To see if I have understood simple sente and reverse sente calculation, let me test my current understanding in the following examples. Are they correct?
EXAMPLE 1:
GOTE ANALYSIS:
Given tree:
x >= 1 (otherwise it would not be a meaningful go tree)
Code:
A
/ \
B 0
/ \
x 1
Gote counts:
Code:
(x+1)/4 : A
/ \
(x+1)/2 : B 0
/ \
x 1
Gote move values:
Code:
(x+1)/4 : (x+1)/4 : A
/ \
(x+1)/2 : (x-1)/2 : B 0
/ \
x 1
CASE ANALYSIS:
gote if (x+1)/4 > (x-1)/2 <=> x < 3
ambiguous if (x+1)/4 = (x-1)/2 <=> x = 3
sente if (x+1)/4 < (x-1)/2 <=> x > 3
Reverse sente applies when sente applies. Gote, sente and reverse sente apply also in the ambiguous case.
SENTE ANALYSIS FOR x>3:
Kept gote move values:
Code:
A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B 0
/ \
x 1
Inherited sente count:
Code:
sente count 1 : A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B 0
/ \
x 1:I
Inherited sente move value:
Code:
sente count 1 : sente move value (x-1)/2 : A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B:I 0
/ \
x 1
It is Black's sente, sente move count and sente move value.
REVERSE SENTE ANALYSIS FOR x>3:
Kept gote move values:
Code:
A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B 0
/ \
x 1
Inherited reverse sente count:
Code:
reverse sente count 1 : A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B 0
/ \
x 1:I
Reverse sente move value:
Code:
reverse sente count 1 : reverse sente move value 1 : A
/ \
gote count (x+1)/2 : gote move value (x-1)/2 : B 0
/ \
x 1
The reverse sente move value is calculated from the leaves 1 and 0:
swing = 1 - 0 = 1
tally = (1 - 1) - (-1) = 0 + 1 = 1
reverse sente move value = swing / tally = 1 / 1 = 1
It is White's reverse sente, reverse sente move count and reverse sente move value. When White plays the reverse sente from A with the reverse sente count 1 to the leaf 0, Black loses the reverse sente move value 1 (because White gains it): 1 - 1 = 0.
SUMMARY OF ALL NON-AMBIGUOUS CASES AT A:
gote (x<3), gote count (x+1)/4, gote move value (x+1)/4
sente for Black (x>3), sente count 1, sente move value (x-1)/2
reverse sente for White (x>3), reverse sente count 1, reverse sente move value 1
How, in general, is the temperature derived from this? Must the min or max of two values be taken?
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EXAMPLE 2:
GOTE ANALYSIS:
Given tree:
x >= 1 (otherwise it would not be a meaningful go tree)
Code:
A
/ \
0 B
/ \
-1 -x
Gote counts:
Code:
A : -(1+x)/4
/ \
0 B : -(1+x)/2
/ \
-1 -x
Gote move values:
Code:
A : -(1+x)/4 : (1+x)/4
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1 -x
CASE ANALYSIS:
gote if (1+x)/4 > (-1+x)/2 <=> x < 3
ambiguous if (1+x)/4 = (-1+x)/2 <=> x = 3
sente if (1+x)/4 < (-1+x)/2 <=> x > 3
Reverse sente applies when sente applies. Gote, sente and reverse sente apply also in the ambiguous case.
SENTE ANALYSIS FOR x>3:
Kept gote move values:
Code:
A
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1 -x
Inherited sente count:
Code:
A : sente count -1
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1:I -x
Inherited sente move value:
Code:
A : sente count -1 : sente move value (-1+x)/2
/ \
0 I:B : -(1+x)/2 : (-1+x)/2
/ \
-1 -x
It is White's sente, sente move count and sente move value.
REVERSE SENTE ANALYSIS FOR x>3:
Kept gote move values:
Code:
A
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1 -x
Inherited reverse sente count:
Code:
A : reverse sente count -1
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1:I -x
Reverse sente move value:
Code:
A : reverse sente count -1 : reverse sente move value 1
/ \
0 B : -(1+x)/2 : (-1+x)/2
/ \
-1 -x
The reverse sente move value is calculated from the leaves 0 and -1:
swing = 0 - (-1) = 1
tally = 1 - (-1 + 1) = 1 - 0 = 1
reverse sente move value = swing / tally = 1 / 1 = 1
It is Black's reverse sente, reverse sente move count and reverse sente move value. When Black plays the reverse sente from A with the reverse sente count -1 to the leaf 0, Black gains the reverse sente move value 1, i.e., -1 + 1 = 0.
SUMMARY OF ALL NON-AMBIGUOUS CASES AT A:
gote (x<3), gote count -(1+x)/4, gote move value (1+x)/4
sente for Black (x>3), sente count -1, sente move value (-1+x)/2
reverse sente for White (x>3), reverse sente count -1, reverse sente move value 1
How, in general, is the temperature derived from this? Must the min or max of two values be taken?
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COMPARISON OF EXAMPLES 1+2:
Because of symmetry, the counts are negated and the move values are equal.