Taking Liberties
This Go problem was presented to me by my Tsumego Pro mobile app this morning. It's not particularly difficult, but I think it nicely demonstrates some ideas about liberties. It's Black's turn to go, and it's pretty obvious that a race is on, and the winner is going to take some stones. If Black wins it'll take the 3 white stones in a row, and if White wins it'll take the six connected black stones just below. A connected group of stones is taken prisoner when the other player removes it's last "liberty", i.e. the last place into which that connected group can grow. At the moment White has 4 liberties and Black has 3. So it would seem Black is on to a loser, since the players can just take turns removing one liberty at a time from each other's stones. However, it's not quite as simple as that. Black's move can leave White's liberties unchanged or reduce them by one. It can also leave it's own liberties unchanged or reduce t