(;FF[4]GM[1]CA[UTF-8]SZ[19]DT[2019-12-06]
RU[Japanese]KM[1]GN[KataGo Igo Hatsuyoron 120]SO[Inoue Dosetsu Inseki]
AB[aj][ak][al][am][bd][bf][bm][bp][bs][ce][co][cp][cr][de][dh][di][dn][ek][el][em][ep][fc][fe][fj][fn][fo][fq][hb][il][ko][lb][lc][ld][le][lj][lk][me][mf][mi][mn][ni][nr][ns][oe][of][og][oh][oi][oo][os][pe][ph][pi][pl][pp][pq][pr][ps][qh][ql][qm][qq][ra][rh][rk][rm][sh][sk][sp][sq]AW[ah][ap][ar][bg][bj][bn][cd][cg][cj][cn][df][dg][dk][dl][en][eq][ff][gg][hc][hg][hi][hm][hp][ib][ir][jb][jd][jj][jk][jl][jm][jn][ke][kg][ki][kp][lg][lp][mb][mp][mr][ms][nd][ng][nj][od][oj][ok][on][op][or][pf][pj][qa][qc][qe][qj][qo][qp][rb][re][ri][rl][rn][ro][rq][si][sl][sm][sn][so]
;B[po]
C[KataGo's solution attempt for Igo Hatsuyoron 120.

In this file, we provide just a high-level summary of the key points of what seems to be KataGo's preferred line and points of deviation, without much commentary where it agrees with prior human solutions, or on the many, many possible variations that need to be considered.

For some coverage of human analysis in the years and decades prior, this external site by a strong amateur player provides a good summary: http://igohatsuyoron120.de/2015/0005.htm]
;W[rr]TR[sn]
C[Unlike human solutions, which often obtained results of a draw or a Black win, KataGo believes that White will be the winner in this problem. KataGo believes White will win by 1 point under Chinese-style scoring.
 
There are 71 white stones but only 70 black stones on this board, with Black first to play. So we will follow the conventional assumption that a black stone was captured at the triangled location, as in much of past human analysis.

If this assumption is made, then Chinese W+1 should correspond to Japanese W+1 OR Japanese W+2. 

KataGo would actually often play various forcing exchanges at a different time or in a different order than actually presented here. However, it also does not strongly object to the ordering presented here, which is chosen for greater human understandability and to be more consistent with past work in the problem.]
;B[qk]
C[The preliminary fight in the lower right establishes what will be the main theme of the problem.]
;W[ml]
C[There are various alternatives that either White or Black may try in these early moves, even entirely abandoning the main theme of the problem and/or playing anywhere else on the board, but KataGo agrees with prior human analysis that nothing appears to be as good for either side as entering into the main line.]
;B[ll]
;W[mm]
;B[lm]
;W[nn]
;B[no]
;W[mo]
;B[ln]
;W[pn]
;B[qn]
;W[rp]
;B[nm]
;W[om]
;B[ol]
;W[nl]
;B[nk]
C[This throw-in is one of those tricky early moves that has implications far, far later in the problem.]
;W[mk]
;B[mj]
;W[nk]
;B[np]
;W[rs]
;B[sr]
;W[oq]
C[For now, the many groups in the lower right are in seki, unable to capture one another due to sharing most of their liberties.]
;B[mq]
;W[lr]
;B[lq]
;W[kr]
C[Because the lower right is a hanezeki, even if White blocks Black's tail here, White cannot actually capture it without losing the entire lower right. So White is forced to fall back and Black can push this tail very agressively.]
;B[kq]
;W[jp]
;B[jq]
;W[jr]
;B[iq]
;W[hq]
;B[gr]
;W[hr]
;B[ip]
;W[jo]
;B[io]
;W[ho]
;B[in]
;W[hn]
;B[im]
;W[hl]
;B[ik]
;W[hk]
;B[ij]
;W[hj]
;B[ii]
;W[ih]
;B[ji]
;W[kj]C[Black continues with A, but if Black plays B at this point, it will lead to some extremely complex fighting that is also necessary to analyze.]LB[jh:A]LB[kh:B]
;B[jh]
;W[kh]
;B[jg]
;W[jf]
;B[ig]
;W[hh]
;B[if]
;W[ie]
;B[hf]
;W[he]
;B[pd]
C[KataGo would usually play this and the following forcing exchanges in the upper right much, much earlier, but some prior human solutions play them now, and there seems to be no problem doing so. There are even some technical advantages to playing them now rather than with KataGo's timing, but that turn out not to actually make a difference, probably.]
;W[pc]
;B[nb]
;W[mc]
;B[ma]
;W[ob]
;B[rg]
C[The surprising guzumi move, discovered only in 2007.

This odd shape is one of the last "human" moves to have been rediscovered by KataGo, and it makes a critical difference to the endgame shape, gaining Black quite many points.]
;W[rf]
;B[pm]
;W[nm]
;B[rj]
;W[qi]
;B[gf]
;W[ge]
;B[fg]LB[hf:A]
C[Black boldly cuts, leaving the entire tail A in atari because White cannot afford to capture (yet) and lose the entire lower right due to the hanezeki.]
;W[ef]
;B[fh]
;W[hs]LB[bi:B][ee:A]
C[The main line continues at A, but during some of the early to middle parts of training, KataGo was suspecting Black could play B to kill White's entire lower left and win big.

If Black tries this, White pushes through at A and we obtain many variations of bewildering complexity. Ultimately, KataGo decided that they do indeed work for White and therefore Black cannot play B, agreeing with human analyses. In the process, KataGo also finds what tentatively appear to be some small errors or oversights in prior human work, though not changing the conclusion.]
;B[ee]
;W[cm]
;B[an]
;W[bo]
;B[ao]
;W[aq]
;B[bi]
;W[ai]
;B[bh]
;W[ag]
;B[bk]LB[ck:B][dm:A]
C[KEY POINT 1

Here is KataGo's first deviation from prior work.

Generally human solutions have proceeded with B.

KataGo instead chooses the atari at A.]
;W[dm]LB[bl:B][dj:A][do:C]
C[Black must play A or B. 

Black cannot save the stone in atari by playing C, or else White will throw in at B and live easily on the left, winning big.]
;B[dj]LB[bl:B]
C[KataGo has Black play here, but Black could equally well have played B. The variations are very similar.

B appears in fact to be potentially better, giving Black bit more flexibility later, although there does not seem to be a way to translate that flexibility into anything concrete.]
;W[ck]
;B[bl]
;W[do]TR[dn][do][en]LB[ck:A][dp:B][eo:C][gb:D][oh:E]
C[Relative to earlier human solutions, White eats into Black's territory. To keep these gains, however, White must take care to select later variations where A ultimately survives.

Black must respond such as at B or C. If Black plays a big point at D, Black will collapse, due to tactics in the lower left. But aside from that (and relevantly to some other variations) groups A and E are caught in a giant race connected by the hanezeki, and if Black plays away, then Black appears to come up exactly one (!) move short in this race, enough to kill A, but not enough to save enough other stones, causing White to win big.]
;B[dp]
;W[fb]LB[gb:A]
C[This is a famous attachment move suggested by Yamada Shinji (professional 6 dan) many years ago, improving White's endgame here compared to playing the simpler and more obvious move at A. KataGo finds and agrees with the move too.]
;B[eb]LB[ec:A][gb:B]
C[KEY POINT 2

Here is KataGo's second deviation from prior work. Unlike earlier solutions that have pulled back at B, KataGo follows up the attachment with an immediate crosscut with A.]
;W[ec]LB[dc:A][gb:B]
C[In the main line, Black continues at A, but there are some highly complicated fights that result if Black resists the crosscut at B, in which subtle weaknesses of Black's upper left corner come into play.]
;B[dc]
;W[ea]
C[As a result of the crosscut, White gains a little value by being able to force here.]
;B[db]
;W[gb]
;B[da]
;W[fr]
;B[er]
;W[fs]
;B[es]
;W[gs]
;B[gd]
;W[gq]
;B[fp]
;W[gc]
;B[fd]LB[eg:A][fa:C][mg:B]
C[KEY POINT 3:

Although likely White can still choose other moves such as B or C, at this point, KataGo plays A.]
;W[eg]
;B[hd]
;W[id]
;B[na]
;W[nc]SQ[en][fm]TR[ei][ej]LB[eg:A][eh:B][fl:C]
C[The value of White's earlier move at A is that if Black blocks at B to attempt to preserve the triangled points, White has a clever move to reduce Black at C, exploiting the squared weakness left by White's earlier capture.]
;B[fk]
;W[gj]
;B[fi]
C[There are many possible permutations of the final cleanup in this problem that are very similar or equivalent.]
;W[mg]
;B[eo]
;W[dn]
;B[fa]
;W[cl]
C[Mixed in with various endgame moves, we start the main race that has been hanging over the heads of both players the entire problem, between White's left side and Black's giant top right group.

During this endgame, Black must still however watch the liberty balance of the main race carefully.]
;B[ak]
;W[aj]
;B[bl]
;W[ao]
;B[am]
;W[bk]
;B[al]
;W[oa]
;B[la]
;W[eh]
;B[ei]
;W[af]
;B[ae]
;W[cf]
;B[be]
;W[qd]
;B[kc]
;W[jc]
;B[ga]
;W[ha]
;B[ea]
;W[kb]
;B[ka]
;W[ja]
;B[br]
;W[kn]
;B[bq]
;W[lo]
;B[as]
;W[lf]
;B[ci]
;W[mh]
;B[li]
;W[sf]
;B[ch]
;W[qf]
;B[bm]
;W[an]
;B[al]
;W[sg]
;B[bl]
;W[lh]
;B[am]
;W[kd]
;B[bm]
;W[ak]
;B[al]LB[bk:B][nq:A][oh:D][qg:C]
C[At this point, White must make a criticial choice that features in a large number of the main lines of the problem, culminating in a large but finely balanced trade.

If White captures at A, White saves the group B, but Black wins all the fights on the right.

If White continues at C, White will kill Black's group D, but have to sacrifice B.

The reason why now is the critical moment is that Black has reduced White's left group enough to be able to non-suicidally play A themselves. So White must either take it now, or concede it to Black.

In KataGo's line, White chooses A, to preserve the gains on the left from the atari and capture, among other things.]
;W[nq]
C[Part of what makes this problem so complex is the fact that so many variations end in this kind of final large trade, whose balance on each side is subtly affected in different ways by an enormous number of the earlier possible choices.]
;B[mq]
;W[oq]
C[This move is easy to overlook, and was overlooked by some much older classical solution attempts. Although it is not winning the local fight for White, it is still worth some points.]
;B[qr]
;W[nq]
;B[qs]
;W[ss]
;B[sq]
;W[lq]
;B[sr]
;W[ne]
;B[nf]
;W[qg]
;B[sp]
;W[pg]
;B[pk]
;W[nh]
;B[sj]
;W[oc]
;B[op]
;W[mq]TR[sn]
C[At least in this variation of the problem, White wins by two points.
(assuming the convention that White earlier captured a stone at T6)

Further analysis will be needed to gain confidence in KataGo's variations if they do indeed turn out to be correct and genuine improvements. 

They provide some fascinating new life to the study of this problem, and hopefully KataGo can also be of use in reconfirming much of the human analysis of some of the immensely complex additional fights off the main branches that are necessary to refute for the main branches to hold up.])
