( ;C[A, which I played during the game is too small. White should answer at B, securing the D14 Group, while also aiming at C later. I played S8 because I was concerned about territory. I know that Blacks fourth line stones do not really form solid territory, but i had no real cue of how to invade yet, so I thought, that I should not give up on my largest source of points by allowing follows ups like E or F. Tbh I did not really know of the possibility of invading C, after playing B. As there is a similar shape around D and might well be at G or H later on, I think it is a good idea to get familiar with this invasion.]TR[cd][ce][cj][cp][dc][dk][dn][dq][eq][fd][id][ld][mc]LB[ci:B][cl:C][kc:D][rh:H][ri:G][rl:A][rm:E][sn:F]AB[cd][ce][cj][cp][dc][dk][dn][dq][eq][fd][id][ir][jr][kr][ld][mc][mq][nr][qg][qj][rk]AW[cf][de][df][di][ep][fi][fp][fq][hr][iq][jo][jq][nc][nd][oq][pd][pp][qe][ql][qn]BR[8k]DT[2020-03-24]GN[Friendly Match]PB[Nath_57]PW[00Noles]RE[B+R]WR[9k]AP[Sabaki:0.34.1]CA[UTF-8] ( ;W[rl] ;B[rf] ;W[re] ;B[oj] )( ;W[ci]C[Lets say Black ignores and comes out with the right side group instead.] ;B[og] ;W[cl]LB[bj:A][ck:B][dl:C]C[I think Black has three options here: A: The drop down to block the connection underneath. B: The empy triangle to also block the connection, but this time putting a little more pressure on the white stone. C: Connecting up the probed two space extension.] ( ;B[bj]C[As C8 was basically asking if either White might slip in blacks territory, by connecting under or cut through the two space high I think cutting through is the only response to blacks drop down.] ;W[dl] ;B[el]C[Natural. Black can not just extend up and let White come out. I see two options for White here, which are A and B. Kata Go also thinks C might be a good idea, but i will stick with the basic responses for now.]LB[co:C][ek:A][em:B] ( ;W[ek]C[This results in a capturing race between the two marked groups of stones. I can not really out situations like this clearly, but given, that the count of liberties on the marked groups should be roughly 4 to 4 and White has a little more space to expand to, while Black can not connect underneath, it seems like White can capture. The options here are to vast to explore them all, but i think A to C are interesting choices for Black right now.]TR[bj][cj][dk]LB[bl:B][dm:A][ej:C]CR[bm][cn]SQ[cl][dl] ( ;B[dm]C[Taking a liberty at C is the only valid idea here. As the liberty count is now 3 on Black vs 2 on White, after White exchanges A and B. Note that White can not Atari at B from the inside, because the cutting point at E10 makes this Gote, turning the liberty count to 3/3 with Black having Sente.]LB[bm:C][ck:B][dj:A] ( ;W[bm]C[If Black still wants to fight this A is the move. B refrains form fighting and secures the, now quite unstable, group.]LB[bn:A][fk:B] ( ;B[fk] ;W[ej] ;B[bn] ;W[dj] ;B[fm]C[This is the sequence Kata Go recommends for Black. Resulting in a winrate ratio of 90/10 for White.] )( ;B[bn] ;W[dj] ;B[ck] ;W[bi] ;B[cm] ;W[bl]C[2/3 libertys.. Black is captured] ) )( ;W[dj] ;B[ck]C[Just for reference]LB[aj:2][bi:1][bk:3][bl:1][cm:2]MA[cl][dl] )( ;W[ck] ;B[dj]LB[ej:A]C[A has to be payed] ;W[ej] ;B[bk]C[3/2 liberties and White has nowhere to go.]MA[ck][cl][dl] ) )( ;B[bl]C[Black might try to connect..] ;W[bm]C[..but White hanes.]LB[ck:A][dm:B] ( ;B[ck]C[If Black just connects..] ;W[em]C[..White comes out.] ;B[fl] ;W[dm] ;B[cn] ;W[cm] ;B[en] ;W[fm] ;B[fn] ;W[gm] )( ;B[dm]C[If Black wants to close White in..] ;W[bk]C[..White just takes..] ;B[ck] ;W[al] ;B[cm] ;W[bl] ;B[bn]C[...and even after all of this..] ;W[bi] ;B[aj] ;W[dj]C[...Black can not win the capturing race, because of the approach liberty at A6.] ) )( ;B[ej]C[This looks kind of intersting, but might get really messy.] ;W[fk]C[Stretch of course. This not only saves whites stone, but also threatens to capture the two marked stones. Black would like to connect at A for sure but maybe making a trade by plaing at B might be a better idea.]LB[bl:B][dj:A]MA[ej][el] ( ;B[dj] ;W[fj]C[Neccesary] ;B[em]C[Safe this stone next] ;W[bm]C[Making liberties, while also lightly aiming at blacks small knight. I have niether interest nor abillity, to read out this fighting situation and even with the help of AI this leads to no clean result. On a general note i would say, this fight is no good for Black, as it seems like she can not safe both, the cross and the square group.]LB[bh:B][do:A]MA[bj][cj][dj][dk][ej]SQ[dn][el][em] )( ;B[bl] ;W[bm] ;B[bk] ;W[dj] ;B[ck] ;W[em] ;B[cm] ;W[dm] ;B[cn] ;W[en]C[Black can keep the clumb of the stones on the left side, but White gets to connect up two groups, resulting in supreme influnece. Next attacking around A and then capping at B would turn the middle into white points.]LB[mo:B][ok:A] ) ) )( ;W[em]C[This seems slightly passive, but is in fact a good move, as it has miai for either coming out or cutting of blacks three stones on the left.]LB[dm:B][fk:A] ( ;B[fk] ;W[dm]C[This does not look to promising for Black] ;B[fm] ;W[en] ;B[do] ;W[ej] ;B[ek] ;W[dj] ;B[ck] ;W[gl] ;B[fl] )( ;B[dm]C[When Black cuts..] ;W[ek] ;B[fl] ;W[bm]C[..it results in capturing the three stones again. Note that A does not work but Black should play B according to KataGo.]MA[bj][cj][dk]LB[ej:A][fk:B] ( ;B[ej] ;W[fk]C[Black has a cutting point at A and continue pushing with B is also not an option, as will be shown.]LB[dj:A][fj:B] ( ;B[fj] ;W[gk]C[At some point Black needs to come back and connect at A, but White B captures blacks two stones in a ladder.]LB[dj:A][fm:B] ( ;B[dj] ;W[fm] ;B[gl] ;W[hl] ;B[gm] ;W[gn] ;B[hm] ;W[im] )( ;B[fm] ;W[dj]MA[bj][cj][dk] ) )( ;B[dj] ;W[fj] ) )( ;B[fk] ;W[ej] ;B[bn] ;W[dj] ;B[ck] ;W[bi] ;B[cm] ;W[bl] ;B[fn]C[Invasion succeeded!] ) ) )( ;W[co]C[There is also this. I did not have this on my radar in this situation, but KataGo states its better then the counter-hane (+6%) and only sligthly inferior to the cut.] ;B[do]C[Black should block here.] ;W[dp]C[At which point White cuts. Black has two potions here. A: Seperate the White stones. B: Connect.]LB[cn:A][cq:B] ( ;B[cn] ;W[cq] ;B[bp] ;W[cr]MA[dq][eq]C[White takes two stones, but even more important is, that Blacks corner is stolen, while the black group on the left side of the board looks still quite unstable.] )( ;B[cq] ;W[cn]C[White also connects.]LB[dm:B][em:A] ( ;B[em]C[Black has to play here!] ;W[dm]C[At which point White can start making eyes.] ;B[fn]C[Defending against a cut.] ;W[bm]C[Halfway alive!] ;B[bo] ;W[bn] ;B[ck] ;W[al] ;B[bk] ;W[bl]C[White is alive here, as Black can not play A, because of the cut at B. Also there is still a weakness at C still.]LB[an:A][bp:B][ek:C] ;B[bp] ;W[an] ;B[ej] ;W[ei] ;B[gk]C[Successfull invasion!] )( ;B[dm]C[This leaves to many cutting points]MA[ek][em] ;W[bl]MA[ek][em]C[Whichever point Black defends now, White will happily take the other one.] ( ;B[ek] ;W[em] )( ;B[em] ;W[ek] ) ) ) ) )( ;B[ck]C[This looks odd, but according to KataGo it is better then the dropdown. I thnk this is because it blocks the connection under, while also taking a liberty away. White has three options here: A: Just extend up. B: Knights jump. C: Fancy Footwork KataGo recommends. Again I did not really have this on my radar, but will see where it goes.]LB[co:C][dl:A][em:B] ( ;W[dl] ;B[el]C[Of course Black will not just let White come out.] ;W[em]C[In this scenario, as Whites two stones have only three liberties I will just cover the counter hane, as I would probably not dare to cut here. Also KataGo thinks this is slightly better too. Black next cuts or hanes to connect.]LB[bl:B][dm:A] ( ;B[dm]C[This is not a good idea.] ;W[ek] ;B[fl] ;W[bl]C[Blacks empts triangle starts to look quite dead. Like in the similar variation, where Black played the dropdown to answer Whites invasion, pushing at A is not valid tactics, due to the ladder.]MA[cj][ck][dk]LB[ej:A]CR[gl][gm][hm][hn][in][io] )( ;B[bl]C[Here is better. Next White connects, then Black connects.] ;W[dm] ;B[bm] ;W[cn] ;B[do] ;W[cm] ;B[bn]LB[ek:A]C[I guess this invasion went quite ok for White. Black is pushed onto the second line and White has a valueable cut at A next, to make huge claims at the center.] ) )( ;W[em]C[The idea behind this move seems to be shifting mor torwards building the center, then reducing Blacks points on the left.] ;B[bl] ;W[fl] ;B[dm] ;W[dp] ;B[cq]C[I guess while Black looses nothing here, White gains quite much. The only white group which could be considered weak is now connected by a wall spanning two thirds of the board. If White next attacks at A and then seals off at B the cetner gets quite huge. During i game i would probably fail to recognize, that this is enough for White, but it surely seems to be, as KataGo gives White a 87% chance of winning on this board.]SQ[fi][fl][fp]LB[mo:B][ok:A] ) )( ;B[dl]C[According to KataGo this is the best move for Black. There are a few tricky variations here, which result in cutting and fighting again, but I will stick to a simple one I would expect to be played at my level.] ;W[bj] ;B[bk] ;W[ck] ;B[bl] ;W[dj] ;B[cm] ;W[dp] ;B[cq]C[This looks fair to me! Nothing died, but Black is on the third line mostly while White got to settle the left side group. Next A, just doing it again, then B and then C and suddenly this board actually looks like White has good chances here.]LB[fe:B][kc:A][or:C] ) ) )