Solution to the problem above
If black plays the natural move at 1, white makes a third eye with 2:
This position is identical to the second to last diagram in the above post - because white has a guaranteed move at G1, black will never be able to successfully start the J7 sequence. All stones on the board are alive, and white wins by 1 point.
The correct move for black is to deny white the third eye! White makes an extra reduction with 2-3 before coming back to 4:
(If white instead tries 2 at J7, black J9 kills)
Now we have reached an extremely delicate position!
- White has a non-passing move at G1, which black cannot remove (note that black suiciding at G1 doesn’t help). This makes it impossible for black to kill the upper right.
- However, this means that white must not play G1 as long as the threat of the J7 sequence remains on the board.
- Thus the single black stone is alive! (and G1 is dame, not a point for white)
- Black must take care not to play J9 or exchange A5-A7, because doing so would remove the threat of killing the upper right, allowing white to safely capture H1.
- Similarly, black must not start the J7 sequence, because it accomplishes nothing except allowing white to capture H1 in the process.
Both players should pass and end the game here, the final score is a tie.
To see exactly where black’s 1 point gain came from, note that:
- The 2-3 exchange is a 2 point swing in white’s favor (black lost 1 point, white gained 1 point).
- The H1 invasion is a 3 point swing in black’s favor (black gained 1 point, white lost 2 points).
This problem is my own creation, so it’s entirely possible that I’ve made some oversight! Please view the analysis with a critical eye and let me know if you find a mistake.