Here are three easy problems to illustrate the basics of kos and dame under area scoring rules. All problems are black to play and win, no komi.
Since these boards have a total area of 25 (and there are no sekis in sight), black needs to secure an area of 13 points to win.
Problem 1
Solution
Black should throw in at 1 to start a ko. Note that the ko is sligthly unfavorable for black: white takes first, so black must be sure that he has more threats than white, otherwise he would be better off playing E1 instead.
In this case, black has one ko threat at 3, and white does not have any threats, so black can recapture and win the ko for a final score of B+1:
(white 6 passes - filling the ko with 7 may be unnecessary depending on the exact rules)
Problem 2
Solution
Black can claim the last dame and still win the ko. 3 is an interesting type of ko threat since it doesn’t directly threaten anything, but rather prevents white from filling the ko. I sometimes like to think of it as “this move would be atari if the ko was filled, therefore it works as a threat”. I’m not aware of a name for this type of move, I think most people would just call it a local ko threat?
Problem 3
Solution
Immediately capturing the ko is a mistake. White has a ko-threat at 2 and black will lose by 1 point.
So black starts by removing white’s ko threat, and threatening to play A1. If white responds at A1, black can now win the ko for a score of B+3:
White does better by filling the ko and letting black have A1:
This sequence is best for both. The result is B+1.
(I originally intended to make these into OGS puzzles as well, but it breaks if you try to add both correct and incorrect variations, since the automatic transposition feature doesn’t take ko bans into account.)