(;AB[ai]AB[bi]AB[ci]AB[bj]AW[ah]AW[bh]AW[ch]AW[di]AW[dg]AW[dj]AB[bl]AB[cn]AB[bo]AB[co]AB[cp]AB[bq]AB[br]AB[cr]AW[bp]AW[cq]AW[dq]AW[dr]AW[dp]AW[do]AW[dn]AW[dk]AW[dl]AW[dm]AW[fr]C[White to reduce.]AP[goproblems] (;W[bm];B[cm] (;W[bk] (;B[ck]C[] (;W[cl] (;B[ak] (;W[cj] (;B[bk]C[] (;W[an] (;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;B[ap] (;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;W[ao];B[al] (;W[ar];B[bs]C[Ko threats, but no seki.]) (;W[bs];B[ar]C[Ko threats, but no seki.]) (;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.])))) (;W[al];B[am]) (;W[ao];B[ap];W[an];B[al] (;W[ar];B[bs]C[Ko threats, but no seki.]) (;W[bs];B[ar]C[Ko threats, but no seki.]) (;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.]))) (;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[an];B[ao] (;W[cj];B[bk];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[am];B[an];W[cj];B[al])) (;B[al];W[am];B[ak];W[cj];B[an]C[Ko to take the marked stones. However, they could have been killed cleanly.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[ak] (;B[cl];W[cj]C[];B[am]C[Great!RIGHT]) (;B[al] (;W[cl];B[aj] (;W[cj];B[am];W[bk]C[Great!RIGHT]) (;W[bk];B[ak] (;W[am];B[an];W[cj];B[bn]) (;W[cj];B[am]))) (;W[cj];B[cl];W[aj]C[The stones are taken, but black's position is more secure than it needs to be.RIGHT])))) (;B[cl];W[ck];B[ak];W[cj]C[Great! Black is avoiding the risk of a ko for a larger set of stones.RIGHT])) (;W[cl];B[bk] (;W[bn];B[ap]) (;W[al];B[an] (;W[am];B[ak]) (;W[ap];B[aq]))) (;W[al];B[bk];W[cl];B[an] (;W[am];B[ak]) (;W[ap];B[aq]))) (;W[cl];B[bk];W[bm];B[cm] (;W[bn];B[ap]) (;W[al];B[an] (;W[am];B[ak]) (;W[ap];B[aq]))) (;W[cm];B[bm];W[bk];B[ck];W[cj];B[ak]) (;W[bk];B[ck]C[] (;W[bm];B[cm] (;W[cl] (;B[ak] (;W[cj] (;B[bk]C[] (;W[an] (;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;B[ap] (;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;W[ao]))) (;W[al];B[am]) (;W[ao];B[ap];W[an];B[al] (;W[ar];B[bs]C[Ko threats, but no seki.]) (;W[bs];B[ar]C[Ko threats, but no seki.]) (;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.]))) (;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[an];B[ao] (;W[cj];B[bk]) (;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[am];B[an];W[cj];B[al])) (;B[al];W[am];B[ak];W[cj];B[an]C[Ko to take the marked stones. However, they could have been killed cleanly.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[ak] (;B[cl];W[cj]C[];B[am]C[Great!RIGHT]) (;B[al] (;W[cl];B[aj] (;W[cj];B[am];W[bk]C[Great!RIGHT]) (;W[bk];B[ak] (;W[am];B[an];W[cj];B[bn]) (;W[cj];B[am]))) (;W[cj];B[cl];W[aj]C[The stones are taken, but black's position is more secure than it needs to be.RIGHT])))) (;W[cl];B[ak];W[bm];B[cm] (;W[cj] (;B[bk]C[] (;W[an] (;B[ao];W[al];B[am]C[This ko is favorable for black. Otherwise, she would have reduced her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;B[ap] (;W[al];B[am]C[This ko is favorable for black. Otherwise, she would have limited her losses to the marked stones.]TR[ai]TR[bi]TR[ci]TR[bj]) (;W[ao]))) (;W[al];B[am]) (;W[ao];B[ap];W[an];B[al] (;W[ar];B[bs]C[Ko threats, but no seki.]) (;W[bs];B[ar]C[Ko threats, but no seki.]) (;W[cs];B[bs];W[ar];B[ds]C[Ko threats, but no seki.]))) (;B[am];W[bk]C[Ko to take the marked stones. However, they could have been taken cleanly.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[an];B[ao] (;W[cj];B[bk]) (;W[al];B[am]C[Ko. This ko is favorable for black. Otherwise, she would have sacrificed the marked stones earlier.]TR[ai]TR[bi]TR[ci]TR[bj])) (;W[am];B[an];W[cj];B[al])) (;W[ak];B[cl];W[cj]C[Great!RIGHT])))