Capturing Race Exercise 7 / Solution

Black first  

This isn't interesting I guess...

White first  

is the tesuji to delay Black's approach move at a. After , being in shortage of liberties, Black is unable to play at a.

White first  

If Black captures with , wins the capturing race by one move.

Bonus question: How many liberties (approach moves) does White have?

If Black plays first, White has one liberty left.

If White plays first, she threatens to capture two stones and live, gaining an infinite number of liberties, so Black must reply. Now White has three liberties.

As a combinatorial game, White's liberties look like this:

    { -1 || -3 | -infinity }

(As with scores, we use negative numbers for White values.)

This is not a number, it is a game. White has a two liberty sente, with a liberty count of -3. Black's reverse sente gains 2 liberties instead of the usual 1.