How to count territory
Let's compare two situations and count the difference in territory. In the first situation, Black plays first and in the second White leads off.
Diagram 1: To make things easy, let's ignore life and death problems and look at the territory. Most of the territory in this diagram is unprotected up to a point. The letters A through I signify points that are unprotected. If one of the players moves onto one of these points, how many points would that player gain? Be careful. A lot of board reading and counting goes into solving these problems. Let's tackle some of them.
Diagram 2: If Black plays at 1, he will make one point, i.e. the point with the triangle.
Diagram 3: However, if White plays at 1, he gains nothing. The point with the triangle becomes no man's land. Whoever plays at 1 first, makes one point (or takes one away). Although playing at 1 is worth a point for Black, he loses his turn because it does not require a response. In go, we use the term gote to signify such a move.
Diagram 4: In situation B, black 1 would ensure four points for Black, one point more than if White played at that spot.
Diagram 5: If White played at 1, Black would be forced to defend with 2 (if White played at 2, Black would be doomed because he would be left with only one eye). Black now has three points. Although the difference between the two diagrams is only one point, White can always play here to force Black to respond. We use the term sente to refer to a situation where a player can play a move that requires an answer.
Gote vs Sente
By playing a gote move, you in effect lose the initiative. A sente move allows a player to play two worthwhile moves because his rival is stuck with responding to the first move.
Problems
Problem 1: Look at points A through J in Diagram 1 and see if you can determine which would be sente moves and which would be gote. Naturally, stopping your opponent from playing a sente move also is good. This is called reverse sente. Can you spot that type of move?
Problem 2: What is the value of playing at A? Is it a gote, sente or reverse sente move?
Problem 3: Calculate the difference in the value of A if Black plays first or if White plays first. Is it gote, sente or reverse sente?
Problem 4: This is slightly trickier. How many points is A worth if Black plays first or if White plays first?
Solution: White should play 1 and 3 (sente). Black has to answer with 8, but before doing so, he can force 4 through 6 (sente). Next, he has to drop back to 8 (gote). After that, white 9 and 11 are best (reverse sente). The last moves to be played are 12 through 14 (gote for both players). What about the top right corner? Is it safe? If Black invades at A, this would be followed by white B, black C, white D, black E, white F, black G and white H. Black is in trouble. So this corner is safe. To compensate for Black playing the first move, White receives two points compensation, called komi. Who wins the game? Black's territory totals 21 points, while White's is 21 + 2 komi = 23 points. White wins by two points.
Reference: If White starts out with the gote move 1 and 3, what happens? Black will get both sente combinations 4 and 6 as well as 8 and 10, then switch to the gote combination 12 and 14. Who wins this time? Black has 23 points against White 19 + 2 komi = 21 points. Black wins by two points. So the difference between sente and gote can be significant.