(;AB[rs]AB[qr]AB[qq]AB[qp]AB[pp]AB[op]AB[oq]AB[qo]AB[rn]AB[qn]AB[so]AB[pm]AB[qm]AB[ql]AB[rk]AB[sl]AB[qh]AW[pq]AW[pr]AW[ps]AW[qs]AW[or]AW[os]AB[nr]AW[ms]AW[mr]AW[nq]AW[mq]TR[mq]AB[ls]AB[lr]AB[lq]AB[lp]AB[lo]AB[ln]AB[lm]AB[ll]AB[lk]AB[lj]AB[mj]AB[nk]AB[ni]AB[oj]AB[ok]AB[pj]AB[pi]AB[qg]AB[pf]AB[pe]AB[qe]AB[re]AB[pd]AW[qd]AB[qc]AB[qb]AW[rd]AW[rc]AW[rb]AW[pb]AW[pc]AW[nc]AW[oc]AW[od]AW[nb]AW[na]AW[mc]AB[mb]AB[ma]AB[lb]AB[lc]AB[ld]AB[le]AB[ne]AB[oe]AW[np]AW[no]AW[oo]AW[po]AW[nm]AW[ol]AW[nl]AW[ml]AW[mk]AW[pl]AW[pk]AW[qk]AW[qj]AW[qi]AW[rj]AW[rh]C[White has just played the marked stone. Black to kill.]AP[goproblems] (;B[ns]C[];W[sg] (;B[sf];W[si];B[rg];W[or];B[sh]C[Ko. Black can do better. Why capture the stones if you can kill all of them anyway?]) (;B[si];W[se] (;B[sj] (;W[ri]C[White escapes.]) (;W[sh];B[sk];W[ri]C[White escapes.])) (;B[rg];W[sh]C[White escapes.])) (;B[sj];W[se]C[White escapes.]) (;B[sh];W[si]C[White will find it easy to make two eyes or to escape now.])) (;B[sg] (;W[rg] (;B[sf]C[] (;W[si]C[CHOICE];B[sh]C[Correct! Finding T13 is the clincher. I had previously thought white was alive unconditionally after N3, and it took me a few hours to find T13.RIGHT]) (;W[sh]C[CHOICE];B[sj]C[Correct! Finding T13 is the clincher. I had previously thought white was alive unconditionally after N3, and it took me a few hours to find T13.RIGHT]) (;W[sj]C[CHOICE];B[sh]C[Correct! Finding T13 is the clincher. I had previously thought white was alive unconditionally after N3, and it took me a few hours to find T13.RIGHT])) (;B[rf];W[si];B[sj]C[];W[sk]C[Ko.]) (;B[sh];W[sf]) (;B[si];W[sf] (;B[se];W[rf];B[sj];W[sh]) (;B[ri];W[sh])) (;B[sj];W[si] (;B[sk];W[sf];B[rf]C[Correct! Thanks to BartTM for finding this variation! Good eye!RIGHT]) (;B[rf];W[sk]C[Ko.]) (;B[sf];W[sk];B[rl];W[sh];B[sj]C[Ko. Probably the most favorable ko I've found though, as in this one black takes first.]))) (;W[si] (;B[sh]C[Correct! Finding T13 is the clincher. I had previously thought white was alive unconditionally after N3, and it took me a few hours to find T13.RIGHT]) (;B[sk];W[sj];B[sh];W[rg];B[sf]C[RIGHT]) (;B[rg];W[sh];B[sj];W[sk]C[Ko.])) (;W[sh];B[sj]C[Correct! Finding T13 is the clincher. I had previously thought white was alive unconditionally after N3, and it took me a few hours to find T13.RIGHT])) (;B[si];W[sj];B[sh] (;W[rg]C[FORCE];B[sg];W[sf]C[However, if white were to mistakenly atari at T13 instead of first extending an extra stone, white would die.]) (;W[sg]C[White should not play this move.];B[rg];W[sf];B[se];W[ri];B[sh]C[This variation was to demonstrate the result of white's mistake.])) (;B[sj];W[si] (;B[rg];W[sk]C[Ko.]) (;B[sk];W[sg]MA[rg]MA[se]C[White lives with either S13 or T15.])) (;B[rg];W[si];B[sj];W[sk]C[Ko.]) (;B[sh];W[rg] (;B[sg];W[sf]) (;B[si];W[sj];B[sg];W[sf]C[However, if white were to mistakenly atari at T13 instead of first extending an extra stone, white would die.]) (;B[sj];W[sg] (;B[si];W[se]) (;B[sf];W[si]) (;B[se];W[si]))) (;B[ri];W[si] (;B[rg];W[sj]) (;B[sj];W[sg] (;B[rg];W[se]) (;B[sf];W[rg]) (;B[se];W[rg]))) (;B[sk];W[sg] (;B[sj];W[se]) (;B[si] (;W[se] (;B[ri];W[sj];B[rg];W[sh]) (;B[sj];W[ri])) (;W[sj];B[rg];W[se];B[sh];W[sf];B[ri];W[rh])) (;B[sf];W[rg] (;B[sj];W[si]) (;B[si];W[sj])) (;B[se];W[rg] (;B[si];W[sj]) (;B[sj];W[si])) (;B[rg];W[sh] (;B[sj];W[se]) (;B[si] (;W[se];B[sj];W[ri]) (;W[sj];B[sf];W[ri])))))