(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Chinese]SZ[19]KM[7.5]TM[0]OT[1x60 byo-yomi]
PW[AlphaGo]PB[AlphaGo]DT[2016-02-29]C[Game 3 - Freedom

Commentary by Fan Hui
Go expert analysis by Gu Li and Zhou Ruiyang
Translated by Lucas Baker, Teddy Collins, and Thore Graepel

Whereas the first two games allowed only five seconds per move, this game was played at a more classical pace of one to two minutes per move. The difference between these time controls is night and day, and the slower pace dramatically improves AlphaGo's calculations. This helps explain why, as you will soon see, White proves more than willing to spurn conventional wisdom in this game!]RE[W+Resign]
;B[pd]
;W[dp]
;B[cd]
;W[pp]
;B[cn]C[Before setting up the Chinese opening, Black approaches the corner. What is this exchange about? When I asked Gu Li and Zhou Ruiyang, they said that while it is unusual, it does not lose anything.]
;W[fq]
;B[ic]C[Here, AlphaGo once again demonstrates its preference for the Chinese opening.]
;W[qf]
;B[nd]
;W[qc]
;B[qd]
;W[rd]
;B[pc]C[Black's block here would strike professional players as soft, but it turns out to be an acceptable move. See the commentary for the first blitz game for a deeper investigation.]
;W[rb]
;B[qb]
;W[rc]
;B[nq]
;W[qn]
;B[jp]TR[jp][nq]C[The approach and extension, a common strategy in AlphaGo's games, are likewise analyzed in the commentary for the first game.]
;W[dd]C[Now we come to White 20. No, that is not a misclick, AlphaGo really played there! Of course, this is not something AlphaGo dreamed up on the spot, but rather a strategy fashioned over time through many self-play games. So, what is the reasoning behind this move? See the variations for an investigation of some tempting but wrong ways for Black to answer it.

While looking through these alternatives with Gu Li and Zhou Ruiyang, we discovered many complex variations. Although we have not reached a definite conclusion about this attachment, we would not be surprised to see it appear in many games to come. AlphaGo has opened our minds and inspired us to reassess conventional Go wisdom regarding what is right and wrong. Sometimes we instinctively reject moves because they clash with our experience or training, or even because we fear the ridicule of others. Yet these concerns obstruct our progress. AlphaGo does not have this layer of human prejudice, and that is what makes it so free, bold and unrestrained! As Go players, shouldn't we also seek to embody such a spirit?]
(;B[ce]C[Black ultimately chooses to extend on the outside.]
;W[de]
(;B[dc]C[When Black plays this hane, it feels as if the corner might transpose to the avalanche joseki. Does Black have any other options? See the variations.]
;W[ec]
(;B[cc]C[As the variation shows, Black would get a bad result from the small avalanche, so Black simply connects.]
;W[df]
;B[cg]C[It looks like Black is poised to attack White...]
;W[id]C[...but White 28 is a severe counter! Gu Li and Zhou Ruiyang praised this move highly. At first it looks like an overplay, but actually, Black has no good response. Thanks to its powerful calculations, AlphaGo can play these sorts of strong moves without reservation. This is perhaps its greatest strength.]
(;B[jd]C[The best response. See the variations for Black's alternatives.]
;W[hc]
;B[jc]
;W[ie]C[Here, Black and White have reached an agreement of sorts. Black hanes on the outside, and White hanes and extends for a very comfortable position.]
;B[je]
;W[lq]LB[if:A]C[Just as we were thinking White would be satisfied with the extension at A, White pleasantly surprised us by invading directly at the bottom! Could it be that AlphaGo does not understand the importance of a hane at the head of two stones? Truly, AlphaGo never ceases to amaze. One would never find a tenuki like this in a game between professionals.

What will happen if Black hanes now? See the variation.]
(;B[lp]C[Once again, both sides have reached a common understanding. Disregarding the normal imperative to hane at the head of two stones, Black attaches on top.]
;W[kp]
;B[kq]
;W[ko]
;B[lr]
;W[jq]
;B[mq]
;W[kr]
;B[lq]LB[ip:A]TR[kp]C[Generally, White cannot wedge with the marked stone when the ladder at A is unfavorable, so I requested that Zhou Ruiyang and Gu Li explore White A a bit further. See the variations.]
(;W[iq]
;B[pr]
;W[co]LB[dn:A][bo:B]C[White 46 is a common attacking technique, but AlphaGo's attitude towards it is quite unusual. The typical reply would be to extend at A, but AlphaGo prefers to tenuki, either right away or after exchanging the hane at B and the atari in sente. It seems AlphaGo has no fear of allowing the tiger's mouth at A.
]
;B[fc]C[Black now clamps on the upper side, prompting White to descend. In the end, it seems neither player was ever concerned with the hane at the head of two stones.]
;W[eb]
;B[fd]
;W[ed]
;B[fe]
;W[dg]
;B[ch]LB[dh:A]C[Black extends, probably anticipating White A, but White has a way to improve on that result.]
(;W[gb]
;B[fb]
;W[dh]LB[fb:B][gb:A]C[With the well-timed exchange of A for B, White's position is clearly better than the variation.]
;B[hd]
;W[di]
;B[ci]
;W[dj]
;B[cj]
;W[cf]
;B[bf]
;W[be]LB[bd:A]C[A well-timed cut - Black has no choice but to connect. The variation shows the consequences of Black's capture at A.]
(;B[bg]
;W[hh]TR[hd]C[White then leaps out into the centre with the magnificent move of 66! This one move embodies all of AlphaGo’s formidable genius. It strengthens White's group on the left, reduces Black's top side, and aims at the aji around the marked stone. One can even hear the faint echoes of a White moyo forming in the centre. If there were an ear-reddening move for AlphaGo, this would be it!]
;B[ql]C[Black 67 is the only reply. Not only does Go theory say to play in the widest area, but this move begins to threaten White's safety in the corner.]
;W[qq]C[This exchange shores up the corner, freeing White to make another big move.]
;B[qr]
;W[cl]C[White's moyo begins to crystallize.]
;B[bo]C[Black takes an extremely direct approach, starting with the hane and atari.]
;W[bp]
;B[do]
;W[cp]
;B[ck]C[Black connects up the left side.]
;W[dk]
;B[bl]
;W[cm]
;B[bm]C[Although the result is clear, this way of connecting is extremely crude, and most professional players would be loath to use it.]
;W[dn]
;B[bn]
;W[em]
;B[km]C[Finally, Black plays a reducing move in the centre.

Up to here, this game conveys the feeling that White is playing with masterful lightness, while Black is being dragged around the board. Gu Li and Zhou Ruiyang felt this to such an extent that they declared the game "totally one-sided," almost as if White were playing by itself. Yet in AlphaGo's own calm-minded assessment, White has a win rate of just 51.5%, a lead by only the slimmest of margins. When I informed the two masters, they sighed deeply. In professional matches, they told me, one often encounters situations in which one feels sure of a tremendous advantage - but after a few soft moves, the outlook has reversed completely.

To analyse the position in detail, Black's territory is not small, and though White has great potential in the centre, it is still unknown how this will be converted to real profit. On top of that, White is not completely safe in the corner, which increases the pressure on the centre. Sometimes the difference between feeling good about a game and feeling great is just a single detail. In such cases, players may lean too much on feelings to guide their judgment. This reminds me of a comment Lee Sedol made after the AlphaGo match. He declared, "I will no longer rely on feeling - I will focus on precise calculation." This could be what he learned from his games with AlphaGo, and the secret behind his subsequent 9-game win streak.]
;W[om]C[White starts a fight with the knight's move.]
;B[qg]C[Black 85 is a very interesting reply. AlphaGo often attaches when the local shape looks like this, and it seems that it has already developed the follow-up into a new joseki.]
;W[pk]
;B[rf]
;W[pb]
;B[ob]
;W[qa]
;B[qk]
;W[pj]
;B[qj]
;W[pi]
;B[rh]C[White continues to build up the centre, and Black continues with the strategy of "profit, then erase." Up to here, Black has secured considerable territory across the board.]
;W[lo]TR[km]C[This turn is necessary to isolate the marked Black stone.]
;B[jj]C[Black 97 throws some support to the lonely centre stone.]
;W[if]
;B[hb]LB[hb:B][if:A]C[The exchange of A for B helps prepare White's coming attack. Here, the two sides diverge slightly in their thinking about the position. See the variation for Black's prediction.]
(;W[lj]C[White chooses to start the attack slowly, hitting the vital point of Black's shape.]
;B[il]C[When I asked Gu Li about these moves, he and Zhou agreed that 'these feel like good moves that will be hard to counter, but the calculations are fundamentally unclear.’ I believe AlphaGo calculated these moves deeply, but sadly we cannot see all of its internal variations.]
;W[im]
;B[hi]
;W[jl]
;B[ih]
;W[hl]C[Through White 106, a trade has developed, and the outlook has reversed: Black's win rate now stands at 56%. In other words, Black believes that the fight in the middle has been a success. However, this judgment is predicated on Black's ability to further harass White in the centre.]
;B[mo]
;W[mn]
;B[nn]
;W[no]
;B[oo]LB[nm:A]C[Black now seals in the White stones on the right. Note that White cannot atari at A - see the variation.]
(;W[mp]
;B[np]
;W[mo]
;B[pm]
;W[rr]
;B[nm]C[Black has successfully cut off the corner, but this has no impact on White's life and death status. Zhou Ruiyang thought Black played poorly here.]
;W[mm]
;B[rs]
;W[rp]
;B[sr]
;W[rq]
;B[nl]
;W[ml]
;B[pn]
;W[pq]LB[jr:A][or:B]C[White 126 is a very strange move, and incurs a definite loss of territory. Before this move, connecting at A may have influenced the status of Black's group, but once White provokes Black B, the connection becomes completely gote. AlphaGo may like to play the clearest variations, but this move must be called a mistake.]
;B[or]
;W[qo]
;B[gh]
;W[lh]
;B[rm]
;W[rn]
;B[nj]C[At this point, Black's win rate stands at 53%.

The game has entered a stage of extreme suspense. When Black jumps to 133, Black believes that White will be overwhelmed trying to balance the middle and the right side. More precisely, Black thinks both sides are in danger of dying, and that is the reason behind this splitting move.]
;W[hg]
;B[gg]
(;W[gf]C[White also believed that the situation was difficult, but when White hanes at 136, the win rate begins to shift. It seems as though both sides failed to foresee this move.

But this move appears to simply give away points. Why make the exchange? See the variation for a deeper analysis.]
;B[ff]
;W[kg]
(;B[ig]LB[jf:A]TR[ff][gf]C[Incredibly, Black chooses not to take the three stones! But why? We researched the variations behind the push and cut at A extremely thoroughly, and it seems there is no way for Black to come out ahead even with the three extra stones, as the marked exchange gives White a great deal of aji to work with. See the variations for all the intricate details.

However, if Black could not come out ahead with the three stones, Black is certainly behind without them, and this choice proves to be the point of no return.]
;W[jf]C[Not only can White extract the three stones...]
;B[hf]
;W[oh]C[...but after Black captures, the kosumi at 142 connects up the whole centre. This is a huge loss for Black! Both sides understand the situation now, and White’s win rate shoots up to 65%.]
;B[kk]
;W[ol]
;B[on]
;W[kl]
;B[ap]
;W[aq]
;B[ao]
;W[bq]
;B[gk]
;W[gl]
;B[so]C[Black 153 is an absolute loss, probably a reflection of Black’s desperation.]
;W[sn]
;B[fk]
;W[fl]
;B[dl]
;W[dm]
;B[ek]
;W[el]
;B[nh]
;W[mj]LB[nh:A]C[Black A is the last real try for a comeback, but White refutes it with this tesuji. See the variation.]
(;B[lg]
;W[mg]
;B[lf]
;W[kh]
;B[ng]
;W[mh]C[At this point, White's win rate exceeds 80%. Black has no chance of victory.]
;B[oa]
;W[re]
;B[pa]
;W[sf]
;B[rg]
;W[qb]
;B[sb]
;W[sa]
;B[kf]
;W[mf]
;B[me]
;W[ne]
;B[md]
;W[jg]
;B[jr]
;W[ir]
;B[ks]
;W[ni]
;B[is]
;W[gr]
;B[gs]
;W[fs]
;B[lk]
;W[mk]
;B[ll]
;W[ij]
;B[ji]
;W[jk]
;B[kj]
;W[lm]
;B[db]
;W[da]
;B[ca]
;W[ea]LB[dd:A][id:B]TR[ff][gf]C[Black resigns.

The most interesting aspects of this game are White's extremely creative attachment in the corner at A, and the stubborn attachment on the top side at B. Although we cannot say for sure that these are good moves, they are without a doubt inspiring and eye-opening. With moves like these to learn from, we can look forward to AlphaGo’s innovations bringing greater diversity to Go.

I would like to thank Gu Li and Zhou Ruiyang once more for their vigorous, precise, and tireless analysis. The variations in the centre were incredibly complex, and we spent many hours in particular investigating White's critical exchange of the marked stones. I feel deep respect for the dedication these two world champions showed to the pursuit of perfection on the Go board.

Finally, I must say that in a game as rich as this one, there are surely many details we have not yet explored. If you have the time and inclination, please play out these fascinating games yourself, and you will be sure to reap the benefit of many new discoveries.])
(;B[nk]C[This stubborn connection is Black's last hope, but Black cannot connect.]
;W[ni]
;B[mi]
;W[oi]
;B[mh]
;W[ng]C[There is no escape for the three stones.]
;B[mg]
;W[mf]
;B[nf]
;W[og]
;B[lf]
;W[me]
;B[lg]
;W[le]
;B[li]
;W[ki]
;B[kh]
;W[kf]C[White completes the squeeze, and Black is dead.]))
(;B[jf]LB[ii:A]C[If Black pushes and cuts, White will cut at A in return.]
;W[ii]LB[jg:A][jh:B]C[Black has two choices: connect at A, or extend at B.]
(;B[jg]
;W[hj]
;B[gi]
;W[jh]
;B[ig]
;W[nk]
;B[ji]
;W[ol]
;B[on]
;W[mj]
;B[ap]
;W[qi]
;B[ri]
;W[aq]
;B[ao]
;W[bq]
;B[fk]
;W[fl]
;B[gk]
;W[hk]
;B[gj]
;W[gl]
;B[pl]
;W[ok]
;B[ek]
;W[el]
;B[kk]
;W[bb]
;B[kl]
;W[jm]
;B[kn]
;W[jn]
;B[jr]
;W[ir]
;B[ks]
;W[cb]
;B[bd]
;W[kh]
;B[ij]
;W[le]
;B[db]
;W[da]
;B[fa]
;W[ea]
;B[is]
;W[hs]
;B[js]
;W[hr]
;B[me]
;W[mf]
;B[nf]
;W[md]
;B[ne]
;W[lc]
;B[lf]
;W[kf]
;B[mg]
;W[ke]
;B[mc]
;W[ld]
;B[mb]
;W[re]
;B[qe]
;W[sf]
;B[pf]
;W[kb]
;B[jb]LB[da:44][ea:46][fa:45][bb:30][cb:38][db:43][jb:69][kb:68][mb:63][lc:56][mc:61][bd:39][ld:62][md:54][ke:60][le:42][me:51][ne:55][qe:65][re:64][jf:1][kf:58][lf:57][mf:52][nf:53][pf:67][sf:66][ig:5][jg:3][mg:59][jh:4][kh:40][gi:7][ii:2][ji:9][qi:14][ri:15][gj:23][hj:6][ij:41][mj:12][ek:27][fk:19][gk:21][hk:22][kk:29][nk:8][ok:26][el:28][fl:20][gl:24][kl:31][ol:10][pl:25][jm:32][jn:34][kn:33][on:11][ao:17][ap:13][aq:16][bq:18][hr:50][ir:36][jr:35][hs:48][is:47][js:49][ks:37]C[Through 69, AlphaGo expects a narrow victory for White. According to Gu Li and Zhou Ruiyang’s analysis, every move looks very reasonable. Although the endgame is the easiest stage to calculate, the fact that AlphaGo can envision a nearly optimal 69-move sequence is truly incredible!])
(;B[jh]
;W[ji]C[If Black extends, this push is White's most tenacious reply.]
(;B[ig]LB[hj:A]C[If Black simply pulls back, White will force at A and take sente to defend the right side.]
;W[hj]
;B[hf]
;W[nk]C[This is no good for Black.])
(;B[jg]C[Black can stubbornly resist with this connection, but now White will secure profit in sente by making use of all the local forcing moves.]
;W[gi]
;B[hj]
;W[ij]
(;B[ki]C[The atari from the right looks like Black's most promising try.]
;W[ik]
;B[gj]
;W[fi]
;B[ig]C[Up to here, however, White has already profited considerably on the left.]
;W[nk]LB[mk:A]C[This wedge is perfectly timed. Black cannot answer on the outside at A.]
(;B[ok]
;W[mk]
;B[oj]
;W[ol]
;B[on]
;W[oh]LB[qf:A]C[Finally, White smoothly links up the left and right. The stone at A plays a pivotal role in safeguarding the connection. If you are curious about why, try experimenting with the cut as Black.])
(;B[mk]C[If Black tries to resist, White will surely counterattack.]
;W[ok]
;B[mj]
;W[mi]
;B[ni]
;W[nh]
;B[li]
;W[mh]
;B[oh]C[No matter how Black struggles, there is no escape for the four stones.]
;W[oi]
;B[lk]
;W[kh]
;B[ll]
;W[kn]C[Black is dead.]))
(;B[ik]C[The atari from below gives White several forcing moves in sente.]
;W[ki]
;B[hk]
;W[fg]
;B[fh]
;W[fi]
;B[eg]
;W[eh]
;B[fg]
;W[jk]
;B[gl]
;W[hm]
;B[gk]
;W[ni]
;B[dl]C[Black can capture two stones on the left...]
;W[el]
;B[dm]
;W[en]C[...but White gets sente to link up on the right, and Black's capture cannot make up for the territorial loss in the centre. White is better.])
(;B[mi]C[Just as we thought we had finally understood White’s move after several hours of research on the previous variations, another thought occurred to us. What if Black peeps here first?]
;W[ki]C[White has no choice but to respond this way.]
;B[gj]
;W[fi]
;B[ig]LB[mi:A]TR[pi][pj][pk][om]C[Now Black settles the left as before, but with Black A in place, White has no way to save the marked stones on the right. We looked many times for another way, but White has no alternatives from beginning to end.

Suddenly a very simple idea struck us: even if the three stones die, is White actually losing?]
;W[nk]C[White can still take advantage of the aji from the three stones.]
;B[ok]
;W[mk]
;B[oj]
;W[re]LB[qm:A]C[When White forces here, Black is at a loss to answer. Because of the wedge at A, Black cannot get much locally, while White still profits handsomely in the centre. Surprisingly, even capturing the three stones turns out to be no good for Black.])))))
(;W[kg]C[If White omits 136, then Black will not need to expend as many moves capturing the white stones.]
;B[jf]
;W[ii]
;B[jh]
;W[ji]
;B[ki]
;W[ij]
;B[hj]
;W[ik]
;B[hf]LB[gf:A]C[Black can now atari directly, which would not be possible if White had made the exchange at A. This way, Black clearly has more points than in the variations shown later.]))
(;W[nm]C[If White chooses to reinforce the centre, the corner will die.]
;B[np]
;W[lm]
;B[pn]
;W[rr]
;B[rp]C[Black's placement is the killing move.]))
(;W[kk]TR[km]C[Black thinks White will play the splitting move here, after which Black will happily sacrifice the marked stone.]
;B[kj]
;W[jk]
;B[ik]
;W[il]
;B[lk]
;W[ll]
;B[hj]
;W[hl]
;B[mk]
;W[lm]C[Although White has secured considerable territory, Black is prepared to hammer at White's weak points.]
;B[pm]C[White is at a loss to defend against this cut.]))
(;B[bd]C[If Black captures directly, the four stones on the left will suffer from shortage of liberties.]
;W[bg]
;B[ae]
;W[ck]
;B[bk]
;W[bl]C[White takes full advantage with the double hane.]
;B[cl]
;W[dk]
;B[bj]
;W[cm]C[Black is completely sealed in.]))
(;W[dh]C[If White presses directly, Black can connect cleanly with the second-line hane.]
;B[hb]
;W[ci]
;B[di]
;W[cf]
;B[bf]
;W[bi]
;B[bh]
;W[ah]
;B[bg]
;W[ck]
;B[ei]
;W[fh]
;B[fi]
;W[gh]
;B[gi]
;W[hh]
;B[hi]C[Black has no qualms about pushing all the way into the centre.]
;W[ih]
;B[ii]
;W[jh]
;B[ji]
;W[kh]
;B[ki]
;W[lh]
;B[bo]C[Finally, Black turns back to fight on the left side. Gu Li and Zhou Ruiyang were not sure about this variation - it would make for a very complicated game.]))
(;W[ip]C[If White starts the ladder, it seems as though Black should run out, but this is actually not the case.]
(;B[jo]C[Zhou Ruiyang showed what might happen if Black escapes. Although the ladder does not work yet, White can activate it with the push and cut in the upper left.]
;W[cf]
;B[bf]
;W[bg]
;B[bh]
;W[jn]
;B[io]
;W[ch]C[Now, Black must either relinquish the three stones at the bottom or allow White to capture in the upper left. This would be a success for White.])
(;B[pr]C["Let’s look at this another way," said Gu Li. Black can also ignore the ladder for now, and play normally with 2.]
;W[jo]C[If White captures...]
;B[cp]
;W[cq]
;B[bq]C[...Black takes sente in the bottom left, and seems to be doing fine.

This is one of the great marvels of Go: it seems that no matter the move, there is some way to make it work!])))
(;B[if]
;W[hf]
;B[hg]
;W[gf]C[When Black hanes at the head of two stones, White must hane in return, and Black's double hane looks very comfortable. But if we look closer, are Black’s profits actually that significant? White is alive with territory, and the aji of the cutting points diminishes Black's advantage in the middle. Furthermore, White has already invaded at the bottom. Has Black truly profited?

Despite this, Zhou Ruiyang emphasised strongly, "If it were me, I would have extended."

Wrong or right, AlphaGo has once again opened our minds to a new perspective. Perhaps we really can play this way.]))
(;B[hd]
;W[hc]C[If Black hanes inside, White will naturally crosscut.]
(;B[jc]C[This is Black's strongest move.]
;W[he]
;B[gd]
;W[gc]C[White fights back tenaciously. Black has two options, neither of which succeeds.]
(;B[ge]
;W[jd]
;B[kd]
;W[if]
;B[gf]
;W[kc]
;B[kb]
;W[lc]
;B[lb]
;W[mc]
;B[mb]
;W[hb]
;B[jb]
;W[ke]LB[ld:A][dg:B]C[White makes miai of A and B, so Black has no way to capture. This is a success for White.])
(;B[fd]
;W[ed]
;B[gf]
;W[jd]
;B[kd]
;W[kc]
;B[kb]
;W[lc]
;B[lb]
;W[mc]
;B[mb]
;W[hb]
;B[jb]
;W[ke]
;B[ld]
;W[if]TR[kc][lc][mc]C[White sacrifices the marked stones, and Black's top side has been effectively flattened.]
;B[ff]
;W[dg]
;B[ch]
;W[dh]C[Black faces a painful fight: the top side has been flattened, and the group in the middle is heavy. Black cannot bear the burden of the komi this way.]))
(;B[gc]
;W[hb]
;B[jc]C[If Black takes this simple approach, White can sacrifice one stone in return for life on the top.]
;W[gd]
;B[he]
;W[gb]
;B[ge]
;W[fd]
;B[je]
;W[lq]C[Black must capture in gote, and White is free to invade at the bottom. This is a success for White.]))
(;B[hc]C[If Black extends solidly, White will press on top.]
;W[hd]
;B[gc]
;W[jd]C[Black's position at the top is cramped, and Black has clearly been taken advantage of.]))
(;B[df]C[Suppose Black chooses the small avalanche.]
;W[cc]
;B[db]
;W[bc]
;B[eb]
;W[fc]C[Since White has the ladder, this extension works.]
;B[ef]
;W[fe]
;B[bb]
;W[cf]
;B[bf]
;W[cg]
;B[bd]
;W[bg]
;B[ac]
;W[ie]
;B[kd]
;W[cj]LB[ie:B][cf:A][cj:C]C[Although Black captures the stones in the corner, White has managed to cut at A, reinforce at B in sente, and finally extend at C. White is racing around the board, while Black has no clear profit. This result favors White.]))
(;B[cf]C[If Black extends once more, White will attach on the top.]
;W[hc]C[This move builds strength while retaining the possibility of claiming the corner.]
(;B[id]C[The extension lets White live easily.]
;W[hd]
;B[ie]
;W[dc]
;B[cc]
;W[ib]
;B[jb]
;W[hb]C[If Black denies White the corner, the hane and connection easily establish a base in the middle of Black's area. Black cannot be satisfied.])
(;B[hd]C[The hane does not turn out well either.]
;W[gc]
;B[id]
;W[cc]
;B[bc]
;W[dc]
;B[bb]
;W[fe]C[White establishes a comfortable base in the corner. This is insufficient for Black.]))
(;B[df]C[Black can also hane at the head of two stones, but now White can hane and connect in the corner.]
;W[cc]
;B[bc]LB[dc:A]C[Black must not cut at A, or the position will transpose to the small avalanche, which is analyzed in another variation.]
;W[dc]
;B[bb]
;W[ef]
;B[dg]
;W[gc]C[White gets a decent position at the top, and Black is dissatisfied.]))
(;B[dc]C[Normally Black's first instinct would be to defend the corner, letting White hane and build influence towards the left.]
;W[ce]
;B[ed]
;W[de]
;B[cc]
;W[ee]
;B[fd]
;W[fe]
;B[ge]
;W[gf]
;B[he]
;W[cj]LB[cc:13][dc:1][cd:3][dd:12][ed:5][fd:7][ce:2][de:4][ee:6][fe:8][ge:9][he:11][gf:10][cj:14]TR[ic]C[Black protects the top, and White extends on the left side. Although Black has built significant territory, the marked stone is inefficiently placed, while White's extension on the left doubles as an ideal pincer. Black cannot be satisfied.

If the result still seems difficult to judge, we might use tewari analysis to better assess its strengths and weaknesses. (This method, in which one permutes the order of moves, aims to clarify the position by creating exchanges that directly contrast good moves with bad ones.) Here, we have re-numbered the moves to achieve the same result in a different order. Now Black's initial stone is at the other 3-4 point. White’s corner approach at 2 is fairly common, but Black 3 and 5 are clearly a mistake in direction. Next, White presses with 6 through 10, an even exchange according to Go theory. Although the push at 12 takes away one of White's liberties, this hardly compensates for Black's losses with 3 and 5. Thus, White is clearly superior.])
(;B[de]C[If Black hanes on the outside instead, White will live in the corner.]
;W[cc]
;B[ed]
;W[dc]
;B[ce]
;W[ec]
;B[fd]
;W[fc]
;B[gd]
;W[ck]C[Although Black can get outside influence, because the side is so open, White can come back to pincer on the left. Black's wall will be very difficult to use effectively, and it is hard to see what Black is doing here! White prevails.]))
