The value of a play indicates its importance or urgency. We may also use the metaphor of temperature. Larger plays are hotter than smaller plays. Normally you should play the largest play, but there are exceptions. (See tedomari.)
velobici: De-iri is a Japanese accounting term for income and expenditure that originated during the Taisho era (1912 - 1924).
Let me start with a couple of examples.
If Black plays first he scores four points, represented as a positive integer, +4.
If White plays first she scores two points, represented as a negative integer, -2.
The deiri value is the difference between these two results (the swing), or 6 points.
We might call the deiri value of a play its swing value.
If Black plays first at a, White must play b to live, and the net score is +2 (Black: 2 points of territory + 2 prisoners; White: 2 points of territory. 2 + 2 - 2 = +2).
If White plays first at a instead, the score is -5. (White: 4 points of territory + 1 prisoner)
The deiri value is the difference between these two results, or 7 points.
We may define deiri values as the difference between the count of the first stable position after Black plays first (called a Black follower) and that of the first stable White follower, assuming normally correct play.
A stable follower is one that is cooler than the original position. There is a potential circularity here, but a line of play eventually ends, as here, in a scorable position, or in a repetition, which is prohibited by the rules. (If it is not, the original position does not really have a value.)
DamienSullivan: I seem to count that if area counting is used, the value of at a seems to be 8 points better for white instead of 7 -- 10 points of territory within the 2x5 rectangle, vs. white 6 and black 4 if black goes first. On the other hand if at a is followed by somewhere else, black should get at least one more point for placing the stone, unless the game just ended, so the - exchange is 7 (or fewer) points better for white than at a followed by at b.
Bill: In general the miai value for area scoring is one point greater than that for territory scoring, because you count the stone played as one point. The main exceptions involve seki, because of the differences about counting points for eyes in seki.
floss 8k: the first diagram with area counting seems to be a deiri difference of 8 vs. 6 for territory.
floss: so... does this mean area and territory do not differ by only 1 point at most?
Bill: In an even game that is ordinarily the case. If each player makes the same number of moves the extra points by area scoring even out, while if Black makes one more play than White, he gets one more point by area scoring. However, there may be other differences related to seki and ko, depending upon the rule set.
floss: are you saying that you can use either method to evaluate ko threats? would you need to keep it consistent with the method you use for positional judgement?
Karl Knechtel: miai and deiri counting are normally for evaluating the size of plays, rather than threats. When you evaluate the size of a threat, in normal situations the local play will consist of either "answer threat" or "ignore threat; opponent follows up on threat", and normally if the threat is followed up on, the local temperature drops greatly, such that a "stable follower" is reached immediately. Thus the two counting systems are basically the same for evaluating ko threats if you do try to use them that way. Unless I'm missing something?
Bill: You should use the same kind of scoring for ko threats as you use for other plays.