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Table of Eyespaces
Path: EyesCollection   · Prev: InstantEyeTester   · Next: TeachingEyesToBeginnersDiscussion
PageType: Path     Keywords: Life & Death

KarlKnechtel offers the following table, to summarize the status and value of various eye spaces. Obviously under territory scoring each eye of a living group is worth one point per point in the eye, plus one point per dead stone within it (except of course in the case of seki).

"# to kill" is the number of times that opponent must play within the eye in order to render it dead (assuming alternating play after that point). Similarly "# for seki". A '-' for "# to kill" indicates that the group can only be killed by capturing it outright. Of course, these values are merely of academic interest in some cases.

"Status" is the status of a group which is surrounded, and has a single eyespace of the indicated size and shape (assuming alternating play with opponent first), with no opponent's stones within the eyespace. "Unsettled" means that the status depends on who plays first (depends on sente); this is the case when "# to kill" is exactly 1.

"# libs" is the effective number of liberties (in the second sense) that the eyespace yields in a capturing race; see BigEyeLiberties. This assumes that life cannot be made immediately (or else the value is '-'), and does not count the stones inside which are used to prevent life from being made. Note that seki is as good as life for a capturing race.

Note that some of these shapes (especially the BentFour) have different properties in the corner (see for example BigEyesCanBeSmallInTheCorner).

 Size       Shape    Status # to kill # for seki # libs
    1           -      dead         0          -      1
    2           -      dead         0          -      2
    3 ThreeInARow unsettled         1          -      3
        BentThree unsettled         1          -      3
    4 SquaredFour      dead         0          -      5
         BentFour     alive         2          -      5
       FarmersHat unsettled         1          -      5
            other     alive         2          -      5
    5 CrossedFive unsettled         1          -      8
        BulkyFive unsettled         1        (3)      8
             ****
               *      alive         2        (3)      8
              ***
               *      alive         2        (3)      8
               *
              *
              ***     alive         2        (3)      8
               *
            other     alive         -          3      8
    6 RabbittySix unsettled         1          -     12
            other     alive    varies        2-4     12
    7                 alive    varies        1-5     17
    8                 alive         -       3?-6      -
  n>8                 alive         -     varies      -
                              (no more than n-2)

The 5-point shapes I've illustrated have the interesting property that they are alive, but give the opponent a ko threat to kill. As well, having killed these groups, opponent can subsequently blunder and make seki! All other 5-point eyespaces are either unsettled or alive, as far as I can tell. (There is a way to make seki inside the BulkyFive, but I can pretty much guarantee you will never see it in a serious game. There is no seki possible within the CrossedFive, however, even with pathologically odd play.) Anyone care to christen this odd shapes? And how about a more in-depth study of the various 6-8 point eyespaces?

Gorobei: if the illustatrated 5-points shapes are alive with a ko threat to kill, shouldn't we also consider the SquaredFour to be dead with a ko threat to live? Dieter: good point !

TDerz Karl, it is a great idea to have this table! Congratulations. "(There is a way to make seki inside the Bulky Five," - the players might be even very serious ones - but it will be the rather seldom Ten-Thousand-Year-Ko and then, also rare, the ko being filled.) I would like to add something on RabbittySeven?, which might become seki. Also from those liberties (17) at least 2 must be deducted for at least two stones inside the eyespace, otherwise it would live outright. I think you indicated this by n-2. The bulky five have less fighting liberties in the corner and all shapes are susceptible to cutting points inside the shape, which swiftly reduce liberties.

Hence I adapted the table (not yet finished) as suggested also for ko-threats: Overview over Dead shapes: If the only eyespace of a group? is almost filled with one of the following shapes, it dies. [Diagrams]

The marked points are the vital points to play: [Diagrams]

The last shape on the lower right would be alive. (seki for rabbity seven)

Table of Eyespaces

    Keywords: Life & Death

In the following table the status and value of various eye spaces is summarized. Obviously under territory scoring each eye of a living group is worth one point per point in the eye, plus one point per dead stone within it (except of course in the case of seki). "# to kill" is the number of times that opponent must play within the eye in order to render it dead (assuming alternating play after that point). Similarly "# for seki". A '-' for "# to kill" indicates that the group can only be killed by capturing it outright. Of course, these values are merely of academic interest in some cases. "Status" is the status of a group which is surrounded, and has a single eyespace of the indicated size and shape (assuming alternating play with opponent first), with no opponent's stones within the eyespace. "Unsettled" means that the status depends on who plays first (depends on sente); this is the case when "# to kill" is exactly = 1. "# libs" is the effective number of liberties (in the second sense) that the eyespace yields in a semeai; see BigEyeLiberties. This assumes that life cannot be made immediately (or else the value is '-'), and does not count the stones inside which are used to prevent life from being made. Note that seki is as good as life for a semeai. Note that some of these shapes (especially the BentFour) have different properties in the corner (see for example BigEyesCanBeSmallInTheCorner).

 Size       Shape    Status # to kill # for seki # libs	ko threats?
    1           -      dead         0          -      1	-
    2           -      dead         0          -      2	-
    3 ThreeInARow unsettled         1          -      3	-
        BentThree unsettled         1          -      3	-
    4 SquaredFour      dead         0          -      5	Y for defender
         BentFour     alive         2          -      5	Y for attacker
       FarmersHat unsettled         1          -      5	-
            other     alive         2          -      5	-
    5 CrossedFive unsettled         1          -      8	-
        BulkyFive unsettled         1        (3)      8	Y
             ****
               *      alive         2        (3)      8	Y
              ***
               *      alive         2        (3)      8	Y
               *
              *
              ***     alive         2        (3)      8	Y
               *
            other     alive         -          3      8
    6 RabbittySix unsettled         1          -     12
            other     alive    varies        2-4     12
    7                 alive    varies        1-5     17
      RabbittySeven? also called     3     2, in gote  15?
      ButterflySeven  alive
    8                 alive         -       3?-6      -
  n>8                 alive         -     varies      -
                              (no more than n-2)

The 5-point shapes I've illustrated have the interesting property that they are alive, but give the opponent a ko threat to kill. As well, having killed these groups, opponent can subsequently blunder and make seki! All other 5-point eyespaces are either unsettled or alive, as far as I can tell. (There is a way to make seki inside the Bulky Five, but it will be either this SekiInsideTheBulkyFive or the rather seldom TenThousandYearKo and then, also rare, the ko being filled.)

Comment still must be improved!

--- DougRidgway Dumb question: shouldn't the "alive" shapes have ∞ for the # liberties? To answer my own question, no: two eyes give just two liberties. It's just that neither can be filled.



Path: EyesCollection   · Prev: InstantEyeTester   · Next: TeachingEyesToBeginnersDiscussion
This is a copy of the living page "Table of Eyespaces" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.