All you need to know about Carpenter's Square - 9

Diagram 9.1: White to play

We will now consider the Carpenter's corner with one extra liberty as well as one first-line stone.

Diagram 9.2: Solution 1

First shown here is the solution on a number of textbooks. From Shape 8, we already know that White 1 is the only move. Black 2 should attach from the side without the first-line hane. After Black 8 the result is a so-called 10000-year ko. White does not have to form the ko immediately. At a later time white can make 'a'/*w5* exchange first, before throwing in 'b' to form the ko. Even after that black can ignore, and white has to play three extra moves to make it a real ko!

Diagram 9.3: Seki

This is sometimes described as a failure for white. If white connects at White 7 , the corner results in seki. However if we take into account that the hope of winning the 10000-year ko in Diagram 9.2 is very remote for white, and white has already sealed the right side by White 7 in this diagram, this seki is not necessarily worse than the 10000-year ko situation.

Diagram 9.4: White fails

White cannot play *w9*. Thanks to the extra liberty, black is able to use 'oshi-tsubushi' tesuji at 'b' to kill white.

Diagram 9.5: Black fails

If Black 2 attaches the wrong side, white can follow the normal Carpenter's Square solution. That would be a big failure for black.

Two external liberties:

Diagram 9.6: Two external liberties

The original series of Chinese articles did not include this case. But it is rather interesting.

Diagram 9.6: White should be satisfied

The solution in Diagram 9.2 still applies. But because of even more extra liberties, white is practically hopeless to win the 10000-year ko. This diagram shows an easy sequence for white to form a seki, destroying black's potential territory in sente. White must feel happy with this result.

Diagram 9.7: 11=a, still a 10000-year ko

If black blocks at Black 2 , things become much trickier. There are a lot of room in this corner and many variations. The given sequence here results in 10000-year ko again (more like a seki). Note that because black's many external liberties, white's strategy is quite different now. White needs to: (1) avoid forming an eye now; (2) be careful with 'oshi-tsubushi'.

Diagram 9.8: seki (white in sente)

Black 2 was not even considered in many shapes we discussed earlier. But now it is not only possible, but gives rather good results for black. Black 4 again is to maintain as much eyespace as possible in the corner. White 5 wants to settle peacefully. Black 6 is a tesuji. Because of the external liberties, white cannot play 'a'. Black would play 'a' whenever white reduces its liberties from outside, to form a seki in the corner.

Diagram 9.10: approach Ko

Unhappy with the previous diagram, white wants to force a ko by White 5 and White 7 . But instead of connecting at 'a' to form a 10000-year ko (which ends in seki 99.9999...% times), black can play Black 8 to form an approach ko to kill white. With two external liberties this is not dangerous to do at all.

Diagram 9.11: seki (white gote)

Finally if white play White 3 , the corner still ends up in seki. But note that white is gote here. In comparison to Diagram 9.9, this is considered a failure for white.

To summarise: the extra liberties change things significantly and both sides need to adjust their strategies. There are many ways to form seki or 10000-year ko. In practice, such corners can be considered alive, but with little or no points when making positional judgement.