GokyoShumyoSection4Problem5/Solution

Reference  

For reference, the problem here obviously is that the two white stones have only 3 liberties, while the black have 4. If White plainly reduces them, Black wins the race. White must use the weakness at a and the special properties of the corner, also known as strange things happen at the 1-2 point.

Solution

Main line  

is a common way (one might say tesuji) to increase liberties in a fight in the corner.

First, it increases the liberties of the chain itself from 3 to 4. More importantly, creates an approach liberty at a which Black must fill if he wants to eat the liberties on that line, which he won't do, because a is an inside liberty. and create another such liberty at b. If Black wants to start from this side, he must play b first to avoid auto-atari.

So, the circled liberties and b add to 4 liberties, then reduces Black to 3.

and can be played in either order. This diagram is the traditional main line, but first is one point better from an endgame perspective; playing at first allows black to choose the variation below.

Variation  

If Black patches the weakness, wins the capturing race. In a real game, this is black's best play, gaining one point of territory compared with the main line. (As usual, the main line is the path of strongest resistance, as opposed to the theoretically best moves.)

Failure

Ko  

here is a crude way to use the Black weakness. The result is a ko.