| Position 1 | Position 2 | Position 3 |
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One of the shapes which causes a lot of problems for the rule scholars in the Go community is the, so called, "bent-four in the corner" shape. The basic pattern is shown in Position 1, Fig 1-1. To live, black has to start a ko with '2' in Position 2 - to which white answers with '3' and the ko fight begins, with the life of the group at stake. If black manages to win this ko (by ignoring white's threat) , he can then kill the white stone by playing at 'a', thus making two eyes and saving his group. If, on the other hand, white wins the ko (by ignoring black's threat), he can connect at '5' in Position 3, thus preventing black from making two eyes and killing the black group.
| Position 1 | Position 2 | Position 3 |
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So far so good - so where is the problem? Well... let us look at Position 4 in Fig 1-2. This is one of the possible real-life bent-four positions - this is how it usually comes up in the actual game. After examining this position you can see that black cannot play neither 'a' nor 'b' - if he does, he would place his stones in atari and his group will die. So - black cannot play there. Fine. Now lets look at white's possibilities. If he plays at 'a', black will kill his stones with 'b' and the black group will be alive. No good. How about white playing at 'b'? The sequence from Position 5 is forced, after which white can play at '3' in Position 6 - and the ko discussed in Positions 1-3 appears. Ok, ko is ko - but still the question remains - what is the problem?
| Position 4 | Position 5 | Position 6 |
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Well - the problem is in the fact that in Position 4 black cannot do nothing, and so it is up to white to start the sequence leading to the ko. This means that white can wait with starting this sequence till there is no ko threats for black left on the board - and black cannot stop him!! Essentially - white can wait till all points are played out at the end of the game and then start the ko - a ko which then black will have to lose! Or he can start the ko earlier, when he judges that he will win the ko for sure! Yeah - white has a sweet deal with such bent-four in the corner (or black has a sweet deal if the colors are reversed, hehe).
Anyways - there are few different ways of dealing with the bent-four. Some rules just outright state that black is dead (in Position 1), others imply that the sequence has to be played out due to the fact that there may be some ko threats in the position which are impossible to get rid of - and so it may never be the case when white can be sure of winning the ko. There is also the issue that even if white can reduce all the ko threats, it may cost him some points to do so - and in case of bent-four being dead by definition, he may be spared the trouble (and the points). Whichever rules you prefer, I suggest that you try to play the ko out, if for no other reason than to gain some better understanding of the bent-four.
Another specific situation which can arise in a Go game (and which arises much more often than the bent-four) is the so-called seki. Seki is a situation of "mutual life", when two group of stones have both no eyes, or only a single eye each, but they share some liberties and so cannot kill each other without committing suicide. Consider the marked groups in the following examples:
| Position 1 | Position 2 |
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Let us examine the Positions 1 and 2 in Fig 2-1. In both positions neither side can play at 'a' in fear that the other side will play at 'b' (at the respective 'b' in Position 2) and kill the enemy stones. For the same reason - neither side can afford to play at 'b' - because this would also allow the opponent to play at 'a' and kill the enemy stones. Impasse! Mutual life. Seki! The only practical difference between Position 1 and Position 2 is that in Position 2 the groups have one eye each, while in Position 1 the groups are both eyeless.
No seki is possible if one group has an eye and the other one does not - the one with the eye wins! (although there are some seki positions in which one group has a real eye and the other a seemingly false eye - I say seemingly because even if the shape of an eye may be false, the shortage of liberties inside a seki may prevent the opponent to cash in on such defect.) A seki also cannot develop if one (or both) of the groups have two eyes each - simply because in such case both groups are alive in the ordinary sense of the word.
The problem remains - how to score the empty intersections within a seki? Again - there are different approaches, but, for the sake of simplicity, lets just ignore these points when scoring the game! Both groups are alive, and this is enough good news to satisfy both players, I believe, hehe...
Note:
A move like 'a' or
'b' in Fig 2-1 can be considered a ko threat which cannot
be eliminated by either side - which may be a good argument for playing
out the bent-four position discussed in a previous chapter. True,
by threatening at 'a' (or at 'b') a player would condemn himself to
losing the stones which were till then alive in a seki - but if such
sacrifice allows him to save a group lost due to bent-four, it may be
worth it. It all depends on relative sizes of the involved groups.
It might be worth it to sacrifice 10 stones in a seki to save 20 stones
in a bent-four.