(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2] RU[Japanese]SZ[19]KM[0.00] PW[White]PB[Black]AW[nc][dd][cn][dp]AB[fc][pd][cf][pf][qk][qo][fq][pq]C[Notes on corner variations and 3-3 invasions]PL[W] (;W[qc]C[3-3 invasion into one space high 4-4 corner] (;B[qd]C[Wrong move] ;W[pc]C[Easy points for white]) (;B[pc] ;W[pb] (;B[ob]TR[ic][jc][kc][id][jd][kd]C[Rule of thumb - Block if black has a stone in the side areas] ;W[qb] ;B[oc] ;W[re] ;B[rf] ;W[qe] ;B[qf] ;W[pe] ;B[oe] ;W[of]C[What if white cuts? DO NOT ATARI] (;B[nf]C[Black has two weaknesses after atari] ;W[og]LB[ne:A][qh:B]C[Now black has two weaknesses] (;B[qh] ;W[ne]C[Painful cut]) (;B[ne] ;W[qh]C[Black Captured])) (;B[ne] ;W[og] ;B[ph])) (;B[qd]SQ[ic][jc][kc][id][jd][kd]C[Rule of thumb - Block here if white has a stone around the square area] ;W[rb] ;B[rc] ;W[qb])) (;AE[nc][dd][pf][qk][cn][dp][fq][pq] ;B[pc] ;W[qd] ;B[qe] ;W[re] ;B[qf] ;W[pb] ;B[ob] ;W[qb] ;B[nc]C[What if white tenuki?] ;W[dp] ;B[rf]C[White can still live] (;W[rd]) (;W[sd]C[White lives but gets reduced a bit] ;B[sf]C[Is this sente for white?] (;W[dd] (;B[pa]C[Hane of death?] ;W[sb]C[not this time. White lives.] ;B[ra] ;W[qa] ;B[se] ;W[oa] ;B[na] ;W[rd]) (;B[sb] ;W[sc] ;B[se] ;W[rb] ;B[rd] ;W[sa]C[White lives in the corner. Good end game, I guess.]) (;B[rd]C[Killing move.] ;W[rc] ;B[sb] (;W[se] ;B[sc] ;W[rd]C[White is dead in the corner]) (;W[pa] (;B[se] ;W[ra]C[White lives with black mistake]) (;B[ra] ;W[rb] ;B[se]C[White is dead in the corner] ;W[rd] ;B[oa]C[Dead four in the corner.] ;B[sa] ;W[pp] ;B[sc] ;W[qa] ;B[sb] ;W[sa] ;B[ra]C[Looks like ko, but this ko can only be started by black. So under most rules, this shape is deemed to be dead.])))) (;W[sb]C[Proper move to live])))) (;B[cq]C[3-3 invasion into knight jump 4-4 corner] ;W[dq] ;B[dr] (;W[cp] ;B[br] ;W[bq] ;B[cr] ;W[ck]C[Even exchange]) (;W[er] ;B[cr] ;W[eq] ;B[bo] (;W[co]C[Typically inferior to blocking B6] ;B[bn] ;W[bm] ;B[cp] ;W[cm]C[White looks strong, but black can do a lot of things here. See model variations] ;B[fr] (;W[es] ;B[fo]C[Black has good shape on the outside]) (;W[fp] ;B[gp] ;W[go] ;B[fo] ;W[ep] ;B[hp]C[White has a dumpling shape and is inefficient])) (;W[bn] ;B[co] (;W[do] (;B[dn]C[What is white cuts? DO NOT ATARI] (;W[dm]C[White has two weaknesses after atari] ;B[en] (;W[fp] ;B[cm]C[Painful cut for white]) (;W[cl] ;B[fp]C[Five white stones are in trouble])) (;W[cl] ;B[en] ;W[fp] ;B[el]C[White can handle both groups] ;W[ao]C[Black is dead in the corner] (;B[ap] ;W[cp] ;B[bp] ;W[bq]) (;B[bp]C[Empty triangle] ;W[ds] ;B[cs] ;W[ap] ;B[aq] ;W[br] ;B[an] ;W[ao]))) (;B[cp] ;W[dn]C[Proper exchange for both sides])) (;W[dn]C[What if white does not want to get cut and extend?] ;B[cf] ;W[ao] ;B[ap]LB[do:A]C[Black can block now since it has a liberty] ;W[ar] ;B[cp] ;W[an] ;B[ds] ;W[bp] ;B[bq] ;W[aq]C[This is ko for life for black])))) (;B[qp] (;AE[dd][pf][qk][cn][pq]AW[lc][qg][oj][qj][co][fq][hq]AB[nc][qe][ol][ql][cm][jp][nq]PL[B] (;W[qc]C[White has stones on both sides of the enclosure. Can black capture? Rule of thumb - white can live if it has help from both sides] (;B[rd] ;W[ob] ;B[oc] ;W[nb] ;B[pb] ;W[mc]C[White reduced black and left a bad aji in the corner]) (;B[qd] ;W[pb]C[Variation for white to live - incomplete..]) (;B[pc] (;W[pb] (;B[ob] (;W[rb]C[Bad move by white. Cannot live.] ;B[rd] ;W[rc] ;B[qa]C[White dead in the corner.]) (;W[rd] (;B[re] ;W[rb] ;B[pa] ;W[qa]C[White has ko for life in black's corner. Good ko for white.]) (;B[qb] ;W[rb] ;B[pa] ;W[re]C[Compromise. White reduced black's corner.]))) (;B[rc] ;W[rb] ;B[rd] ;W[nb]C[Marked stone is helping white. Black must block. ] ;B[mb] ;W[ob] ;B[mc] ;W[sb]C[White lives? Not really.] ;B[na] ;W[oa] ;B[qa]SQ[pb]C[White is dead, despite all the help. Q18 is a bad move for direct life.])) (;W[rd] (;B[re] ;W[pb] (;B[rb]C[Kill white] ;W[qb] ;B[ob] ;W[ra] ;B[sb] (;W[pa] ;B[sd]) (;W[se] ;B[sf] ;W[sd] ;B[rf] ;W[pa]C[White lives... because there are helping stones around.])) (;B[ob] ;W[rb]C[Ko variation])) (;B[dd] ;W[cc]LB[ec:A][ce:B]C[Black's enclosure is not perfect, despite three stones. Should have played at A or B. White invades. Black can still capture! but leaves some bad aji behind.] (;B[cd] ;W[dc] (;B[ec] ;W[bd] ;B[be] ;W[bb] ;B[ad] ;W[ac]C[Ko variation.]) (;B[eb]C[Strong move to kill!] ;W[ec] ;B[ed] ;W[db] ;B[fb] ;W[bb]C[White lives outright without ko.])) (;B[eb]C[Move to kill.] (;W[cd] ;B[ce] ;W[dc] ;B[ec] ;W[db] ;B[bd]C[White can't live]) (;W[be] ;B[bf] ;W[ce] ;B[de] ;W[db] ;B[ae]C[White dies in the corner.] (;W[bd] ;B[bb]) (;W[bb] ;B[ac]C[White is dead here as well.] ;W[ab] ;B[ca]))))))) (;B[cq]C[Black has stones on only one sides of the enclosure. Can White capture? Rule of thumb - black can't live if white has help on one side] ;W[dq] (;B[dr] (;W[er]C[Ko variation - black can do better] ;B[bp] ;W[bo] ;B[br] ;W[ds] ;B[cs]) (;W[bq] ;B[br] ;W[bp] ;B[er] ;W[fp] ;B[fr] ;W[gr] ;B[ar] ;W[fs] ;B[es] ;W[cs]C[Black dead in the corner])) (;B[bp] ;W[bo] (;B[br] ;W[dr]C[Prevent the double tiger's mouth] ;B[aq] ;W[cr] ;B[cp] ;W[ao] ;B[ap] ;W[bs]C[Black dead in the corner]) (;B[dr] ;W[br]C[Prevent the double tiger's mouth] ;B[cr] ;W[bq] ;B[cp] ;W[ap] ;B[do] ;W[er]C[Black dead in the corner])))) (;AE[dd][qk][pq]AW[pf][qf][qj][ck][qn]AB[kc][nc][qe][jp][mp][oq] (;W[od]C[Tricky play by white] ;B[oc] ;W[qc] (;B[pc]C[No good by black] ;W[re] ;B[qd] ;W[rd] ;B[rc]C[White reduces black]) (;B[qd]C[Empty triangle] ;W[pc] ;B[oe]SQ[od][cn]C[Ladder does not work for black right now]) (;B[re]C[Sealed off white with weaknesses] ;W[pc] ;B[oe] ;W[pe]LB[nd:A][qd:B]C[Black can choose A or B, but white will take the other]) (;B[pe]C[Empty triangle, but a tesuji] (;W[pc] ;B[oe] (;W[rd] ;B[re] ;W[rb] ;B[of]C[black gets out strongly]) (;W[nd] ;B[md] ;W[ne] ;B[of]C[White is divided on all sides])) (;W[re]C[Proper move by white] ;B[rd] ;W[rf]TR[rc]C[Black must continue] (;B[dd] ;W[rc]C[White gets in the corner]) (;B[rc] ;W[oe]SQ[pc]C[Black must continue] (;B[dd] ;W[pc] ;B[qd] ;W[rb]C[White captures black stones]) (;B[pc]C[Good variation]))))) (;W[eq]C[Kicking stone may be sente, but worth very little as it does not defend the corner.] ;B[fp] ;W[en]C[White realizes mistake and comes back to fix. It already has some help from one side.] ;B[cq] (;W[cp] ;B[er]C[White lets black have some territory. White can do better.]) (;W[er]C[Block to capture.] ;B[bo] ;W[cp] ;B[bp] (;W[bn]C[This block actually lets black live] ;B[br]C[Black alive]) (;W[cr] ;B[br] ;W[dq] ;B[bn] ;W[cm] ;B[bq] ;W[bs] ;B[bm] ;W[bl]C[Black dead in the corner. 6 stones in a row on the second line dies.]))))) (;B[qo] ;AE[dd][pf][qk][fq]AW[lc][qf][qj][fp][jq]AB[nc][dj][cn]PL[W] (;B[rd]C[Proper move to defend the corner]) (;B[qe]C[Sente move for now but does not defend the corner] ;W[pf]C[White will come back to 3-3...] (;W[qc] (;B[re] ;W[ob] ;B[nb] ;W[oc] ;B[od] ;W[nd] ;B[md] ;W[ne] ;B[mc] ;W[rc]C[Black is captured in it's own corner]) (;B[pc] ;W[re] (;B[qd] ;W[rd] ;B[rc] ;W[le]C[Black takes one stone... but it is still not fully alive] ;B[dd] ;W[rb] ;B[qb] ;W[sc]C[Black can still be attacked]) (;B[rd] ;W[qd] (;B[pe]C[Black cannot connect because...] ;W[rc]C[white gain a lot]) (;B[rc] (;W[qb]C[White cannot extend because...] ;B[pe]LB[rb:B][rf:A]C[White's 3 stones are captured]) (;W[pe] ;B[qb]C[Black is fully alive.]))))) (;B[ne]TR[qe][pf][qf]C[Black needs to further defend with this move to secure the corner, since it kicked the white stones with marked stones.] ;W[qc] (;B[rd]C[Improper way to defend] ;W[pc] ;B[oc] ;W[rc] ;B[qd] ;W[ob] ;B[nb] ;W[oa]C[White shape has ko in the corner. ] ;B[rb] ;W[sb] ;B[qb] ;W[pb] ;B[qa] ;W[ra] ;B[sa]C[Here is the ko. Good for white.]) (;B[qd] ;W[pc] ;B[oc] ;W[rc] ;B[rd] ;W[ob] ;B[nb] ;W[oa]C[Ko variation for white's group in black's corner. Good for white.]) (;B[re]C[Proper move to kill white] (;W[pc] ;B[oc] ;W[ob] ;B[nb] ;W[oa] ;B[sb]LB[oa:C][pa:A][pb:B]C[Black kills with monkey jump. Same even if white defends differently. ]) (;W[ob] ;B[nb] ;W[oc] ;B[od] ;W[rb]C[White has good shape... but...] ;B[oa] (;W[pb] ;B[sc] ;W[sb] ;B[qa]C[White is dead in the corner.]) (;W[rd] ;B[qa] ;W[ra] ;B[sc]C[White is dead in the corner])))) (;B[dd] ;W[oj]C[White jumps.] ;B[rf] ;W[rg]C[This exchange MAY be beneficial for black. Only do this when white is already strong.] ;B[lq] ;W[qc] ;B[pc] (;W[re] ;B[rd]LB[qd:A]C[White cannot push!] (;W[qd] ;B[pe] ;W[sf] ;B[rc]C[Black keeps the corner.]) (;W[sf] ;B[rc]C[Usual variation for white. White gets sente.])) (;W[rd] ;B[re] (;W[pb] ;B[rb] ;W[qb] ;B[ob] ;W[ra] ;B[sb]C[White dies in the corner.]) (;W[rb]C[Can white live with this?] ;B[pb] ;W[sc] ;B[qb] ;W[qd]LB[pe:A]C[Weakness at A] ;B[pe] ;W[ra]C[White lives. But this made black strong on the outside, and may not be worth the points in the corner. Reduction variation is usual.])))) (;W[bp]C[Proper move to defend the corner]) (;W[co]C[Sente but does not defend the corner] ;B[dn] ;W[dd] ;B[cq] (;W[dq] ;B[bo] ;W[cp] ;B[bp] ;W[bq]C[White gives up territory to black in gote]) (;W[bo]C[White blocks, hwo to live?] ;B[eq] ;W[ep] (;B[dq]C[Bad move..] ;W[fq] (;B[br]C[Black lives small]) (;B[fr]C[Death for black group] ;W[gr] ;B[er] ;W[ar] ;B[br] ;W[ap])) (;B[fr]C[Proper move to live] (;W[dq] ;B[dr] ;W[fq] ;B[er] ;W[gr] ;B[br]C[Black alive in the corner]) (;W[fq] ;B[er] ;W[gr] ;B[br]C[Black alive in the corner]))))) (;B[kd] ;AE[pf][cn][fq]AW[cc][df][cj][dn][jq][mq]AB[db][nc][hd][qg][po] (;W[qc]LB[qe:A]TR[qg]C[Black's corner is undefended. Marked stone should have been at A] ;B[qd] ;W[pc] ;B[oc] ;W[rd] ;B[re] ;W[rb]C[Can black kill?] (;B[pb] ;W[qb] ;B[ob] ;W[sc]C[White alive in the corner]) (;B[sd] ;W[sc]C[Ko for life in black's corner. Good for white.] ;B[rc] ;W[cb] ;B[eb] ;W[rd] ;B[se] ;W[ob] ;B[nb] ;W[pb] ;B[rc] ;W[sb] ;B[qa] ;W[ra] ;B[oa] ;W[qb]C[White alive in the corner])) (;W[gp] ;B[cq]C[White's corner was totally undefended. Black can live outright.] ;W[dq] (;B[cp] ;W[co] ;B[dr] ;W[er] ;B[br] ;W[ds] ;B[cs]C[Ko variation for black, but black can do better]) (;B[bp] ;W[cr] ;B[br] ;W[cp] ;B[bq] ;W[dr] ;B[bn] ;W[bm] ;B[cn] ;W[cm] ;B[bs] ;W[an] ;B[ao]C[Black is alive in the corner.]))) (;B[ee]C[What if black completely covers white? Can white live?] ;W[cc] ;B[bd] ;W[bc] ;B[cd] ;W[eb] ;B[ec] ;W[dc] ;B[fb]C[Does white has a living shape?] (;W[db]TR[db][eb][bc][cc][dc]C[Worst possible move. This is a dead shape.] ;B[ea] ;W[da] ;B[ac] ;W[ab] ;B[ba]) (;W[da]C[Also a dead shape] ;B[ac] ;W[ab] ;B[ba]C[White is dead]) (;W[de]C[Exploit black's weakness] ;B[df] ;W[ad] ;B[bg] ;W[da] ;B[ac]C[Black throw in] (;W[ab] ;B[ba]C[White is still dead!]) (;W[bb]C[Empty triangle. But white has life.] ;B[ae] ;W[ab]C[White is alive in the corner]))))