Big Eye Wins Semeai

    Keywords: Tactics, Theory

Japanese 大ナカ小ナカ (oonaka - konaka), 大ナカデ小ナカデ (oonakade - konakade)

In a capturing race a big eye (大ナカデ) has an advantage over a small eye (小ナカデ) similar to the advantage a group with an eye has over a group with no eye. See eye versus eye capturing race and Eyes win semeais.

[Diagram]
Seki?  

Both groups have an eye and all liberties are internal. This looks a lot like a seki, but Black is dead.[10]

[Diagram]
Playing it out (1)  

B2, B4, B6 = pass

[Diagram]
Black is dead  

No matter who starts first, white can win the semeai because of his big eye.

The group with the big eye has a big advantage in a semeai. Not only does the big eye confer extra liberties, the big eye gets the shared dame for liberties. The group with a small eye needs more external liberties if he is to have a chance of winning. This is very much like eye vs no eye semeai.


[Diagram]
Bigger eye wins  

If both players have big eyes, the one with the bigger eye has the advantage. Here White is dead.

[Diagram]
Playing it out (1)  

W2 = pass

[Diagram]
Playing it out (2)  



[Diagram]
Playing it out (3)  

After B1 White has 4 liberties, Black has 7. White is dead.


[Diagram]
Critical position  

This is the critical position in this semeai. Black has 4 obvious liberties. It looks like White has 3 liberties, but big eyes have more liberties, as a rule. The rule of thumb is that the 4-point big eye has 5 liberties. Black has played one, so White has 4 left. Whoever plays first wins.

[Diagram]
Black wins  



[Diagram]
Black wins (continued)  

Black is plainly one move ahead, now. White is dead.

[Diagram]
White wins  



[Diagram]
White wins (continued)  

Now White is plainly one move ahead. Black is dead.


[Diagram]
Seki?  

We have altered the position by giving the groups one shared dame, circle. Since the groups started with the same number of liberties and each has an eye, is this seki?

Actually, no. The shared dame is a liberty for the big eye, White, so Black is dead.

To show that, Black to play loses and cannot make seki.

[Diagram]
Black loses  

Now if Black plays at circle White will take Black's corner stones and Black will lose, so B5 passes.

[Diagram]
Black loses (ii)  

B7 passes.

The order of play is important. If White takes Black's stones before almost filling Black's eye, Black can make seki.

[Diagram]
Black loses (iii)  

After W10 Black is lost.



[10] tderz: Formula:
Black IL + OL < White's IL + SL
SL = 4 , i.e. both have 4 shared liberties
IL(B) = 3-2 = 1
IL(W) = 5-3 = 2 , hence one more.
The number 5 derives from the sequence (1-2-3-) 5, 8, 12, 17 ... -> (?)


See also:


Big Eye Wins Semeai last edited by Bill on November 10, 2005 - 21:29
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