Real Half Point Ko
This ko, commonly known as a half point ko, has a miai value of only 1/3.
As a rule, there will be no smaller plays between this ko and dame, so that the only question is who wins the ko, and it will behave as though it were a half point ko.
However, this ko really does have a miai value of 1/2. Unless Black is komaster, that is.
elsewhere,
fills the ko at
.
Result: +1 (for Black).
Result: 0.
A (local tally) difference of two moves makes a difference of one point, so the miai value of the ko is 1/2.
-
(ko threat) and reply.
takes the ko back.
elsewhere.
at
.
Result: -1.
elsewhere.
-
= ko threat and reply.
takes ko back.
elsewhere.
at
.
Result: 0.
Again, a difference of two plays makes a difference of one point. Miai value of ko = 1/2.
When Black is komaster the ko has a miai value of 7/12.
fills, leaving a 1/2 point play at a.
Result: -1/2.
elsewhere.
takes ko.
-
= ko threat and reply.
at
.
Result: +2/3. (Black has taken one stone for one point, minus 1/3 point for the black stone in ko.)
After the local temperature drops to 1/3. Black has a sente sequence with
-
.
Two plays make a difference of 1/2 + 2/3 = 7/6 points. The miai value of the ko is 7/12.
-- Bill Spight