(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Chinese]SZ[19]KM[7.50]TM[480]OT[3x30 byo-yomi]
GN[友谊赛]PW[12bTurboSai]PB[天可汗]WR[4d]BR[3d]DT[2020-04-29]PC[OGS: https://online-go.com/game/23499524]C[This is a KataGo-aided amateur analysis of a fascinating and complex endgame that came up in the LZ discord in the SAI channel. Commentary starts at move 232.

Overall, I am far from confident about the correctness of this commentary. Still, it is a fun exploration.]RE[B+Resign]
;B[pd]
;W[dp]C[12bTurboSai: [object Object\]
]
;B[pq]
;W[dd]C[12bTurboSai: [object Object\]
]
;B[fq]
;W[hp]C[12bTurboSai: [object Object\]
]
;B[cq]
;W[pp]C[12bTurboSai: [object Object\]
]
;B[op]
;W[qq]C[12bTurboSai: [object Object\]
]
;B[oq]
;W[dq]C[12bTurboSai: [object Object\]
]
;B[cp]
;W[do]C[12bTurboSai: [object Object\]
]
;B[dr]
;W[er]C[12bTurboSai: [object Object\]
]
;B[cr]
;W[eq]C[12bTurboSai: [object Object\]
]
;B[cn]
;W[qp]C[12bTurboSai: [object Object\]
]
;B[oo]
;W[qm]C[12bTurboSai: [object Object\]
]
;B[jq]
;W[qc]C[12bTurboSai: [object Object\]
]
;B[pc]
;W[qd]C[12bTurboSai: [object Object\]
]
;B[qf]
;W[rf]C[12bTurboSai: [object Object\]
]
;B[rg]
;W[re]C[12bTurboSai: [object Object\]
]
;B[qg]
;W[pe]C[12bTurboSai: [object Object\]
]
;B[qe]
;W[pb]C[12bTurboSai: [object Object\]
]
;B[ob]
;W[qb]C[12bTurboSai: [object Object\]
]
;B[nc]
;W[oe]C[12bTurboSai: [object Object\]
]
;B[nd]
;W[og]C[12bTurboSai: [object Object\]
]
;B[qk]
;W[oi]C[12bTurboSai: [object Object\]
]
;B[sf]
;W[sd]C[12bTurboSai: [object Object\]
]
;B[ph]
;W[oh]C[12bTurboSai: [object Object\]
]
;B[ql]
;W[rm]C[12bTurboSai: [object Object\]
]
;B[pi]
;W[jd]C[12bTurboSai: [object Object\]
]
;B[mf]
;W[li]C[12bTurboSai: [object Object\]
]
;B[jb]
;W[ld]C[12bTurboSai: [object Object\]
]
;B[ne]
;W[kc]C[12bTurboSai: [object Object\]
]
;B[fc]
;W[kg]C[12bTurboSai: [object Object\]
]
;B[od]
;W[ec]C[12bTurboSai: [object Object\]
]
;B[fd]
;W[nf]C[12bTurboSai: [object Object\]
]
;B[le]
;W[ke]C[12bTurboSai: [object Object\]
]
;B[mg]
;W[mh]C[12bTurboSai: [object Object\]
]
;B[lb]
;W[mb]C[12bTurboSai: [object Object\]
]
;B[mc]
;W[kb]C[12bTurboSai: [object Object\]
]
;B[ma]
;W[lc]C[12bTurboSai: [object Object\]
]
;B[nb]
;W[df]C[12bTurboSai: [object Object\]
]
;B[ka]
;W[ib]C[12bTurboSai: [object Object\]
]
;B[ff]
;W[ch]C[12bTurboSai: [object Object\]
]
;B[cc]
;W[db]C[12bTurboSai: [object Object\]
]
;B[fb]
;W[cd]C[12bTurboSai: [object Object\]
]
;B[ic]
;W[jc]C[12bTurboSai: [object Object\]
]
;B[ja]
;W[hc]C[12bTurboSai: [object Object\]
]
;B[id]
;W[he]C[12bTurboSai: [object Object\]
]
;B[ie]
;W[if]C[12bTurboSai: [object Object\]
]
;B[hb]
;W[je]C[12bTurboSai: [object Object\]
]
;B[ia]
;W[hr]C[12bTurboSai: [object Object\]
]
;B[hf]
;W[ig]C[12bTurboSai: [object Object\]
]
;B[ir]
;W[iq]C[12bTurboSai: [object Object\]
]
;B[jr]
;W[jp]C[12bTurboSai: [object Object\]
]
;B[kp]
;W[jo]C[12bTurboSai: [object Object\]
]
;B[ko]
;W[kn]C[12bTurboSai: [object Object\]
]
;B[ln]
;W[lm]C[12bTurboSai: [object Object\]
]
;B[jn]
;W[km]C[12bTurboSai: [object Object\]
]
;B[mn]
;W[kq]C[12bTurboSai: [object Object\]
]
;B[lq]
;W[dm]C[12bTurboSai: [object Object\]
]
;B[cm]
;W[kr]C[12bTurboSai: [object Object\]
]
;B[lr]
;W[pj]C[12bTurboSai: [object Object\]
]
;B[qj]
;W[is]C[12bTurboSai: [object Object\]
]
;B[ks]
;W[cl]C[12bTurboSai: [object Object\]
]
;B[bl]
;W[dl]C[12bTurboSai: [object Object\]
]
;B[hg]
;W[hh]C[12bTurboSai: [object Object\]
]
;B[fh]
;W[gh]C[12bTurboSai: [object Object\]
]
;B[fg]
;W[fi]C[12bTurboSai: [object Object\]
]
;B[mm]
;W[lk]C[12bTurboSai: [object Object\]
]
;B[bk]
;W[ej]C[12bTurboSai: [object Object\]
]
;B[dn]
;W[co]C[12bTurboSai: [object Object\]
]
;B[bo]
;W[en]C[12bTurboSai: [object Object\]
]
;B[fr]
;W[es]C[12bTurboSai: [object Object\]
]
;B[ho]
;W[gp]C[12bTurboSai: [object Object\]
]
;B[fp]
;W[bn]C[12bTurboSai: [object Object\]
]
;B[bm]
;W[bp]C[12bTurboSai: [object Object\]
]
;B[an]
;W[fo]C[12bTurboSai: [object Object\]
]
;B[go]
;W[in]C[12bTurboSai: [object Object\]
]
;B[js]
;W[ao]C[12bTurboSai: [object Object\]
]
;B[ap]
;W[bq]C[12bTurboSai: [object Object\]
]
;B[br]
;W[hd]C[12bTurboSai: [object Object\]
]
;B[ib]
;W[io]C[12bTurboSai: [object Object\]
]
;B[gr]
;W[pr]C[12bTurboSai: [object Object\]
]
;B[or]
;W[rl]C[12bTurboSai: [object Object\]
]
;B[rk]
;W[bi]C[12bTurboSai: [object Object\]
]
;B[eb]
;W[cb]C[12bTurboSai: [object Object\]
]
;B[qr]
;W[rr]C[12bTurboSai: [object Object\]
]
;B[ps]
;W[rs]C[12bTurboSai: [object Object\]
]
;B[mk]
;W[mj]C[12bTurboSai: [object Object\]
]
;B[ll]
;W[kl]C[12bTurboSai: [object Object\]
]
;B[ml]
;W[gn]C[12bTurboSai: [object Object\]
]
;B[sg]
;W[pa]C[12bTurboSai: [object Object\]
]
;B[sb]
;W[ra]C[12bTurboSai: [object Object\]
]
;B[se]
;W[rd]C[12bTurboSai: [object Object\]
]
;B[rb]
;W[gg]C[12bTurboSai: [object Object\]
]
;B[gf]
;W[lf]C[12bTurboSai: [object Object\]
]
;B[me]
;W[lg]C[12bTurboSai: [object Object\]
]
;B[sa]
;W[sk]C[12bTurboSai: [object Object\]
]
;B[sj]
;W[pn]C[12bTurboSai: [object Object\]
]
;B[oa]
;W[eh]C[12bTurboSai: [object Object\]
]
;B[ed]
;W[dc]C[12bTurboSai: [object Object\]
]
;B[cj]
;W[fe]C[12bTurboSai: [object Object\]
]
;B[ee]
;W[rj]C[12bTurboSai: [object Object\]
]
;B[sl]
;W[ef]C[12bTurboSai: [object Object\]
]
;B[ge]
;W[bj]C[12bTurboSai: [object Object\]
]
;B[ck]
;W[di]C[12bTurboSai: [object Object\]
]
;B[sm]
;W[sn]C[12bTurboSai: [object Object\]
]
;B[sk]
;W[rn]C[12bTurboSai: [object Object\]
]
;B[hs]
;W[hq]C[12bTurboSai: [object Object\]
]
;B[de]
;W[ce]C[12bTurboSai: [object Object\]
]
;B[oj]
;W[nj]C[12bTurboSai: [object Object\]
]
;B[ok]
;W[pl]C[12bTurboSai: [object Object\]
]
;B[pk]
;W[dk]C[12bTurboSai: [object Object\]
]
;B[ol]
;W[pm]C[12bTurboSai: [object Object\]
]
;B[po]
;W[qo]C[12bTurboSai: [object Object\]
]
;B[eg]
;W[dg]
;B[ci]
;W[ng]
;B[aj]
;W[bh]
;B[ds]
;W[om]
;B[nm]
;W[on]C[Analysis based on KataGo, several tens of thousands of playouts in each position, 32 threads, combined with my own amateur dan understanding.]
;B[nn]C[Right now, white should be winning. The thing white has to be careful of is the thousand year ko shape in the upper right. If it ends as seki, and all other areas of the board resolve "as normal", then white will win easily.

But if black kills the upper right, AND does not lose any moves in the endgame on the rest of the board, including filling the dame, then black will win (by 1.5). If black loses even one extra dame to white (a swing of 2 points), white will win even if black kills the upper right white group.

Black must prepare at least one *big* threat more than white before starting the ko in the upper right in order to win it. A small threat is not enough - white will happily ignore any small threat to live with points on the upper right, and win the game.

Since ko is black's only way to win, the upper right becoming ko is completely inevitable in this game. White has no way to stop it, and black WILL start it at some point.

Also, mostly it doesn't help white much to "fight" the small ko in the upper right early on, because white has no followup to win it. Black can take it back any time later. The only thing that fighting it does is to delay and mess with the exact moment that black can start it, and to buy white a little bit of time to remove bigger threats, so white must wait until the end to try to fight it.]
;W[qs]LB[kk:B][gq:A]C[Because ko for life in the upper right is inevitable, white's focus should be to eliminate all ways black can make big ko threats, and to preserve White's own big ko threats.

White has some small advantage in that black cannot afford to give up even one single dame extra in the endgame. But it is not a huge advantage. White has the less-solid shapes, so if both players straightforwardly just play all the endame and exchange dame, once all the dame are filled, black can start the ko and possibly be favored to win.

So white will have to take some time off of endgame moves to remove black ko threats. But the moment white does so, then the pressure is off from black too - black also gets time off because white got time off. If black uses that time off to play one more dame, then Black can even have a move of slack, and then can stop worrying about keeping up on endgame and *only* needs one big ko threat somewhere. So if white is not removing enough ko threats early, then white can lose this game.

The primary uncertainty comes from how many big enough ko threats black can make in the center. Ko threats like A and B are NOT directly big enough, so black needs to find ways to magnify their value first.
]
;B[pr]TR[rp]C[Fascinatingly, KataGo's neural net appears to understand a lot of this. The MCTS winrates seem to correspond pretty closely with the ko threat status of the board despite not reading all the way out, and the policy head is suggesting moves that indicate that it understands ko threat creation and destruction are the theme. For example, S4 is often suggested by the raw policy in variations as a good move for white. This would be a complete waste of a move in any other kind of position, but here is often good because it prevents black ko threats.

But the tactics are complicated, and KataGo is definitely not confident in many of the lines after white blunders a few times and makes the game close. It would be easy to imagine KataGo missing some key tactics or failing important part of the judgement in this kind of position.

Currently Black winrate 5%, -6 points.]
(;W[ea]C[For most of this endgame, both sides do not appear to understand the theme of this position. White should not be bothering with endgame moves like this.

This move is still okay, but see variation.]
;B[fa]
;W[gd]C[Major blunder by white. White loses their biggest threat on the board for nothing.

White's ko threats are important for giving white the ability to parry the black ko threats that cannot be eliminated in time. Losing them is very bad with a forced upcoming ko. White is still winning, but it is closer now.

Black winrate 15%, -3 points.]
;B[gc]
(;W[ai]LB[kk:A]C[Blocking here is perhaps a mistake. Now that white lost a big ko threat, connecting at A has become more important. See variation.

Black winrate 33%, score estimate close to 0.]
(;B[ak]C[Black probably should cut first in the center. See variation.]
;W[da]LB[kk:A]C[Again Kata wants white to protect A.]
;B[dj]
;W[fm]C[Black winrate 38%.]
;B[pg]
;W[of]
;B[nk]
;W[eo]
;B[qa]
;W[aq]
;B[ar]
;W[ra]C[Black winrate around 40-45% now.

White has done a poor job of removing threats, and is running out of time by playing out the endgame as usual.]
(;B[rq]C[This cut makes it too easy for white. Black helps white eliminate the big ko threats and seals black's own loss when he might have had some chances.

Black winrate drops to 23% now.

See variation.]
(;W[sq]C[White blunders right back. Now black's ko threats in this corner still threaten the entire white group's life. See variation for how white could have punished.

Black winrate back to about 40%.]
;B[qa]
;W[fs]C[Another mistake, white wastes a big ko threat. 

White cannot afford to use these ko threats on the "small" ko, because white has no followup to "win" the small ko, as discussed before. Black can simply take the small ko right back later.

Black might be winning now. Black 60%.
]
;B[gs]
(;W[ra]C[See variation for an example KataGo line.]
;B[rp]C[Black in this game also doesn't seem to understand that fighting the small ko is not so useful.

But at least this threat loses not as much. After white answers, black still has a threat for the whole white group, which is big enough. And both before and after white could remove the threat in 1 move, which white may often do in variations, in which case black is net neutral on big threats.]
;W[ro]
;B[qa]
;W[nq]C[Another blunder, white's move here does help white generate threats later, so it is not as bad as passing, but threat removal in the center is much better.

Black is finally almost surely winning now. KataGo has black at 90%.]
(;B[sc]C[Very likely a blunder. Black winrate drops from 90% to 25% and going lower over time.

Black doesn't have the big threats ready yet. Black needs to enlarge their threats first. So suddenly black is losing again.

Unfortunately, now is the moment that white chooses to resign this game, right after black's blunder likely hands the game back to white, so black wins anyways.

See variation.])
(;B[pf]LB[md:A][pf:B]C[Black should be able to win this game like so. Many other lines might also work too.

First calmly remove the dame, else A <-> B could serve as white's ko threat (black still needs to not fall behind on dame).

Some example variations follow.]
(;W[ra]C[If white tries to fight the small ko to delay black's final big ko...]
;B[kk]
;W[lj]
;B[qa]
;W[no]
;B[np]
;W[ra]
;B[ni]C[This ko threat is not big enough for the big ko, but is plenty fine for the small ko, since white has no way to permanently win the small ko even if ignoring this move.]
;W[nh]
;B[qa]
;W[mp]C[White can make use of the earlier O3 move to try to generate some threats for the big ko, but it's not enough. Black can even just start the big ko anyways.]
(;B[sc]
;W[ra]
;B[jl]
;W[jm]
;B[qa]
;W[nr]
;B[mo]
;W[ra]
;B[sr]
;W[sp]
;B[qa]
;W[os]
;B[no]
;W[ra]
;B[im]C[If white answers, white has no threats left, so white loses the game.])
(;B[mo]C[Black can also just answer.]
;W[ra]
;B[jm]
;W[jl]
;B[qa]
(;W[he]C[Moves like this can sometimes be ko threats for the small ko by virtue of generating a ko threat for the big ko if unanswered.]
;B[sc]LB[lh:B][jk:A][sr:C]C[But again here black can just bully through anyways with A,B,C available.])
(;W[sp]LB[lh:B][jk:A]C[White removing a threat isn't enough because black still has A,B.])))
(;W[sp]C[If white removes a threat...]
;B[kk]C[Black first magnifies the center threat, otherwise it would be too small.]
;W[lj]
;B[sc]C[Then starts the big ko.]
;W[ra]
;B[jl]C[Now this is big enough.]
;W[jm]
;B[qa]C[White is out of threats.])
(;W[md]LB[ep:A][gq:B]C[If white resists and tries to keep the dame as ko threats at A,B...]
;B[kk]C[Black is fine, those last dame aren't enough ko threats for white, as long as we magnify the center threat here first.]
;W[lj]
;B[sc]
;W[ra]
;B[jl]
;W[jm]
;B[qa]
;W[hn]
;B[ep]
;W[ra]
;B[im]
;W[jn]
;B[qa]
;W[gq]
;B[is]
;W[ra]
;B[sr]C[White is out of threats.])
(;W[kk]C[If white guards the center...]
;B[sc]
;W[ra]
;B[sr]C[Black still has this threat, and white has no threats.])))
(;W[rp]C[Example line for how play might proceed if white removes this ko threat.

Super complicated. A lot of the "weird"-looking moves are because this battle is about playing threats to make or remove threats, or to enlarge or diminish the size of threats.

The winrate of 60% reflects that white has no major ko threats any more, black's primary task now is just to make some big center threats while not falling behind on dame. It's looking more favorable for black.

]
;B[gi]C[The tactics are incredibly unintuitive still though.

]
;W[hi]
;B[pf]
;W[lj]LB[kk:A]C[For example of unintuitive tactics, this move, if played at A, loses much more quickly for white, KataGo jumps to 97% black winrate.

A was the suggested correct move in many earlier points in this game, but now, assuming we don't have some sort of blind spot issue, it seems connecting here is the right move instead for some reason.]
;B[gj]
;W[md]C[White squirms a little. Black can't ignore since black has to match dame.]
;B[is]
;W[ra]
;B[ep]
;W[hn]
;B[qa]
;W[ei]
;B[ek]
;W[ra]
;B[kk]
;W[jk]
;B[qa]
;W[he]C[This move makes sense as an attempted ko threat in the small ko because it threatens to make a ko threat for the big ko.]
;B[sc]C[But at least in this variation, it's not enough. Black starts the big ko anyways.]
;W[ra]
;B[fj]
;W[dh]
;B[qa]
;W[gd]
;B[hd]
;W[ra]
;B[em]LB[jl:A]C[And now black wins the game. This threat is too big to answer, but also white is out of threats.

As another example of how tricky things are, if black played A here instead, KG believes it's not big enough for black to win, white will ignore to live in the upper right and still be winning.]
;W[el]
;B[qa]
;W[gq]
;B[rc]C[In this particular line, black wins, but there are many other variations too.]))
(;W[rp]LB[gs:A]TR[rr][qs][rs]C[Like this, black will never have a big ko threat in this corner again. Black has ko threats, but only threatening these 3 stones. These small ko threats will not help black win the upper right ko.

Black still needs A, so white gained a whole free move to help solidify the center against any big ko threats.]))
(;B[kk]LB[rp:A][gs:B]C[At this point Kata is completely unsure about the game result, black winrate 45%. 

White still owes a move at A, which buys black precious time to do things like eliminate white's threat at B. Black has not fallen behind on endgame, and has lots of cuts in the center to try to generate threats. The dame help white a little since black still cannot fall behind on them, but again only a little since if white takes time off to remove ko threats, black gets to take time off too to generate ko threats.
]
;W[lj]C[Example variation.

Super complicated as both players try to create and destroy threats.]
;B[gs]
;W[jm]
;B[ni]
;W[nh]
;B[pf]
;W[rp]
;B[qa]
;W[jh]C[There are tons of other possiible moves and move orderings for both players in all of these variations. KataGo with mere tens of thousands of playouts is nowhere near able to solve this position.]
;B[gi]
;W[hi]
;B[im]C[Here's the tesuji from before, in this variation!]
;W[ra]
;B[ro]C[Funnily enough, moves like this are *not* entirely meaningless. It creates a threat if unanswered - T5 next is a big enough threat for black. 

But if white answers to stop this black future threat, it lets black take back R19. So a move that is not a direct ko threat but makes a future big ko threat can act a ko threat in this situation for the small ko.]
;W[hm]
;B[qa]
;W[sp]
;B[cf]
;W[ei]LB[lh:B][jl:A]C[And on and on. Probably both players have made mistakes in all of this maneuvering in this variation.

White needs to be very careful that black doesn't get a big enough ko threat. A and B are both big threats, but not big enough! Black needs to find a way to make them even bigger.]
;B[gj]LB[lh:A]C[It's not clear that black can win the game, and I suspect personally that white is winning with proper play, but it's extremely easy also for white to mess up too - there are tons of traps in all of these lines. For example...]
;W[ek]LB[dg:C][ei:A][dl:B]C[If white connects here to guard against threats on the left against A/B/C that might start with black cutting here... (NOT the move kata would play for white).
]
;B[ik]LB[ii:B][jl:A]C[Then kata believes white is in trouble after this move. It makes miai of A and B as ko threats, and now finally these threats will be big enough with J9 helping them out.]
;W[ra]C[But at this moment now white can complicate by starting the small ko again. White can't win the small ko permanently, but it buys white time to answer both threatened ko threats.]
;B[bb]C[So black makes another threat to make a threat here. This move looks very funny, like many other moves we've seen, normally we'd call this move dead in gote, but here it is very strong.]
;W[il]
;B[qa]
;W[ih]C[Suppose white answers both of the original threatened ko threats, just for demonstration.]
;B[gq]
;W[hn]
;B[sc]C[Big ko starts!]
;W[ra]
;B[bc]C[Now black has this ko threat. White has no threats...]
;W[rc]
;B[bf]C[So for example, this is winning for black.

There are of course a gazillion other variations. Who wins with proper play? Maybe white, hard to tell for sure for me given that KataGo is unable to understand it well enough.]))
(;B[kk]C[KataGo thinks black should cut here first.]
;W[lj]
;B[ak]C[Black still needs to come back and protect in order to not fall behind on endgame. But the cut first might be important. Why?]
;W[jm]C[Suppose that white now protects.

If white connected right away before black's cut, black would have:
* No big ko threats 
* No way to create a big ko threat such that white could not immediately remove the threat in response, restoring back to 0 threats.

But now white's shape is bad. Black has:
* No big ko threats
* BUT black sometimes hasa tesuji to create a big ko threat that white cannot remove in response!

In some deeper variations this actually matters. White still wins with proper play, probably, but it is closer.

What is the tesuji?
]
;B[gi]
;W[ih]C[White has other moves besides this, but for simplicity, suppose white just connects.]
;B[im]C[Tesuji!

None of white's moves can stop black from having a huge ko threat now.]
(;W[jk]C[This move does not stop the threat.]
;B[jl])
(;W[jl]C[This move does not stop the threat.]
;B[hm]C[This is a huge ko threat because...]
;W[aa]
;B[hn]
;W[jn]
;B[gq]
;W[ip]
;B[jk]
;W[il]
;B[hl]
;W[ik]
;B[ij]
;W[hk]
;B[gk]
;W[hj]
;B[hi])
(;W[jn]C[This move does not stop the threat.]
;B[hm]C[This is a huge ko threat because...]
;W[aa]
;B[hn]
;W[jl]
;B[gq]
;W[ip]
;B[jk]
;W[il]
;B[hl]
;W[ik]
;B[ij]
;W[hk]
;B[gk])))
(;W[kk]C[KataGo prefers white to connect here as a straightforward way to win.

Black winrate 15%, estimate -3 points.

Example variation follows.]
;B[qa]LB[cf:C][ih:B][gi:A]C[Because white make a non-endgame points move, black has the slack to make a non-endgame points move, like capturing here.

Black could also play A,B,C, or take a moment to get one move ahead on the endgame so as to permanently have endgame slack. The problem is that white will keep removing threats and leave black no way to win the ko at all.
]
;W[eo]C[White eliminates threats.]
;B[sc]C[KG wants black to try to generate more threats before starting this ko or to get ahead on the endgame, and evaluates starting the ko right away as a total loss. But we explore it just to see how the ko threat situation plays out.]
;W[ra]
;B[so]
;W[rp]
;B[qa]
;W[fs]
;B[gs]
;W[ra]
;B[ro]
;W[sp]
;B[qa]LB[gd:A]C[Because white lost the huge threat at A earlier, white will die in the upper right. So now we see how white's blunder makes a difference. But white still wins, because black falls behind on endgame.]
;W[da]
;B[rc]
;W[ai]
;B[ak]
;W[nk]C[White wins by 2.5 points, I think, which is not far from the original score estimate.]))
(;W[kk]C[KataGo wants white to ignore endgame moves and just connect solid here. This move eliminates black's ability to create future big ko threats here and wins easily.

It's conceivable that a move like this is even best for maximizing score. The fewer big ko threats black has, the less compensation black can get out of the upper right ko.

Example variation follows.]
;B[gi]C[Black cuts to try to generate bigger ko threats here before starting the upper right ko.]
;W[ih]C[White denies black several ko threats here.]
;B[qa]C[Black first needs to spend a move to be able to start the bigger ko.]
;W[eo]C[White simply uses the time to deny more black ko threats.]
;B[sc]C[If white simply ignores all the endgame moves and just focuses on removing ko threats, black will quickly find themselves unable to ever win this ko. 

So once white starts doing so, black might actualy be in quite a rush to try to start the ko before it's too late, since it's their only hope of winning. So suppose black starts it now.]
;W[ra]
;B[so]
;W[rp]
;B[qa]
;W[gd]
;B[gc]
;W[ra]
;B[ro]
;W[sp]
;B[qa]
;W[fs]C[Big enough for white to win, black can't afford to give white this much.]
;B[gs]
;W[ra]
;B[fj]LB[gq:A]C[Black has no big enough ko threats. This threat is not big enough, neither is A.]
;W[rc]
;B[ei]
;W[hj]C[This is a comfortable win by white. Many other moves for white here also work. Black behind by 5 or 6ish points here.]))