I made an endgame analysis of the only game between Fan & Alphago that was played out to the end. It starts at 146 and ends at 250.
My overall impression of the endgame:
Of all the important areas identified at 146, White only got 1 gote and its follow-up.
Black got the other big gote at but more importantly Black got all the sente moves:
(...)
To my surprise, it seems that Fan Hui played a much better endgame than Alphago, while one would expect that the closer you get to the end, the better the evaluation system of the algorithm would be. Of course, it might simply maximize the probability of winning, even if by a small margin, rather than maximizing the win.
Also, while I don't know if Kim Myungwan meant this part of the game when he said that Alphago doesn't know the value of sente, this endgame analysis certainly supports the idea.
(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Chinese]SZ[19]KM[7.50]TM[3600]OT[3x30 byo-yomi]
PW[AlphaGo]PB[Fan Hui]BR[2p]DT[2015-10-05]EV[AlphaGo vs Fan Hui five game match]RO[Game 1]PC[London, England]WT[Computer]BT[Human]SO[https://gogameguru.com/]C[Start at 146
Conclusion at 250]RE[W+2.50]
;B[pd]
;W[dd]
;B[pp]
;W[dq]
;B[co]
;W[dl]
;B[dn]
;W[fp]
;B[bq]
;W[jq]
;B[cf]
;W[ch]
;B[fd]
;W[df]
;B[dg]
;W[cg]
;B[dc]
;W[ce]
;B[cc]
;W[hc]
;B[fb]
;W[nc]
;B[qf]
;W[pb]
;B[bf]
;W[be]
;B[ef]
;W[de]
;B[qc]
;W[kc]
;B[qn]
;W[cm]
;B[cr]
;W[mq]
;B[oq]
;W[qm]
;B[pm]
;W[ql]
;B[rn]
;W[pl]
;B[om]
;W[qi]
;B[hq]
;W[hp]
;B[gq]
;W[gp]
;B[iq]
;W[ip]
;B[jr]
;W[kq]
;B[er]
;W[rg]
;B[qg]
;W[rf]
;B[re]
;W[qh]
;B[kr]
;W[ln]
;B[sf]
;W[rh]
;B[qb]
;W[fe]
;B[el]
;W[ek]
;B[fk]
;W[ej]
;B[fl]
;W[dm]
;B[fj]
;W[il]
;B[fi]
;W[ei]
;B[fh]
;W[gd]
;B[dh]
;W[ci]
;B[di]
;W[cj]
;B[fn]
;W[em]
;B[hn]
;W[in]
;B[en]
;W[oo]
;B[np]
;W[nn]
;B[po]
;W[hm]
;B[fm]
;W[nl]
;B[og]
;W[nr]
;B[or]
;W[nh]
;B[oj]
;W[ol]
;B[oh]
;W[ni]
;B[oi]
;W[ng]
;B[nf]
;W[mf]
;B[ne]
;W[me]
;B[gc]
;W[hb]
;B[bd]
;W[ed]
;B[fc]
;W[ff]
;B[ae]
;W[bg]
;B[af]
;W[eh]
;B[fg]
;W[eg]
;B[ge]
;W[hd]
;B[gf]
;W[ee]
;B[if]
;W[fa]
;B[ga]
;W[gb]
;B[ea]
;W[ec]
;B[eb]
;W[nd]
;B[je]
;W[pe]
;B[oe]
;W[od]
;B[of]
;W[pc]
;B[qd]
;W[jh]
;B[kd]
;W[lc]
;B[nj]
;W[hh]
;B[hg]
;W[mj]
;B[mk]
;W[lj]
;B[nk]
;W[lk]LB[pa:B][jc:G][hj:D][qj:H][sk:C][ml:I][bn:A][eq:E][os:F]SQ[nr][or]C[We can discuss the endgame from here, although White got an early endgame exchange in at move 92
Black has 11+10+13+14 = 48
White has 12+12 + 18+ 4 +6, 5 = 52,4
A - mutual reduction of territory but not impacting critical eyespace
B - sente for White as it impacts Black's second eyespace but only reducing territory from Black's perspective
C - reducing white territory AND impacting eyespece, white not fully connected
D - reducing territory
E - threatening to cut off black group / white stone
F - reducing territory and impacting eyespace
At G and H Black can make a dent into White's territory
At I there is a cut/connect with uncertain value
If Black plays and tries maintaining sente, I would go like this:
C sente, B probably sente, D destroy territory and affect thickness
from White's perspective
B' sente, F sente, C' gote
A and E seem to come latest]
;B[pa]C[Fan aims for double sente]
;W[rm]LB[sn:A][os:B]C[alphago takes gote and makes miai of A & B]
;B[mp]
;W[lp]
;B[lr]
;W[lq]LB[na:A][jc:E][hj:B][bn:C][eq:D]C[Black can continue eatng territory at A. If White keeps ignoring, then E threatens to cut off the 5 stones.
Black B, C & D are still available]
;B[bn]C[Shapewise this is not ideal.]
;W[qq]
;B[rp]
;W[rq]
;B[qp]C[IS White aiming for a force to capture?]
;W[ag]C[White executes a 1 pt sente.]
;B[ad]
;W[cp]
;B[bp]LB[bm:A]C[This exchange reduces the value of blocking at A]
;W[oa]C[So White moves to this gote]
;B[qa]
;W[dr]
;B[ds]
;W[ob]
;B[ml]LB[hj:B][bm:A]C[Black seems to think this is now bigger tan A & B]
;W[nm]
;B[pn]
;W[hj]
;B[kg]LB[bm:A]C[A is now the last big point]
;W[jg]
;B[kf]
;W[kh]
;B[bl]C[Black gets it]
;W[bm]
;B[am]LB[pa:B][ag:H][hj:D][ml:G][rm:C][bn:A][cp:E][qq:I][ns:F]C[If we recover,
Black got A in gote then followed up in sente
Black got B in (postponed) sente
Black took G in gote
White took C in gote
White took D in gote
White took E in sente and followed up in sente
White injected a 1 pt sente at H
White created some aji in I
Nobody took F
]
;W[bk]LB[jc:F][lg:D][ll:C][sm:E][eq:A][os:B]C[Black can now play A to prevent a White sente there but is it any points?
B remains a 2 pt sente but it destroys all aji in the corner
C makes a dent in White's central territory
D is an ugly move that destroys some territory
E is a two point gote and creates some aji
F is a 1 pt sente
I expect C first then perhaps a reverse sente at B]
;B[jc]C[Fan chooses this sente]
;W[jb]
;B[lm]C[Then he picks my first area but not the exact spot]
;W[km]LB[ll:A]
;B[mn]
;W[mo]
;B[mm]
(;W[no]C[I wonder if this is best]
;B[kl]
;W[jm]
;B[ll]LB[lg:B][jk:A]C[This was clearly a better sequence. Question is now if White will protect his central territory
A and B look like miai]
;W[lg]C[Alphago prefers this 2-3 point reverse sente]
;B[jk]C[indeed Black executes the miai]
;W[cl]
;B[qj]C[This move hinges on the aforementioned aji]
(;W[rj]
;B[gm]C[This is about 3-4 gote with some follow-up]
;W[ho]
;B[al]C[3 gote]
;W[ak]
;B[an]
;W[ic]C[1 gote with some follow-up?]
;B[mr]
;W[nq]
;B[ns]
;W[op]
;B[pq]LB[lg:D][ll:C][sm:E][eq:A][ns:B]TR[ic][rj][al][ho]SQ[jc][qj][gm]C[Black makes points at the bottom, sacrifices 2 stones and fixes his aji. Recovering, ...
A - nobody cares
B - Black made a trade there
C - Black found a tesuji there to intrude
D - White got it
E - nobody cared
Other than that Black and WHite got in a few sente (squared) and gote (triangled) moves. It seems to me that Black gained here.
]
;W[jd]LB[ld:D][jj:B][pj:A][hl:G][sm:E][gn:F][fq:C]C[this is 2 gote with follow-up
A - is miai with the current move
B - is a few points
C - looks like a valuable reverse sente with follow-up
D - is a point in almost sente for White
E - and there is this 2 point gote
F - is about 2,5 pt
As Black I would probably play C now or else A and keep D/F as miai]
;B[pj]
;W[sg]
;B[ii]
;W[se]
;B[sd]
;W[ih]
;B[ji]
;W[hi]
;B[ie]
;W[ld]
;B[ke]
;W[he]
;B[gg]
;W[eq]
;B[fq]
;W[ep]
;B[cq]
;W[gn]LB[ld:D][ji:B][pj:A][sm:E][gn:F][fq:C]C[Pause:
Black got A, B and C
White got D & F
Nobody cared about E
Again I have the sense that Black gained
]
;B[ki]
;W[li]
(;B[ik]LB[ha:D][id:G][sf:F][ph:H][hk:I][qk:C][sn:B][fo:E][dp:A]C[This is necessary to avoid a tesuji
9 moves remain
A - 2,5 gote
B - 2 gote
C - 1 sente Black
D - actually this is white's privilege
E - 1,5 pt gote
F - a half pointer
G - 1,5 gote
So likely we'll see
H - 1 gote with follow-up
I - 2,5 gote (or 1 sente)
White A, Black C, Black B', White E, Black G, White D and F
]
;W[sn]C[nope]
;B[so]
;W[sm]
;B[dp]
;W[eo]
;B[id]
;W[jc]
;B[do]
;W[fo]
;B[hk]
;W[hl]
;B[cb]
;W[ph]
;B[pg]
;W[qk]
;B[ha]
;W[ia]
;B[fa]
;W[ca]
;B[ba]
;W[dj]
;B[cd]
;W[sf]LB[pa:C][jc:D][qj:E][kl:G][rm:A][bn:B][ns:F]C[The game is done.
My overall impression of the endgame
Of all the important areas, White only got A and its follow-up.
Black got the big gote at B but more importantly Black got all the sente moves:
C was almost double sente, which White ignored for a while but eventually answered
Black reduced at D and E
With F Black made a conscious trade at the bottom, removing another sente endgame by White
And Black also intruded White's centre at G, almost without cost.
To my surprise, it seems that Fan Hui played a much better endgame than Alphago, while one would expect that the closer you get to the end, the better the evaluation system of the algorithm would be. Of course, it might simply maximize the probability of winning, even if by a small margin, rather than maximizing the win.
Also, while I don't know if Kim Mingyuan meant this part of the game when he said that Alphago doesn't know the value of sente, this endgame analysis certainly supports the idea.]
;B[gl]
;W[gj]
;B[gk]
;W[ij]
;B[kk]
;W[lh]
;B[ig]
;W[lf]
;B[le]
;W[gh]
;B[kj]
;W[jf]
;B[hf]
;W[jl]
;B[jj]
;W[gi]
;B[pi]
;W[cn]
;B[pk]
;W[ok]
;B[on])
(;B[dp]
;W[jj]
;B[ij]
;W[ik]
;B[kj]
;W[kk]))
(;W[pj]C[I dismissed the black move because it can be taken]
;B[pk]
;W[pi]
;B[ok]
;W[qk]
;B[rj]C[Black creates aji in gote. I don't see the point except a force to capture?]))
(;W[kn]
;B[no]
;W[rk]))