(;AB[qq]AB[pq]AW[oq]AW[op]AW[po]AW[qp]AW[mq]C[It certainly doesn't appear as if these stones will be able to live, but by playing his first stone at the vital point, Black can hope to save his stones. It's important to try everything in your power, right up to the end.]AP[goproblems] (;B[rr] (;W[rp]C[CHOICE] (;B[or];W[nr] (;B[qs]LB[pr:a]LB[os:b]LB[rr:1]LB[rp:2]LB[or:3]LB[nr:4]LB[qs:5]C[The vital point for the first move is Black 1. If White descends at 2, Blacks hanes at 3; after White blocks at 4, the diagonal play at 5 is important If White plays atari at 'a , Black has the descent at 'b', which secures two eyes. Instead of Black 5RIGHT]) (;B[ps];W[sr] (;B[qr];W[rs];B[sq];W[rq]LB[ss:a]LB[ps:1]LB[sr:2]LB[qr:3]LB[rs:4]LB[sq:5]LB[rq:6]C[Black would like to play the open connection at Black 1 here, but if he does, he won't be able to live unconditionally. White can play the attachment at 2 and in response to Black 3, continue with the hane at 4. After Black 5 and White 6, a ko fight develops at 'a'. In this position, ko is a failure for Black.]) (;B[sq];W[rq];B[ss];W[qs];B[qr];W[ns]LB[pr:a]LB[ps:1]LB[sr:2]LB[sq:3]LB[rq:4]LB[ss:5]LB[qs:6]LB[qr:7]LB[ns:8]C[What if Black answers White 2 with 3 and 5, capturing one stone? In this event, the placement at White 6 becomes the vitalpoint. Now, even if Black connects at 7, White descends to 8 and Black can no longer make an eye at 'a'. In either case, Black 1 is a mistake.CHOICE]))) (;B[qs];W[or];B[pr]C[RIGHT])) (;W[pr];B[rp];W[ro];B[qr];W[or];B[sp]LB[rr:1]LB[pr:2]LB[rp:3]LB[ro:4]LB[qr:5]LB[or:6]LB[sp:7]C[After Black's diagonal play at 1, if White plays a hane at 2, living is simple. Following Black 3 and White 4, Black can force with 5 and make life by descending at 7. Even if Black makes the empty triangle shape at 5 first, he still cannot be kept from living.RIGHT]) (;W[sp];B[or];W[nr];B[sq] (;W[qs];B[ps]C[RIGHT]) (;W[ps];B[pr];W[os];B[qs]C[RIGHT]))) (;B[rp];W[ro] (;B[rq];W[pr];B[qr];W[or]LB[rp:1]LB[ro:2]LB[rq:3]LB[pr:4]LB[qr:5]LB[or:6]C[If Black begins by playing hane and connection at 1 and 3, he makes a shape which is no longer alive. White will respond with the hane and connection at 4 and 6, and Black cannot get enough space to make life. Instead of 4, White can also simply descend to 6.]) (;B[rr];W[sp] (;B[sq];W[rq]LB[rp:1]LB[ro:2]LB[rr:3]LB[sp:4]LB[sq:5]LB[rq:6]C[What about if Black begins with the hane at 1 and then steps down to 3? While Black 1 looks to be a productive move, it's actually a poor play. When White plays atari at 4, Black is forced to block at 5 and all he gets is a ko.]) (;B[or];W[nr] (;B[qs];W[sr]LB[rp:1]LB[ro:2]LB[rr:3]LB[sp:4]LB[or:5]LB[nr:6]LB[qs:7]LB[sr:8]C[After Black 1 to White 4 of the previous diagram, lets take a look at what happens if Black tries the technique of Solution 1, by playing 5 and 7. Unfortunately, this time White has the attachment at 8, so Black ends up dead. Black 1 turns out to have been superfluous.]) (;B[sq]C[ko])))))