Answer



Dia. 1. Correct
Dia. 1. Atari from underneath
The atari from underneath with Black 1 is the key move. With the sequence to 6, Black ends in sente, so he can capture three stones at the bottom. White takes the last two points with 8 and 10.

The result:
Black: 21 points.
White: 20 points.
Black wins by one point.


Dia. 2. Capturing a stone
Dia. 2. Capturing a stone
Many players might be quite satisfied with capturing a stone with 1 and 3 while securing three points of territory. However, White ends in sente and immediately rescues his three stones at the bottom with 4. Next, Black plays 5 for an additional two points. White 6 takes the last point and Black defends with 7.

The result:
Black: 20 points.
White: 20 points.
A draw.

Capturing a stone with 1 and 3 in Dia. 2 is territorially a big endgame move, but, as this problem illustrates, keeping sente may sometimes be a more important consideration than capturing three points. Despite White's territorial loss at the top, he has gained more by capturing the three stones at the bottom in Dia. 1.

Recommended reading
Get Strong at the Endgame is one of the most practical books ever written on the endgame. In it you will find the calculations for the value of endgame moves in over 100 common positions, as well as 120 endgame tesuji problems. Also included in its problems are 28 endgame positions on 11x11-size boards, where you can study the interplay between sente and gote. It may be that the biggest move is not the move that should be played first.