(;AW[ar]AW[as]AW[br]AW[dq]AW[er]AW[fr]AW[gr]AB[ds]AB[es]AB[hs]AB[is]AB[js]AB[kr]AB[lr]AB[ls]AB[eq]AB[fq]AB[gq]AW[hq]AW[hr]AB[hp]AW[iq]AW[jq]AW[kq]AW[lq]AB[mq]AB[nq]AB[nr]AW[mr]AW[ns]AB[lp]AB[kp]AB[ip]AB[jp]AB[dp]AB[cp]AB[bo]AB[cn]AP[goproblems] (;W[dr] (;B[cs]C[] (;W[gs] (;B[cr]C[];W[cq];B[bq] (;W[aq] (;B[bp]C[];W[fs];B[ap];W[bs] (;B[ds]C[] (;W[cs];B[cr];W[br] (;B[cs]C[CHOICE] (;W[bs];B[ar];W[es];B[cs] (;W[jr] (;B[aq];W[ir];B[as] (;W[ks];B[js] (;W[is];B[cr];W[ks]C[Hoping to deceive white, black refused his best ko opportunity; he now pays the price fighting a direct koRIGHT]) (;W[cr];B[is])) (;W[cr];B[ds])) (;B[cr]C[This path is for informational purposes only; the computer will not play it];W[ds];B[cr];W[cs];B[aq];W[ir]C[RIGHT])) (;W[ir];B[jr]C[Oops...])) (;W[ar];B[bs];W[es];B[ms];W[as];B[cs])) (;B[bs]C[CHOICE] (;W[cs]C[];B[ar] (;W[as]C[] (;B[nn]C[Well done! You live if you survive what is almost a 1-step ko! To illustrate this, black starts with a ko threat which you choose to ignore. Please play at ARIGHT]LB[aq:A];W[aq]C[];B[mn]C[Black cashes in and white is not yet safe. You can only leave this situation if you have superior ko threats. Please play at A]LB[ar:A];W[ar]C[];B[ln]C[FINISHED. Black takes sente as is typical for a 1-step ko.RIGHT]) (;B[aq]C[This path is for informational purposes only; it will not be played by the computer];W[es];B[bs]C[This is a 'black take first' ko but it is not as good as starting it one move earlier which is almost equal to a 1-step koRIGHT])) (;W[es]C[No point in being defensive yet. Your chances of winning the ko are the same but you'll lose a few points in the corner.])) (;W[ar];B[cs]C[FORCE];W[es];B[ms];W[as];B[cs]))) (;W[jr];B[cs];W[ir];B[cr];W[ks];B[js]) (;W[ir];B[jr]) (;W[cr];B[jr])) (;B[cs]C[This path is for informational purposes only; the computer will not play it];W[ds];B[cr];W[br]C[RIGHT])) (;B[ap]C[This path is for informational purposes only; the computer will not play it.];W[bp]C[White will play the ko; he won't get anything better in the main lineRIGHT])) (;W[fs];B[aq];W[bs];B[ds] (;W[cs];B[cr];W[br];B[cs];W[bs];B[ar];W[es];B[cs];W[jr];B[as];W[ir];B[cr];W[ks];B[js];W[is];B[ms]C[Not quite there]) (;W[jr];B[cs];W[ir];B[cr];W[ks];B[js]) (;W[es];B[cs]))) (;B[jr];W[cr]C[SekiRIGHT])) (;W[fs];B[cq]) (;W[cq];B[gs];W[fs];B[bq] (;W[jr];B[ms] (;W[cr];B[os]C[Black escapes in time with his bottom stones]) (;W[ir];B[cr])) (;W[aq];B[bp];W[jr];B[ms] (;W[cr];B[os]C[Black escapes in time with his bottom stones]) (;W[ir];B[cr]))) (;W[cr];B[gs] (;W[jr];B[os];W[fs];B[ms]) (;W[fs];B[os];W[jr];B[ms]))) (;B[gs]C[This path is for informational purposes only; it will not be played by the computer] (;W[fs];B[cs];W[jr] (;B[ms];W[ir];B[cr];W[ks]C[And black loses 4 more stones on the left or the rightRIGHT]) (;B[cr];W[cq];B[bq];W[bs]C[RIGHT])) (;W[cs]C[This would be an error!];B[fs];W[jr];B[cr];W[cq];B[bq];W[aq];B[bp];W[cr];B[ap]C[White cannot approach];W[ir];B[bs])) (;B[cq]C[This path is for informational purposes only; it will not be played by the computer];W[cr] (;B[cs];W[gs];B[ms]C[SekiRIGHT]) (;B[gs];W[cs];B[fs];W[jr];B[bq];W[ir]C[Just in time!RIGHT]))) (;W[cq];B[cs] (;W[bp];B[dr] (;W[ap];B[gs]C[Over and out!]) (;W[cr];B[ap])) (;W[dr];B[gs];W[fs];B[bq] (;W[jr];B[ms] (;W[cr];B[os]C[Black escapes in time with his bottom stones]) (;W[ir];B[cr])) (;W[aq];B[bp];W[jr];B[ms] (;W[cr];B[os]C[Black escapes in time with his bottom stones]) (;W[ir];B[cr]))) (;W[cr];B[gs];W[fs]C[Easy for black even playing tenuki]) (;W[jr];B[dr];W[cr]C[Black can play tenuki here]) (;W[aq];B[bp]C[The last exchange won't help; navigate the variations without it])) (;W[cs];B[cq];W[dr];B[cr]) (;W[cr];B[dr];W[cq];B[cs];W[bp];B[ap]) (;W[jr];B[cq]))