Locally Speaking
Bill: There are two basic kinds of yose problems, whole board problems and local problems. In the typical whole board problem the task is to find the best technical line of play for each player to maximize his score and to determine the result. In the typical local problem the task is to find the best local play for each player and to determine the size of a play and the count of the position.
But what do we mean by best local play? That's ambiguous. Best local play in yose problems is also called orthodox play. Here I want to contrast the two main ways of looking at local play, and explain the perspective of yose problems.
Example 1
This example is a slightly modified version from Hane-connect Exercise 3/Discussion. I added a couple of stones so we can count the territory.
The rest at this point is miai. Let's look at the final position.
Black has 11 points of territory. White has 8 points of territory plus 1 captured stone, for 9 points.
Net local score: +2.
The local count is now +5 2/3. That is also the count of the original position, which is a 3 2/3 point Black sente.
To see why, let's look at the follow-ups from here.
at
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Black has 12 points of territory plus 2 captured stones, for 14 points. White has 6 points of territory plus 2 captured stones, for 8 points.
Net local score: +6.
at
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elsewhere.
at
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Black has 12 points of territory plus 2 prisoners, for 14 points. White has 6 points of territory plus 3 prisoners, for 9 points.
Net local score: +5
From the position before the follow-ups, it took Black 1 net play to reach +6, and it took White 2 net plays to reach +5. So that position has a local count of 5 2/3, as advertised. And the value of a play in that position is 1/3 by miai counting.
{It's late. More mannana. --Bill}