(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Japanese]SZ[19]KM[0.00]
PB[Black to play]C[Just play through the moves to move 30 which is the problem position. 
These do not represent a game sequence!]
;B[pr]
;W[ps]
;B[qr]
;W[qs]
;B[or]
;W[nr]
;B[oq]
;W[ns]
;B[nq]
;W[ms]
;B[mr]
;W[rr]
;B[lr]
;W[qq]
;B[ls]
;W[qp]
;B[mq]
;W[op]
;B[]
;W[np]
;B[]
;W[mp]
;B[]
;W[lq]
;B[]
;W[kq]
;B[]
;W[kr]
;B[]
;W[ks]C[This is the problem position. Black to play.]
(;B[os]C[Black threatens to make two eyes]
;W[ns]C[So white plays the vital point]
(;B[rs]C[Capturing two stones looks good]
(;W[rq]C[White must not connect]
;B[qs]C[This is two eyes for black])
(;W[qs]C[White must throw in]
;B[rq]
;W[ss]
;B[sq]
;W[rp]
;B[sr]
;W[sp]C[And the black stones are captured]))
(;B[sr]C[The clamp is sometimes a tesuji, especially in the corner.]
;W[rq]C[But white connects calmly]
;B[rs]
;W[qs]C[And this throw in kills.])
(;B[rq]C[This may be a tesuji]
;W[ss]
;B[rs]
;W[qs]
;B[sq]
;W[rp]C[But it is too late.])
(;B[ss]
;W[rq]
;B[rs]
;W[qs]C[This leads to a false eye.]))
(;B[rs]C[Trying this throw in does not work]
;W[ss]
(;B[os]
;W[ns]
(;B[rs]
;W[qs]C[Only one eye])
(;B[rq]C[Again this is too late]
;W[sq]
;B[rs]
;W[qs]C[One eye]))
(;B[rq]
;W[rp]
;B[os]
;W[ns]
;B[rs]
;W[qs]
;B[ps]
;W[sq]C[Still only one eye.]))
(;B[rq]C[Playing the cut is often a tesuji]
(;W[rs]C[If white connects...]
;B[os]
;W[ns]
;B[sr]C[This way white gets captured giving two eyes,
but can he do better?])
(;W[rp]C[If white captures the cutting stone...]
;B[os]
;W[ns]
;B[rs]
;W[sq]
;B[qs]C[Black has time to make the second eye, 
so what else can white do?])
(;W[ss]C[Steve Bailey found this reply.]
(;B[rp]
;W[ro]
(;B[sq]
;W[so]
(;B[sp]
;W[sr]
;B[os]
;W[ns]
;B[rq]
;W[sq]
;B[rs]
;W[qs]C[Only One eye])
(;B[os]
;W[ns]
;B[sr]
;W[sp]
;B[rq]
;W[sq]
;B[rs]
;W[qs]C[Still one eye.]))
(;B[qo]
;W[sp]
;B[pp]C[Can black break out here?]
;W[sq]
;B[os]
;W[ns]
;B[pq]
;W[po]
;B[oo]
;W[pn]
;B[lp]
;W[nn]C[Black cannot break through and capture on the outside.]))
(;B[sq]
;W[rp]
;B[os]
;W[ns]
;B[rs]
;W[qs]
;B[ps]
;W[sp]C[Still one eye])
(;B[sp]
;W[rp]
;B[sq]
;W[so]C[Again one eye])
(;B[sr]
;W[sq]
;B[rp]
;W[ro]
;B[os]
;W[ns]
;B[rs]
;W[qs]C[And again one eye.])))
(;B[ss]
;W[rq]C[Still the best is one eye.])
(;B[sr]C[As said earlier the clamp is often a tesuji, does
it work if played immediately?]
(;W[rs]C[If white connects here...]
;B[rq]
;W[rp]
;B[os]C[...black easily lives.])
(;W[sq]C[If white plays atari...]
;B[os]
;W[ns]
;B[rs]
;W[rq]
;B[qs]C[...again black lives])
(;W[rq]C[So what if white connects?]
(;B[os]
;W[ns]
;B[rs]
;W[qs]C[... this way black dies.])
(;B[rs]C[So black has to play the self-atari here next.
This is the correct sequence.]
(;W[sq]
;B[os]
;W[ns]
;B[qs]C[This way black also lives and its illegal to connect
the three and two white stones together.])
(;W[pq]
;B[os]
;W[ns]
;B[qs]C[Also black lives])
(;W[ss]C[So white must take the stone and fight the ko.
Ko is best result for black, so is correct result.]
(;B[os]C[Is this a ko threat for black?]
;W[ns]
;B[rs]
;W[qs]C[No as the black group dies. 

])
(;B[pd]C[Black has to play ko threats elsewhere on the board.]
;W[qc]
;B[rs]C[This ko is the correct result.]
;W[qd]C[White plays a ko threat and if black ignores it...]
;B[os]
;W[ns]
;B[qs]C[...Black wins the ko to live.]))))))
