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EyeLiberties

 

Nakade Liberties
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    Keywords: Tactics

This page discusses the number of virtual liberties the different eyeshapes have, which is slightly different from the usual meaning in the liberties page. Here, it refers to the difference between the number of moves required to remove the group containing the eye off the board and the number of defensive moves needed to prevent immediate capture. This value can be compared with the opponent's value in a semeai: in general the player with the highest number of liberties wins the semeai. The player who knows the sequence (3,5,8,12) has an advantage over a player who has to read the semeai.

Two Space Eye

[Diagram]
Diag.: Two-space eye

Not much discussion here, but I'll use it as the base. Each case builds on from the previous case.

Anyway, a two-space eye has 2 liberties.



Three-space eye

[Diagram]
Diag.: Three-space eye

A three-space eye has three liberties. We count 1 move at the marked stone. Then White plays at a, and Black replies at b, ...

SIDE NOTE: If Black fails to reply in this case, the strategic result is the same as if Black had. But under Chinese scoring, White has one more point at the end of the game. Under Japanese scoring the points are the same too. -- Derek Grant

Bill Spight: Under either form of scoring, it is costly for Black to reply unless necessary, except after the dame stage. In that case it is costly under territory scoring but not under area scoring.

[Diagram]
Diag.: Three-space eye, continued

We are back to a two-space eye. Note that after playing the marked stone, Black has two liberties (the same as the two-space big eye, since White a is answered by b, so that liberty doesn't count).

Thus a three-space eye has 1 + 2 = 3 liberties.



Eyes of more than 3 spaces are big eyes

Four-space big eye

[Diagram]
Diag.: Four-space big eye

Using the same theory, we do the same counting for the four-space eye, the first big eye. First we count two liberties at the marked stones; now Black has three liberties left, because after White plays atari at a, and Black answers at b, we get...


[Diagram]
Diag.: Four-space big eye, continued

... a three-space eye.

So a four-space big eye has 2 + 3 = 5 liberties.

That's three liberties for the "three-space eye" and two more liberties for the additional step above.



Five-space big eye

[Diagram]
Diag.: Five-space big eye

The same theory goes, counting three marked stones, and after the exchange of White a and Black b, we have...


[Diagram]
Diag.: Five-space big eye, continued

... a four-space big eye with five liberties.

Summing up, a five-space big eye has 3 + 5 = 8 liberties.

By the way, this shape is also known as the bulky five.

That's five liberties for the "four-space big eye" and three more liberties for the additional step above.... You get the idea.



Six-space big eye

[Diagram]
Diag.: Six-space big eye

The last case, a six-space big eye...


[Diagram]
Diag.: Six-space big eye, continued

... will get reduced to a five-space big eye.

It has 4 + 8 = 12 liberties.



See also: Four is Five and Five is Eight and Six is Twelve and Eyes Collection


Contributors:

  • unkx80
  • Dieter, removing the big for eyes that are not big as defined in big eye. The terminology is debatable.


Path: GiveMeLiberties   · Prev: FourIsFiveAndFiveIsEightAndSixIsTwelve   · Next: EyesThatLoseLiberties
Path: EyesCollection   · Prev: FourIsFiveAndFiveIsEightAndSixIsTwelve   · Next: EyesThatLoseLiberties

This is a copy of the living page "Nakade Liberties" at Sensei's Library.
(C) the Authors, published under the OpenContent License V1.0.