All you need to know about Carpenter's Square - 16

Diagram 16.1: White to play

Black is blocked from the bottom side instead. This shape is commonly seen in real games. What can white do?

Diagram 16.2: Solution 1

White 1 is absolutely the key point. If black plays *b2*, White 5 is good - it forces black to connect at Black 6 and at the same time creates a ko shape.

Diagram 16.3: Solution 1 (continued)

To continue, Black 10 is the correct answer. White 13 is important to avoid a double-ko. The final result is an approach ko. White has to play 'a' first to make it a direct ko. Black 10 cannot play Black 12 - that would be a direct ko immediately.

Diagram 16.4: Variation

Black 4 may connect first. White 5 is correct, recovering to the shape in Diagram 16.2.

Diagram 16.5: White fails

White 5 here would be an overplay. Black would win the capturing race. Or ......

Diagram 16.6: White fails

If white plays White 9 here, the result is a seki.

Diagram 16.7: Solution 2

Black 2 can also play the other side. Interestingly white can form a ko fight in a fashion similar to Diagram 16.2.

Diagram 16.8: Solution 2 (continued)

To continue, this results in a different approach ko (white needs to play 'a' first to make it a direct ko). So which one should black choose? Solution 1 or 2? The difference is very small. However, assume white manages to reach the direct ko stage (getting 'a' in Diagram 16.3 or 16.8), and black eventually wins the ko fight to live in the corner, black would be better off by 2 points if choosing Solution 1 (an easy way to validate this argument is to count the number of cross-sections black would occupy - 18 in Solution 1 and 17 in Solution 2).

Diagram 16.9: Black fails

Finally, it is important to remember Black 4 here won't work. White 5 is good.

Diagram 16.10: Black fails (continued)

Unlike in Diagram 16.5, black is mysteriously short of liberty here. Black 12 has to play 'a' to form a ko. But that would be a failure because the ko is a direct ko.

Conclusion: black corner is not in immediately danger. There are two different ways to form approach ko. I recommend readers to remember the sequence in Diagram 16.2 and 16.3.