Real Half Point Ko

So-called half point ko  

This ko, commonly known as a half point ko, has a miai value of only ⅓.

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. When there are many of them, however, with one player leading in most of them, that player can expect ⅓ of a point for all that remain after cancelling those where their opponent leads with ones where they lead; see the section Half-point-ko § Playing order of third-point kos for details.

Real half point ko  

This ko really has a miai value of 1/2.

White wins the ko  

If White wins the ko White gets 3 points of territory locally.

Black wins the ko  

elsewhere

Black wins the ko with , unless that is ko-banned in which case Black wins the ko with . Either play is sente and White responds at .

Two points  

In the end White will net only 2 points of territory locally.

A net difference of two plays in the ko makes a net difference of one point. Each play has a miai value of 1/2.

Real half point ko (2)  

This ko also has a miai value of 1/2, unless Black is komaster.

No ko threats (Black first)  

elsewhere, fills the ko at .

Result: +1 (for Black).

No ko threats (White first)  

Result: 0.

A difference of two moves makes a difference of one point, so the miai value of the ko is 1/2.

White komaster (White first)  

- (ko threat) and reply. takes the ko back. elsewhere. at .

Result: -1.

White komaster (Black first)  

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.

Black komaster (White plays)  

fills, leaving a 1/2 point play at a.

Result: -1/2.

Black komaster (Black plays)  

elsewhere. takes ko. - = ko threat and reply. takes ko.

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