Somebody asked me how I could count a value of a certain move in the endgame, so that the result was 8 and 19/48 points. I’ll try to explain.

There is a situation like on this diagram.We look just at this what happens at the first line (from C1 to H1). We assume, that both groups (black and white) live certainly. In D1 black has 1 point. White has 0 points.

Another situation. How many points has each of players? White has 0 points and has no chance to get any point. What about black? If black plays at E1, he has 1 point. If black doesn’t play on the first line, but in the other place on the board, white might play at E1.Black has 0 points now. We count an average.

(1+0)/2 = 1/2 Black has 1/2 point.

Different situation.Black played at F1.How much was worth this move?

After playing at F1 black has 2 points (at D1 and at E1). If black didn’t play there, but white played at F1.We know from the previous situation, black would have 1/2 point. So, the F1 move was worth 2-1/2 = 1 and 1/2 points.

But how many points has black here?We count an average again. (2+1/2)/2 = 1 and 1/4 points.

But how many points has black now and how much is worth G1 move?If black played at G1, he’d have 3 points. If white played at G1, black’d have 1 and 1/4 points. So, the G1 move is worth 3 – 1 and 1/4 = 1 and 3/4 points. But without playing at G1, how many points has black? An average, so (3 + 1 and 1/4)/2 = 2 and 1/8 points.

But how it looks like, when there is a ko?

Playing with black at E4 doesn’t make any sense, because white might connect and black doesn’t get anything on this exchange. White doesn’t have to connect, however. Assuming, that white wouldn’t connect, how much is worth playing at E4 by black? To get 1 point, black has to play first at E4, then capture the stone at E6 and then connect at E5. So, black needs 3 moves, to get 1 point, so the E4 move is worth 1/3 point.

But how many points has black right now?Black has 1/3 point. After capturing white’s stone black will have 2/3 point. After connection at E5 black will have 1 point.