Deiri counting is one way of estimating the value of playing in a position where either player might eventually play: the deiri value is defined as the swing, i.e. the difference in the counts of the positions that result when Black or White plays first.
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De-iri is a Japanese accounting term for income and expenditure that originated during the Taisho era (1912 - 1924).
Deiri counting is one of two main styles of evaluating moves in Go; the other is miai counting. Conceptually we judge the value of a play by its size or its urgency. Miai values directly indicate the urgency of plays, while deiri values do so indirectly.
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.
Deiri counting is considered less helpful in mathematical analysis than miai counting.
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.
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 (also known as a stable follower) after Black plays first (called a black follower) and that of the first stable white follower, assuming normally correct play.
Miai v. deiri value
The miai value is defined to be the swing divided by the local tally, which is the difference in the excess of black moves over white moves when Black first and that excess when White plays first. The miai value is thus infinite for a double sente, equal to the deiri value for a one-sided sente and half the deiri value for a double gote.
Area v. territory scoring
In general the miai value for area scoring is one point greater than that for territory scoring, because one counts the stone played as one point. The main exceptions involve seki, because of the differences about counting points for eyes in seki.
If each player makes the same number of moves, the extra points due to area scoring even out, while if Black makes one more play than White, he gets one more point by area scoring. Thus a one-sided sente yields an extra point, while gote and double sente do not. However, there may be other differences related to seki and ko, depending upon the rule set.
On the value of ko threats
One should use the same type of counting for ko threats as for other plays. However, the value of a ko exchange involves not only the size of the threat but also the size of the ko itself and the value of sente.