RTG Problem 24 / Solution

Common pitfall.  

A common pitfall is to play the descent at , assuming that capturing at a and the connection at are miai.

Common pitfall. (6 at marked stone)  

This problem is deliberately set up in such a way that capturing the four Black stones directly does not live - it is a pyramid four big eye.

Common pitfall.  

However, one should notice that if the stone (which was ) is at a instead, then White at b can make the second eye and live. This observation leads to the improved sequence below.

Improved sequence

Improved sequence.  

An improved sequence is the diagonal at , threatening a connection at as well as a ko at .

Improved sequence (7 at marked stone)  

If does not play the ko and destroys the eye at the side instead, then is sente, so White has time to live at the vital point of . However, the improved sequence is not yet the solution, since Black takes the ko first.

Solution

Solution.  

White makes a throw-in at followed by an atari at . Observe that cannot connect at .

Solution.  

If insists on killing the White group, then takes the ko first. From the usual life-and-death perspective, this is the best play by both players.

If Black avoids this ko, White can live, as the variations below show.

Variation 1a  

Black may try this way after takes the ko.

Variation 1b  

Must White fight this ko to live?

Variation 1c  

at .

White can play this way.

Variation 1d  

goes all out to kill.

takes four stones, but cannot make an eye there because of under the stones play.

Variation 1e  

But White takes sente and lives.

Variation 2a  

Backing up, Black can do no better than , allowing to live.

Solution (practical)  

Since this ko is so large, it is reasonable to assume that neither player has a ko threat, and also that the temperature of the board is not too high, so that there will be no ko exchange. Then the best way for Black to play is to simply capture at , allowing to connect to the group outside.