Explanation of the previous problem solution:

Black E12 is the best move. Black loses if they do anything else (well, apart from playing a ko threat now for no reason, and then E12).

Whiteās best response is N8. Then, since the D7 and H5 kos would normally ācancel outā each other, the only remaining move would normally be black E11 to finish the game. But black loses by half point playing this way.

No matter how many ko threats the players have, the two kos D7 and H5 cancel out, as long as there is a **finite** number of ko threats. Here, due to the double-ko in the lower-right corner (white is alive and black is dead due to double-ko), black has an **infinite** number of ko threats.

So, after playing Black E12 - White N8, black now takes the ko at D7, instead of playing the normal E11. Black now has taken the three kos. You can imagine black exclaiming out loud: āI have an infinite number of ko threats, thus, I win THE THREE kos. So, I win by half a pointā.

White cannot finish the game and avoid black winning the three kos, because black has infinite ko threats. To avoid losing now, the best white can do is to keep taking the kos, after which black keeps playing a ko-threat in the lower-right and then recapturing. So, the game enters a long cycle and is thus judged as no result.

Note that blackās infinite ko threats are NOT unremovable. White can at any time capture at N2 in the initial position, and blackās ko threats dissapear. However, that costs white one point (because they filled their own territory, as the black stones were already dead) and a whole turn. Since the game is so close, if white tries at any time to eliminate these ko threats, the loss is enough for black to win the resulting game.

You can check that other lines by either player do not work: Black cannot win without using this ālet me take the three kos or void the gameā trick. And similarly, no matter how White tries to prevent Black from using his infinite ko threats to capture all the kos, White ends up losing enough points that Black wins the game.

Note that this game would be winning for white if Black had any **finite** number of ko threats, no matter how large. If black had a thousand ko threats, white wins by just playing a lot until black runs out of ko threats.