Consider the following board position under Chinese rules with a 5.5 point komi
- Which stones are alive or dead?
- Who will win this game and by how much?
- What is the best line of play?
The purpose of this example is to explore how life and death is handled under Chinese rules. The rest of this discussion has been hidden in case you wish to treat this example as a problem before reading on.
Click to expand discussion
Note that white’s group in the top-left forms a “bent four in the corner”, which is typically dead. However, the presence of an “unremovable ko threat” (marked by “a” in the next diagram) changes the situation. Consider what might happen if black attempts to capture white in the top-left, by beginning with…
White’s threat in response to the ko poses a choice to black…
If black responds to ko threat…
White will live in the top-left, since black does not have any ko threats to play (so move 9 by black can be a pass or arbitrary). While the players have traded captures, breaking up the sekis in the process, black is now losing by 0.5 points.
Alternatively, if black ignores the ko threat…
White will capture black’s bottom-right group in exchange for black capturing white’s top-left group. Yet again this exchange is not in black’s favor, since black will now lose by 2.5 points.
However, black can simply pass and accept that both the top-left and bottom-right positions are seki. With all of the stones being alive, black wins by 0.5 points (after applying the 5.5 point komi). White cannot force anything to happen, except to self-atari and increase black’s margin of victory.
Thus, it would be an absolute blunder for black to attempt to capture white’s stones in the top-left. While it is in fact true that black can claim that white’s stones in either the top-left or bottom-right could be captured, either claim could only come at the cost of sacrificing black’s stones in the opposite corner, which white would happily play out since it also flips the outcome of the game in favor of white.
Consider another very similar example, where black is now initially losing by 1.5 points (if black were to accept all stones being alive in two sekis as is).
In this game, black should play out the capture of the bent four in the corner, while sacrificing the stones in the bottom-right (black move 5 at 1)…
After this exchange, black is now winning by 1.5 points, making the sacrifice worthwhile.
Taken together, these two examples illustrate how life and death under Chinese rules depend not only on just the local position, but also whole board strategic considerations.
Under Japanese Rules
Note that these examples are handled quite differently under Japanese rules, where the bent four in the corner would be ruled dead, even in spite of the presence of an unremovable ko threat. An older version of the Japanese actually explicitly stated that bent four in the corner was simply dead. In the more recent versions, it follows as a consequence of the life and death resolution procedure, which essentially considers the locally optimal play while disallowing any ko threats besides passing.
It should also be noted that under the modern Japanese rules, it is not automatic that bent four in the corner is always dead either. Here is an example where two interacting bent fours in the corner produces a seki: http://warp.povusers.org/go/UndeadBentFours/