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.
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.
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 . elsewhere. at .
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.
Now, a value of 1/3 is much less than a value of 3 2/3. In a real game, in the vast majority of cases after playing his sente Black will play elsewhere, leaving the local position until near the end of the game.
However, if the local region is the only place left to play Black will of course continue to get a net local score of +6.
This is pretty clear to most players, but it does show the ambiguity of what is best local play. Is it to stop after in the Black plays first diagram, or to continue?
When White plays first the first three moves are obvious. But what now? Should Black connect or play elsewhere?
connects at .
White's threat is to save the stone and capture the stone. This play has a miai value of 3 points, as you may verify.
Normally you would expect that Black should protect at instead of allowing the possibility that White can play , but maybe not.
But Black has this tesuji.
Black threatens this 3 point sente. So Black's descent at is worth 2 points more than the hane-tsugi.
So the descent is correct for Black and a play in the original position is a 4 point gote, as you may verify.
In this example the ambiguity concerns not only whether to continue play locally or play elsewhere, but also which play to make. From the standpoint of yose evaluation, Black to play should descend, but if play is restricted to the local region, the hane-tsugi is correct.
Why show you that it is often ambiguous what best local play is? My point is that best local play typically depends upon the rest of the board. The rest of the board may affect not only when to stop local play and play elsewhere but also which local play to make. Simply judging local play without regard to other possible plays elsewhere on the board is myopic and can lead you astray.
Fortunately, taking the perspective of evaluating plays is very helpful. As a rule, the biggest play is the correct play, and all we have to ask about the rest of the board is what is the biggest play elsewhere (the ambient temperature). Also, except for hyperactive or active positions involving kos, we may determine the size of plays locally. Doing so tells us what correct local play will be in a real game in the vast majority of cases.
However, it is tempting to judge local play by thinking about play only in the local region and ignoring the rest of the board. Doing so leads to two pervasive errors: first, judging incorrectly when to play elsewhere, and so getting sente and gote wrong; second, getting the play wrong.
In the second example, for instance, some players might think that best play for Black is the hane-tsugi, and many players might think that White's hane-tsugi is sente.
Such errors even show up in textbooks. See, for instance, Yose Errors in Magic of Go.