Shape [1]
White is dead. (1 liberty)
Shape [2]
White is dead. (2 liberties)
Shape [3]
Black can kill.
White can live with 2 points.
Shape [2,1]
Black can kill.
White can live with 2 points.
Shape [4]
White is alive with 4 points.
Black has 1 ko threat.
Shape [3,1]
Bent four
Black can start a ko to kill.
Black takes the ko first.
White can live with 3 points.
This is the best way to live.
This 1 also lives but leaves a ko threat.
Shape [2,2]
White is dead. (3 liberties)
White has one ko threat to live.
Shape [5]
White is alive with 5 points. Black does not have any ko threats.
However...
If white ignores 1, black 3 is a threat to make seki. This can be useful for an approach ko or a multi-stage ko or a 10,000 year ko.
Shape [4,1]
White is alive with 5 points.
Black has 2 ko threats.
If white ignores 1, black can’t outright kill, but does get a favorable ko:
(if white ignores 3 as well, black can extend to 4 to create a Bent four in the corner)
Shape [3,2]
Bulky five
White can live with 4 points.
White 1 is the only move that lives. It leaves no immediate ko threats.
White can ignore 2 but must respond to 4.
Black can kill.
After 1, white is dead (with 3 liberties).
White has a ko threat at 2 (threatening a ko which black takes first). If black responds at 3, white still has 3 liberties.
Shape [3,1,1]
White is alive with 5 points.
Black has 1 ko threat.
If white ignores 1, black 3 makes a Bent four in the corner.
Shape [4,2]
Big P
Black can make a seki.
Seki.
This white 2 is usually a mistake. After black 3 white can only get an unfavorable ko or else dies in bent four.
White can live with 5 points.
This is the best way to minimize ko threats.
Black only has a 2-step threat.
Shape [3,3]
Rectangular six
Black can kill.
White can live with 5 points.
If white lives this way, black has two threats. The first threatens to kill, the second threatens a ko which black takes first.
If white lives this way, black still has two threats. This time the first one threatens a ko which black takes first, and the second one threatens direct capture.
Shape [3,2,1]
Gun six
Black can make seki.
White should play the atari right away, otherwise black can make trouble at the 1-1 point:
If the game does reach this postion, white should tenuki. Whoever plays first from here, the result will be a ko which black takes first.
White can live with 5 points.
This is the best way to live. Black has a single ko threat to make seki.
This move also lives, but now black’s ko threat is bigger.
Shape [5,2]
White is alive with 7 points.
Black has 2 ko threats.
Shape [4,3]
Walkie talkie seven
Black can make a 10,000 year ko.
White can live with 6 points.
This is the best way to live. Black has no ko threats.
Shape [4,2,1]
White is alive with 7 points.
Black has 2 ko threats.
If white is careless, black gets an extra ko threat:
Shape [3,3,1]
Bulky seven
Black can make a seki.
White may choose to add a move, to ensure seki:
White may also tenuki, in which case black can create a 10,000 year ko:
Note that even if this becomes a seki in the end, this seki is better for black compared to the other one. In Japanese rules, black gets one extra point (from capturing the stone marked 2). In Chinese rules, the difference is 6 points (black has 3 extra points in this corner, white 3 fewer).
Black may prefer to create the seki this way:
If white omits 4, black can start a 2-stage ko for the corner. This could be slightly more threatening for white than the 10,000 year ko.
White can live with 6 points.
This is the best way to live. Black has no ko threats.
Shape [5,3]
White is alive with 8 points.
Black has 2 ko threats.
Shape [4,4]
Rectangular eight
Black can make seki.
Black makes seki in sente.
Black 1 is worse – the result is still seki but now white has sente.
White can live with 7 points.
This is the best way to live. It leaves only one ko threat at 2.
Shape [4,3,1]
Gun eight
Black can make seki.
White could play 4 at 5, but this ko would be very heavy for white.
Other seki variations:
Note that under Chinese rules, white should choose the left variation as it gives 1 point less to black.
White can live with 7 points.
This is the best way to live. Black has no ko threats.
Shape [4,2,2]
White is alive with 8 points.
Black has 3 ko threats.
If white is not careful, she may be tricked into a seki:
Shape [3,3,2]
Bulky eight
Black can make a ko or seki.
After 3 white can not avoid ko. For example:
If white has a lot of ko threats, black may choose to avoid the possibility of ko:
This was black gets a seki in sente. The possibility of 10,000 year ko remains until white adds another move.
White can live with 7 points.
This is the best way to live. Black has no ko threats.
Shape [5,4]
White is alive with 9 points.
Black has 3 ko threats.
This black 1 is the best way to maximize ko threats.
If black starts here instead, he only gets 2 threats:
Shape [5,3,1]
White is alive with 9 points.
Black has 3 ko threats.
Black 1 threatens a follow-up at 3.
No matter how white responds black gets at least 3 threats:
Shape [4,4,1]
White is alive with 9 points.
Black has 3 ko threats.
Shape [4,3,2]
Bulky nine
Black can make seki.
Both sides may tenuki earlier in the sequence, depending on the game situation. (There are some potential variations that involve ko, but if white wants seki there is no way for black to force a ko.)
White can live with 8 points.
This is the best way to live. Black has no ko threats.
Shape [4,3,1,1]
White is alive with 9 points.
Black has 3 ko threats.
Shape [3,3,3]
Square nine
Black can make seki.
In fact, even if white ignores 1, black cannot get more than seki.
White can live with 8 points.
This is the best way to live. Black has no ko threats.
