B[pp];W[rs]MA[qr][rr])(;B[pp];W[rq];B[qo];W[qs]MA[qr]))(;B[rq];W[qn];B[pr];W[pp];B[oq];W[rr](;B[rs];W[ro]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr][rp][rq][rs])(;B[ro];W[qs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][qr])))(;B[qn];W[pp];B[oq];W[qq];B[pr];W[rr](;B[qs];W[qm]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pn][pq][pr][qn][qr][qs])(;B[qm];W[qs];B[pl];W[ps];B[ro];W[rs]SQ[ns][ss]C[White has two eyes and is alive.]))(;B[qq];W[rp];B[oq];W[mr];B[kr];W[rq];B[ps];W[pp];B[np];W[rr]MA[mn][mo][nl][nm][nn][no][np][oo][op][oq][pq][ps][qq][qr])(;B[rq];W[pp];B[oq];W[qq];B[pr];W[rp];B[rr];W[sq];B[ps];W[rs]MA[mn][mo][nl][nm][nn][no][oo][op][oq][pq][pr][ps][qr][rq][rr]))(;B[pp];W[qn];B[qm];W[pn];B[rp];W[qq];B[rq];W[qo];B[rn];W[ro];B[so];W[rm];B[pr];W[rr]MA[mn][mo][nl][nm][nn][no][oo][op][pp][pq][pr][qr][rn][rp][rq][so]))(;B[ls];W[on];B[no];W[qp];B[ok];W[mi]C[This reverts to the previous variation.]))(;W[mi]BM[1]C[This is black's dream. White secures the cutting stone, but the inside group will die anyway.];B[ls](;W[nk];B[on];W[pn];B[qp]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][or][os]C[Because the stones inside are now safe, black merely needs to win the capturing race against the remaining white stones.])(;W[on];B[nk];W[no];B[np];W[ok];B[oj];W[pj];B[no];W[pp];B[oq](;W[qq];B[pr];W[rr]C[Black is running very short on liberties, but this is an overplay by white.];B[oi]TE[1];W[oh];B[ph];W[og];B[qi];W[qj];B[rj];W[qk];B[ql];W[rk];B[rl];W[sk];B[sl];W[pl];B[sj];W[pk];B[pn]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][ok][ol][om][on][or][os][pi][pj][pk][pl][qj][qk][rk][sk])(;W[qk];B[qp]MA[jq][jr][js][kp][kq][ks][mp][mq][ms][nq][nr][or][os]))))(;B[nk];W[nj];B[oi];W[oj];B[ok];W[pj])))(;W[nj]BM[1];B[oj]TE[1](;W[mj];B[lj];W[ni];B[oi];W[mh];B[ji]C[In this version of the ko, black can use normal laddering moves as local ko threats, making this impossible to win for white.];W[kh];B[mi];W[is];B[gr]C[Black can freely answer even the most minor of ko threats.];W[mh];B[jh];W[kf];B[mi];W[pp]C[This looks like a ko threat, but actually it is a failure for white.];B[oq];W[mh];B[nk];W[mi];B[jf];W[lf];B[mf];W[le];B[ld];W[me];B[ne];W[md];B[mc];W[nd];B[od];W[nc];B[nb];W[oc];B[pc];W[ob];B[pa];W[oa];B[na];W[pa];B[rb];W[sa];B[rc];W[sd];B[rd];W[se];B[re];W[sf];B[rf];W[sg];B[rg];W[sh];B[rh];W[si];B[ri];W[sj];B[sk];W[rj];B[qj];W[rk];B[rl];W[sl];B[qk];W[sk];B[rm];W[sn];B[so];W[rn];B[qn];W[ro];B[rp];W[qo];B[pn]TR[pp]C[White's ko threat filled its own liberty, allowing black to resolve the ko and capture in a ladder.];W[sp];B[qp]MA[is][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][le][lf][li][lm][ln][lo][md][me][mh][mi][mj][mk][ml][mm][mp][mq][ms][nc][nd][ni][nj][nq][nr][oa][ob][oc][or][os][pa][pb][po][pp][qa][qo][ra][rj][rk][rn][ro][sa][sb][sc][sd][se][sf][sg][sh][si][sj][sk][sl][sm][sn])(;W[ni];B[nk];W[mj];B[oi];W[mh];B[ji]C[As in the previous variation, black's laddering moves work as local ko threats.];W[kh];B[mi];W[is];B[gr];W[mh]C[White can continue to fight the ko as in the previous variation, equally unsuccessfully.];B[jh];W[kf];B[mi];W[lj]C[White also has the option to connect and resume the ladder.];B[jf];W[lf];B[me]C[Black is now strong enough to play the net.]MA[is][jq][jr][js][kf][kg][kh][ki][kp][kq][ks][lf][li][lj][lm][ln][lo][mj][mk][ml][mm][mp][mq][ms][ni][nj][nq][nr][or][os]))))