At the time of writing this article, I think the ko page and the linked pages do a very good job now of explaining this key concept, at a basic and intermediate level. The advanced to expert stuff however is very much in discussion mode. Myself I still do not fully grasp ko from a theoretical point of view. Below chapters more or less reflect my current understanding. As such, this article is probably only of interest to myself.
Basic ko fight
A basic ko fight consists of
More intricate ko fights
- Instead of answering a ko-threat, a player can enlarge the ko (E). The opponent can then retake the ko for free but the effect of losing it will have become larger for that player.
- If the ko is a direct ko for one player but an approach ko for another, the former player can use the difference to reduce the ko (R), i.e. the effect of losing it.
- If the effect of the ko is much larger than any ko threat on the board, a player may yield locally to minimize a loss (Y) which means losing the ko without compensation
- Sometimes players will mutually decide that the ko is (temporarily) less important than developments elsewhere, (possibly) brought about by a ko threat (L)
Decision to finish a ko
This is the first kind of decision an amateur is confronted with, regarding ko. When to end a ko? Should one respond to a threat and have the ko continue instead? How does the threat compare to the ko itself? Here are some thoughts:
- If I finish a ko (F1), the opponent will execute his threat (X1) and I have sente.
- If I respond to the threat (A1), the opponent will recapture the ko (C). Next I play a threat (T) and the opponent may finish the ko (F2), I execute the threat (X2) and sente goes to the opponent.
The difference between these two branches of the ko fight, is:
- the local difference between F1 and F2, being the sum of values of winning the ko for either side
- the local difference between the opponent's execution X1 and a potential answer (A1)
- the local difference between my threat plus execution T2+X2 and these moves unplayed
The basic decision is: if the difference between either side winning the ko plus having sente is worth more than the sum of my opponent's threat execution and my next threat plus execution, then I finish the ko. Otherwise, I continue the ko.
However, there is also the possibility that the ko goes on, if my opponent needs to respond to my next threat, according to the same reasoning as above. This is another good reason to continue the ko.
It is very hard for amateurs to do this kind of calculation, especially under time pressure. In general I believe amateurs tend to underestimate the value of sente and err on the side of answering ko threats too often. This may be especially true if the threat is about territory only, while the ko is about thickness.
Decision to fight a ko
Like any move, such a decision may be and likely is a mistake, since we haven't found perfect play. All imperfection aside, the decision to go for a ko fight may be inspired by
- the evaluation of all alternatives as timid or bad altogether; i.e. the ko has become inevitable
- having a thicker position overall, so that the opponent is likely to suffer more from unasnwered ko threats (or his will be exhausted)
- envisioning of the resulting position which may be a simplification of a currently advantageous position (see lose a ko to win the game)
- not envisioning the resulting positon very clearly, so that the ko serves to make the game complex, which can be a measure to get out of a losing position
It occurs to me that such motives are more likely to be found during a real game than the decision of who's ko master, which is a useful theoretical concept but requires very profound reading.
Ko fight examples from pro games
I have created the following articles, to induce some good examples of ko fights from professional games, exposing all the aspects of ko.
- Ko fight example from a pro game - 1 about direct ko, approach ko and reduce the ko
- Ko fight example from a pro game - 2 another direct ko vs approach ko, enlarge the ko and lose a ko to win the game
- Ko fight example from a pro game - 3 about local ko threats
- Ko fight example from a pro game - 4 launching a second ko before resolving the first one
- Ko fight example from a pro game - 5 a decisive endgame ko with calculations
- Ko fight example from a pro game - 6 about enlarge the ko and yield the ko