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Table of Eyespaces
Path: EyesCollection   · Prev: InstantEyeTester   · Next: Alive
    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 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
    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 !



Path: EyesCollection   · Prev: InstantEyeTester   · Next: Alive
This is a copy of the living page "Table of Eyespaces" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.