Pretty cool endgame problem

[Bill Spight]

gonuts solved the subproblem.

(;FF[4]GM[1]SZ[19]AP[GOWrite:2.2.21]ST[2]CA[ISO8859-1]PB[ ]PW[ ]FG[259:]AW[br][bo][cl][bl][dq][dp][co][cn][bk][cm]PM[2]GN[ ]AB[cj][bj][aj][dl][cp][bp][do][dn][ck][dm]
;B[an]
(
;W[ao]
;B[al]
;W[am]
;B[bm]
;W[bn]
;B[ak]
;W[am]
)
(
;W[ap]
;C[Gonuts solved this subproblem.]B[ao]
;W[am]
(
;C[Black does best to sacrifice his stones. This is sente.]B[ak]
;C[Note the dame at A-08. In the main variation Black got to play there with sente, which means that White gets one more point in this veriation.]W[bn]
)
(
;B[aq]
;C[White makes an eye.]W[ak]
;C[Black loses this semeai.]B[bn]
;W[bq]
;B[ap]
;C[Eye vs. no eye.]W[cq]
)

)

)

White gets one point more in this variation than in the main variation.

[Bill Spight]

(;FF[4]GM[1]SZ[19]AP[GOWrite:2.2.21]ST[2]CA[ISO8859-1]PB[ ]PW[ ]FG[259:]AW[br][bo][cl][bl][dq][dp][co][cn][bk][cm]PM[2]GN[ ]AB[cj][bj][aj][dl][cp][bp][do][dn][ck][dm]
;B[an]
(
;W[ao]
;B[al]
;W[am]
;B[bm]
;W[bn]
;B[ak]
;W[am]
)
(
;W[ap]
;B[aq]
)

)

What is White's play after in the variation?

[gonut]

Endgames are the worst part of my game, except for joseki, fuseki, middle game, yose, and tsumego. But here goes an attempt to answer Bill's last question anyway...

[sgf-full](;
AB[aj][bj][cj][ck][dl][dm][dn][do][cp][bp][an][aq]
AW[bk][bl][cl][cm][cn][co][bo][dp][dq][br][ap]
(;
W[am]
C[May be best, but depends on the rest of the board?];
B[ak];W[bn];B[al]
C[Black ends in sente.]
)
(;
W[ao]
C[Another possibility.];
B[al]
C[White loses 3 points relative to the main line, and later loses 2 more points capturing the A3 stone. But Black ends in gote.

So this line would be better for White, given at least a 5 point play elsewhere.]
)
)[/sgf-full]

[Bill Spight]

gonuts has solved this subproblem too.

I have added some comments to his SGF file.

(;ST[2]SZ[19]CA[ISO8859-1]GM[1]AP[GOWrite:2.2.21]FF[4]PM[0]FG[259:]AW[br][bo][cl][bl][dq][dp][co][cn][bk][cm][ap]AB[cj][bj][aj][dl][cp][aq][an][bp][do][dn][ck][dm]
(
;C[May be best, but depends on the rest of the board?

*** Correct. It is almost always best, but that depends upon the rest of the board. ]W[am]
;B[ak]
;W[bn]
;C[Black ends in sente.]B[al]
;C[*** Right. Note that the net result is the same is the main line.]W[ao]
)
(
;C[Another possibility.]W[ao]
;C[White loses 3 points relative to the main line, and later loses 2 more points capturing the A3 stone. But Black ends in gote.So this line would be better for White, given at least a 5 point play elsewhere.

*** It is possible that this is best for White, but your conclusion does not follow. The position after the White connection is worth 1 point less for White, on average, than the position in the other line. But B2 gains only 4 points. If there were a play elsewhere that gained 5 points, Black should take it, as a rule.

Going back to the original problem, however, this line is not good for White, because White does not have the throw-in at A-07. If White is going to play at A-05, he should not play at A-04 first. ]B[al]
)

)

And that means that, along with his earlier work, gonuts has solved the original problem, as well. Correct play for Black in it is the atari at A-03, which yields this subproblem.

The end result is the same as in the main line in Gokyo Seimyo, so I did not find an improvement. And that line is cool for both players. However, I thought that the atari (A-03) was pretty cool. The cut (A-05), while it looks natural, loses a dame and, hence, 1 point by comparison.

[Harleqin]

[sgf-full](;AP[another subproblem]CA[ISO8859-1]ST[2]FF[4]SZ[19]GM[1]PB[ ]AB[aj][bj][cj][ck][dl][dm][dn][do][cp][bp]FG[259:]AW[bk][bl][cl][cm][cn][co][bo][dp][dq][br]PW[ ]PM[2]GN[ ]
;B[an]
(;W[am]))[/sgf-full]

What happens here?

[Bill Spight]

(;AP[another subproblem]CA[ISO8859-1]ST[2]FF[4]SZ[19]GM[1]PB[ ]AB[aj][bj][cj][ck][dl][dm][dn][do][cp][bp]FG[259:]AW[bk][bl][cl][cm][cn][co][bo][dp][dq][br]PW[ ]PM[2]GN[ ]
;B[an]
(;W[am]))

What happens here?

(;ST[2]GM[1]AP[GOWrite:2.2.21]SZ[19]FF[4]CA[ISO8859-1]AB[cj][bj][aj][dl][cp][bp][do][dn][ck][dm]PM[2]AW[br][bo][cl][bl][dq][dp][co][cn][bk][cm]GN[ ]PW[ ]FG[259:]PB[ ]
;B[an]
;W[am]
;B[ak]
;W[bn]
;C[Later Black has this one point sente.]B[al]
;W[ao]
)

This also gives the same result as the main line.