BeginnersEndgameExercise2/Solution

captures the three White stones, for a local score of +6.

Knowing that this is a problem, you can easily guess White's play.^[1] If White played at a instead, would capture White's stones, for no gain.

It may not be obvious, but is gote. The question now is subsequent play.

If White takes Black's stones, the result is -4.

captures four White stones.

Now White plays , putting the Black stones in atari.

This shows the beauty of White's original play. Because of that sacrifice, Black cannot save his three stones.

Because the effect of White's sacrifice depends upon White's later play where one of White's original stones was, this kind of play is referred to as an under the stones play.

was sente. A quick way to see that is to note that, if White allowed Black to fill with , Black would get 7 points, which is better than he could have done originally.

The question now is subsequent play.

captures Black's three stones. Later, - may be a ko threat for Black.

Black has captured 4 White stones, while White has captured 3 Black stones and has 3 points of territory.

Result: -2.

is sente, threatening to save his stones. Later, White will have to fill at .

The number of stones each side has captured is the same as above, but White has 1 point less territory.

Result: -1.

Making a sente play as sente does not change the local count. So all of the positions below, along with the captured stones, have the same count.

3 Black prisoners, 4 White prisoners.

4 White prisoners.

Since White can gain 1 point by playing first, this is a 1 point Black sente.

Since White can gain 3 points by playing first, this is a 3 point Black sente.

If Black plays first the local count is +6. If White plays first it is -1. The local count for the original position is their average, or 2 1/2.

A play by either player gains 3 1/2 points, on average.

This is a gote.

Game tree

With a game tree

  2 1/2 (3 1/2)
 /     \
6      -1 (3)
      /  \
   -1(1) -4
   /  \
 -1   -2