All you need to know about Carpenter's Square - 23

Diagram 23.1: White to play

Let's study this 'incomplete' Carpenter's Square.

Diagram 23.2: Benchmark

We will use this diagram as a benchmark. We already know this corner should result in a direct ko (Diagram 2.2 and Diagram 3.5). Can white find anything better?

Diagram 23.3: 2-2 not key point

Unlike many other carpenter's square shapes, White 1 here is not a good move. After Black 2 / White 3 exchage, Black 4 is good ('a' would be suicidal because it reduces the eyespace). White has two options from here ......

Diagram 23.4: A direct ko

If white plays White 5 , black can form a ko easily after Black 8 . If White 7 plays Black 8 instead, black would make 'a'/'b' exchage first before playing White 7 - which is a seki.

Diagram 23.5: A direct ko

If white plays White 5 here instead, black makes Black 6 / White 7 exchage before playing Black 8 (the familiar tesuji to avoid large-eye killing shapes). Note the result here is a direct ko after Black 10 - if black forces white to connect at 'a', black can then play 'b' to get a seki shape while continue to fight the ko. So it looks like White 1 in Diagram 23.3 is no better than the benchmark case.

Diagram 23.6: Solution, but...

White 1 is the vital point in this shape. White 3 is a related tesuji. The purpose of White 3 is to make an eye in the corner to form Eye versus No Eye capturing race. However, one needs be careful to implement this idea correctly.

Diagram 23.7: Incorrect sequence

This is the solution given in Cho Chikun's Life & Death Dictionary. What's presented here is that white can win this capturing race by one liberty. But something appears to be wrong here ......

Diagram 23.8: Approach ko

Normally Black 6 is the previous diagram is the tesuji, but Black 6 here is better. Black 10 can create a ko this way. This is an approach ko - black need to win the ko and play 'a' to make it a directly ko. But any way, this is better than dead.

Diagram 23.9: Solution (continued)

It turns out that White 5 in Diagram 23.7 is not accurate. White 5 here instead would be flawless. If Black 6 plays Black 8 first, the result is exactly the same. If Black 6 plays White 7 , the corner is a Pyramid Four dead shape. Black is dead unconditionally.

Diagram 23.11: White fails (11=a; 12=b)

If white misses the tesuji White 3 in the solution, for example, if white plays White 3 here instead, black occupies the key point Black 4 and a ko fight is inevitable. For example, the sequence here results in an approach ko. I will leave the readers to work out other variations in this diagram and we will revisit this in the next article in this series.

To summarise: Diagram 23.6 + 23.9 is the only solution. White needs to play very accurately to avoid ko fights.