Count of Basic Ko and Dame
Posted: Fri Oct 26, 2012 12:15 am
This discusses the count and local temperature of a ko ensemble consisting of one basic endgame ko and one dame under territory scoring and area scoring. The start is about only one basic endgame ko.
ABBREVIATIONS
C = count of the initial position's locale
B = count of the black follower
W = count of the white follower
T = local temperature in the locale = size per play = miai value
b = excess number of black plays to the black follower
w = excess number of white plays to the black follower
N = b + w = tally
P = prisoner difference = white prisoner stones minus black prisoner stones
Positive counts favour Black, negative counts favour White.
All counts apply to the locales only.
ONE BASIC KO OPEN FOR BLACK UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1
B = 0
w = 2
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (0 - (-1)) / 3 = 1/3
C = B - b*T = 0 - 1 * 1/3 = -1/3
Interpretation:
- One black move increases the initial count -1/3 by 1/3 to create the black follower's count 0.
- Two white moves decrease the initial count -1/3 by 2*(-1/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR BLACK UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1
B = 2
w = 2
W = -2
N = b + w = 1 + 2 = 3
T = (B - W) / N = (2 - (-2)) / 3 = 4/3
C = B - b*T = 2 - 1 * 4/3 = 2/3
Interpretation:
- One black move increases the initial count 2/3 by 4/3 to create the black follower's count 2.
- Two white moves decrease the initial count 2/3 by 2*(-4/3) to create the white follower's count -2.
ONE BASIC KO OPEN FOR WHITE UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2
B = 1
w = 1
W = 0
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - 0) / 3 = 1/3
C = B - b*T = 1 - 2 * 1/3 = 1/3
Interpretation:
- Two black moves increase the initial count 1/3 by 2*1/3 to create the black follower's count 1.
- One white move decreases the initial count 1/3 by -1/3 to create the white follower's count 0.
ONE BASIC KO OPEN FOR WHITE UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2
B = 2
w = 1
W = -2
N = b + w = 2 + 1 = 3
T = (B - W) / N = (2 - (-2)) / 3 = 4/3
C = B - b*T = 2 - 2 * 4/3 = 6/3 - 8/3 = -2/3
Interpretation:
- Two black moves increase the initial count -2/3 by 2*4/3 to create the black follower's count 2.
- One white move decreases the initial count -2/3 by -4/3 to create the white follower's count -2.
After these warming up exercises, now we come to the more interesting examples.
ONE BASIC KO OPEN FOR BLACK AND ONE DAME UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1 // only the play in the ko is counted
B = 0
w = 2 // only the plays in the ko are counted
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (0 - (-1)) / 3 = 1/3
C = B - b*T = 0 - 1 * 1/3 = -1/3
Interpretation:
- One black move increases the initial count -1/3 by 1/3 to create the black follower's count 0.
- Two white moves decrease the initial count -1/3 by 2*(-1/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR BLACK AND ONE DAME UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1 // only the play in the ko is counted
B = 1
w = 2 // only the plays in the ko are counted
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (1 - (-1)) / 3 = 2/3
C = B - b*T = 1 - 1 * 2/3 = 1/3
Interpretation:
- One black move increases the initial count 1/3 by 2/3 to create the black follower's count 1.
- Two white moves decrease the initial count 1/3 by 2*(-2/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR WHITE AND ONE DAME UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2 // only the plays in the ko are counted
B = 1
w = 1 // only the play in the ko is counted
W = 0
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - 0) / 3 = 1/3
C = B - b*T = 1 - 2 * 1/3 = 1/3
Interpretation:
- Two black moves increase the initial count 1/3 by 2*1/3 to create the black follower's count 1.
- One white move decreases the initial count 1/3 by -1/3 to create the white follower's count 0.
ONE BASIC KO OPEN FOR WHITE AND ONE DAME UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2 // only the plays in the ko are counted
B = 1
w = 1 // only the play in the ko is counted
W = -1
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - (-1)) / 3 = 2/3
C = B - b*T = 1 - 2 * 2/3 = -1/3
Interpretation:
- Two black moves increase the initial count -1/3 by 2*2/3 to create the black follower's count 1.
- One white move decreases the initial count -1/3 by -2/3 to create the white follower's count -1.
QUESTIONS
1) Have I made any mistakes and which?
2) Why do the numbers of ko threat plays not count for the tally?
ABBREVIATIONS
C = count of the initial position's locale
B = count of the black follower
W = count of the white follower
T = local temperature in the locale = size per play = miai value
b = excess number of black plays to the black follower
w = excess number of white plays to the black follower
N = b + w = tally
P = prisoner difference = white prisoner stones minus black prisoner stones
Positive counts favour Black, negative counts favour White.
All counts apply to the locales only.
ONE BASIC KO OPEN FOR BLACK UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1
B = 0
w = 2
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (0 - (-1)) / 3 = 1/3
C = B - b*T = 0 - 1 * 1/3 = -1/3
Interpretation:
- One black move increases the initial count -1/3 by 1/3 to create the black follower's count 0.
- Two white moves decrease the initial count -1/3 by 2*(-1/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR BLACK UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1
B = 2
w = 2
W = -2
N = b + w = 1 + 2 = 3
T = (B - W) / N = (2 - (-2)) / 3 = 4/3
C = B - b*T = 2 - 1 * 4/3 = 2/3
Interpretation:
- One black move increases the initial count 2/3 by 4/3 to create the black follower's count 2.
- Two white moves decrease the initial count 2/3 by 2*(-4/3) to create the white follower's count -2.
ONE BASIC KO OPEN FOR WHITE UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2
B = 1
w = 1
W = 0
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - 0) / 3 = 1/3
C = B - b*T = 1 - 2 * 1/3 = 1/3
Interpretation:
- Two black moves increase the initial count 1/3 by 2*1/3 to create the black follower's count 1.
- One white move decreases the initial count 1/3 by -1/3 to create the white follower's count 0.
ONE BASIC KO OPEN FOR WHITE UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2
B = 2
w = 1
W = -2
N = b + w = 2 + 1 = 3
T = (B - W) / N = (2 - (-2)) / 3 = 4/3
C = B - b*T = 2 - 2 * 4/3 = 6/3 - 8/3 = -2/3
Interpretation:
- Two black moves increase the initial count -2/3 by 2*4/3 to create the black follower's count 2.
- One white move decreases the initial count -2/3 by -4/3 to create the white follower's count -2.
After these warming up exercises, now we come to the more interesting examples.
ONE BASIC KO OPEN FOR BLACK AND ONE DAME UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1 // only the play in the ko is counted
B = 0
w = 2 // only the plays in the ko are counted
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (0 - (-1)) / 3 = 1/3
C = B - b*T = 0 - 1 * 1/3 = -1/3
Interpretation:
- One black move increases the initial count -1/3 by 1/3 to create the black follower's count 0.
- Two white moves decrease the initial count -1/3 by 2*(-1/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR BLACK AND ONE DAME UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 1 // only the play in the ko is counted
B = 1
w = 2 // only the plays in the ko are counted
W = -1
N = b + w = 1 + 2 = 3
T = (B - W) / N = (1 - (-1)) / 3 = 2/3
C = B - b*T = 1 - 1 * 2/3 = 1/3
Interpretation:
- One black move increases the initial count 1/3 by 2/3 to create the black follower's count 1.
- Two white moves decrease the initial count 1/3 by 2*(-2/3) to create the white follower's count -1.
ONE BASIC KO OPEN FOR WHITE AND ONE DAME UNDER TERRITORY SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2 // only the plays in the ko are counted
B = 1
w = 1 // only the play in the ko is counted
W = 0
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - 0) / 3 = 1/3
C = B - b*T = 1 - 2 * 1/3 = 1/3
Interpretation:
- Two black moves increase the initial count 1/3 by 2*1/3 to create the black follower's count 1.
- One white move decreases the initial count 1/3 by -1/3 to create the white follower's count 0.
ONE BASIC KO OPEN FOR WHITE AND ONE DAME UNDER AREA SCORING
The marked intersections are the considered locale, for which count and local temperature shall be determined.
b = 2 // only the plays in the ko are counted
B = 1
w = 1 // only the play in the ko is counted
W = -1
N = b + w = 2 + 1 = 3
T = (B - W) / N = (1 - (-1)) / 3 = 2/3
C = B - b*T = 1 - 2 * 2/3 = -1/3
Interpretation:
- Two black moves increase the initial count -1/3 by 2*2/3 to create the black follower's count 1.
- One white move decreases the initial count -1/3 by -2/3 to create the white follower's count -1.
QUESTIONS
1) Have I made any mistakes and which?
2) Why do the numbers of ko threat plays not count for the tally?
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