Endgame problem, what's the best move order?

dany · #1

Click Here To Show Diagram Code: [go]$$c Black to play $$ +---------------------------------------+ $$ | . O X X X X X O O O O . O . . . . . . | $$ | O O . O O . X O O O X X O . . . . . . | $$ | . O . . O X X X X X X O O . . . O . . | $$ | O O X , . X O O O , O O . . . O . . . | $$ | O X X O X X O O O X . O . . O . . . . | $$ | O X . O X X X X X X . O . . . . . . . | $$ | O X X X X O O O . O O O . . . . . . . | $$ | O O O O X O O X X X O O O O O O O O O | $$ | . O X X X X X X O X X X X X O . . . . | $$ | . O . O O . X O O , O O . X O , . . . | $$ | O O . . O O X O O . . O . X O O O O O | $$ | . O X . . X X O O X . . . X X X X X X | $$ | O X X O X X O O X X O X X . . . . . . | $$ | O X O O X O . O X . O X . X . . . . . | $$ | O X X X X O O O X O O . X . X . . . . | $$ | O O O O O O . O X X X X . . . X . . . | $$ | . . . . . O O O O O O X . . . . X . . | $$ | . . . . . O . O . . O X . . . . . . . | $$ | . . . . . O . . . . O X . . . . . . . | $$ +---------------------------------------+[/go]

ez4u · #2

dany wrote:

Click Here To Show Diagram Code: [go]$$c Black to play $$ +---------------------------------------+ $$ | . O X X X X X O O O O . O . . . . . . | $$ | O O . O O . X O O O X X O . . . . . . | $$ | . O . . O X X X X X X O O . . . O . . | $$ | O O X , . X O O O , O O . . . O . . . | $$ | O X X O X X O O O X . O . . O . . . . | $$ | O X . O X X X X X X . O . . . . . . . | $$ | O X X X X O O O . O O O . . . . . . . | $$ | O O O O X O O X X X O O O O O O O O O | $$ | . O X X X X X X O X X X X X O . . . . | $$ | . O . O O . X O O , O O . X O , . . . | $$ | O O . . O O X O O . . O . X O O O O O | $$ | . O X . . X X O O X . . . X X X X X X | $$ | O X X O X X O O X X O X X . . . . . . | $$ | O X O O X O . O X . O X . X . . . . . | $$ | O X X X X O O O X O O . X . X . . . . | $$ | O O O O O O . O X X X X . . . X . . . | $$ | . . . . . O O O O O O X . . . . X . . | $$ | . . . . . O . O . . O X . . . . . . . | $$ | . . . . . O . . . . O X . . . . . . . | $$ +---------------------------------------+[/go]

Thanks dany! This was interesting. But without a little more info, it was hard to judge how interesting at a glance. So let me confirm the situation.

Assuming Japanese rules and no komi, the overly straight-forward sequence below appears to be jigo. Note that Black has gained 36 points under the captured stones plus 1 additional point with moves 7 and 9 for a total of 37 points in the contested areas. The problem then becomes how can Black do better than this and how does White resist? From here I think there are people that can attempt this in their heads without needing an editor.

Click Here To Show Diagram Code: [go]$$c For Reference $$ +---------------------------------------+ $$ | . O X X X X X O O O O 1 O . . . . . . | $$ | O O . O O . X O O O X X O . . . . . . | $$ | . O . . O X X X X X X O O . . . O . . | $$ | O O X 6 . X O O O 3 O O . . . O . . . | $$ | O X X O X X O O O X . O . . O . . . . | $$ | O X . O X X X X X X . O . . . . . . . | $$ | O X X X X O O O 5 O O O . . . . . . . | $$ | O O O O X O O X X X O O O O O O O O O | $$ | . O X X X X X X O X X X X X O . . . . | $$ | . O . O O . X O O , O O . X O , . . . | $$ | O O . . O O X O O . 8 O 9 X O O O O O | $$ | . O X 4 . X X O O X 2 7 . X X X X X X | $$ | O X X O X X O O X X O X X . . . . . . | $$ | O X O O X O . O X . O X . X . . . . . | $$ | O X X X X O O O X O O . X . X . . . . | $$ | O O O O O O . O X X X X . . . X . . . | $$ | . . . . . O O O O O O X . . . . X . . | $$ | . . . . . O . O . . O X . . . . . . . | $$ | . . . . . O . . . . O X . . . . . . . | $$ +---------------------------------------+[/go]

RobertJasiek · #3

Since there are no kos, the "4" and "6" local endgames can be treated as such, in which Black has an essentially simple follow-up (comprising a 3-move sequence) and White has none. Therefore, my theory about several (here: two) such local endgames applies. Without having to calculate the actual move values and follow-up move values, we can simply denote them as M4 and F4, and M6 and F6, respectively. We have M4 >= M6 and F4 >= F6 hence may compare these two local endgames as "4" >= "6", for which my theory states: first play in the larger one. So play in "4" before playing in "6".

By my theorem on simple gotes without follow-ups, they are played in decreasing-or-constant order so "1" before "3" before "5".

You have implicitly applied both in your sample sequence.

As soon as a follow-up becomes available in "4" or "6", or the "2" local endgame becomes a simple gote, these simple gotes deserve evaluation for play in order of all remaining simple gotes without follow-ups.

For more strategic choices, we do not have simplifying theory so must resort to the method of reading and counting by analysing the tree of all remaining strategic choices while applying the simplifications above.

2 EDITs.

ez4u · #4

My answer...

There seem to be multiple versions that come down to a 1-point win for Black.
Black can start at 1 below and White has nothing better than the big point at 2. However, 3 leaves White without a good play. If 4, then 5 secures 21 points so far and Black will get 18 more (for a total of 39) with one of the 10-point plays at a through c plus the 8-point play at d. If White plays 4 at 5, Black will play 5 at 4. That will secure 28 points with 10 more to come from one of the plays a through c. This gives a total of 38 points and Black wins by 1 point.

Click Here To Show Diagram Code: [go]$$c Black to play $$ +---------------------------------------+ $$ | . O X X X X X O O O O 2 O . . . . . . | $$ | O O d O O . X O O O X X O . . . . . . | $$ | . O . . O X X X X X X O O . . . O . . | $$ | O O X 5 . X O O O 4 O O . . . O . . . | $$ | O X X O X X O O O X . O . . O . . . . | $$ | O X . O X X X X X X . O . . . . . . . | $$ | O X X X X O O O c O O O . . . . . . . | $$ | O O O O X O O X X X O O O O O O O O O | $$ | . O X X X X X X O X X X X X O . . . . | $$ | . O a O O . X O O b O O . X O , . . . | $$ | O O . . O O X O O . . O . X O O O O O | $$ | . O X 3 . X X O O X 1 . . X X X X X X | $$ | O X X O X X O O X X O X X . . . . . . | $$ | O X O O X O . O X . O X . X . . . . . | $$ | O X X X X O O O X O O . X . X . . . . | $$ | O O O O O O . O X X X X . . . X . . . | $$ | . . . . . O O O O O O X . . . . X . . | $$ | . . . . . O . O . . O X . . . . . . . | $$ | . . . . . O . . . . O X . . . . . . . | $$ +---------------------------------------+[/go]

However, it seems that Black can also start at 1 below. After 2, Black continues with 3. Now it is actually White that has to vary. If White plays 4 as in the reference diagram, Black will play 7 rather than 4. Black ends up 2 points better off than the reference diagram. White has to play 4 as shown. Black gets to force with 5 and 7 before making the last point, starting with 9. Black's captures with 5 and 7 are 1 point better than the reference diagram.

Click Here To Show Diagram Code: [go]$$c Black to play $$ +---------------------------------------+ $$ | . O X X X X X O O O O 1 O . . . . . . | $$ | O O 8 O O . X O O O X X O . . . . . . | $$ | . O . . O X X X X X X O O . . . O . . | $$ | O O X 7 . X O O O 3 O O . . . O . . . | $$ | O X X O X X O O O X . O . . O . . . . | $$ | O X . O X X X X X X . O . . . . . . . | $$ | O X X X X O O O 4 O O O . . . . . . . | $$ | O O O O X O O X X X O O O O O O O O O | $$ | . O X X X X X X O X X X X X O . . . . | $$ | . O 6 O O . X O O b O O . X O , . . . | $$ | O O . . O O X O O . . O . X O O O O O | $$ | . O X 5 . X X O O X 2 9 . X X X X X X | $$ | O X X O X X O O X X O X X . . . . . . | $$ | O X O O X O . O X . O X . X . . . . . | $$ | O X X X X O O O X O O . X . X . . . . | $$ | O O O O O O . O X X X X . . . X . . . | $$ | . . . . . O O O O O O X . . . . X . . | $$ | . . . . . O . O . . O X . . . . . . . | $$ | . . . . . O . . . . O X . . . . . . . | $$ +---------------------------------------+[/go]

dany · #5

What is the miai value of local positions?

Endgame problem, what's the best move order?

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