mitsun wrote:

Here are the graphs for the two positions Bill provided as Go diagrams earlier. The node counts and branch move values are for the gote assumption, with probability 50% for every branch.

**Code:**

o 5.25 o 2.75? really 3

/ \ / \

/ \ -2.75 / \ gote -1.25,

/ \ / \ really sente

/ \ / \

8 o 2.5 4 o 1.5

/ \ / \

/ \ -2.5 / \ -1.5

/ \ / \

5 0 3 0

Bill demonstrated that the W branch is local gote in the first graph and local sente in the second graph. Is there an easy way to see this from the graphs? I guess the contradiction in the second graph is that the gote count of the starting position (2.75) is less than a terminal position (3) which B can always guarantee reaching, by treating the W move as sente.

Is there an easy way to see this from the graphs? Yes, indeed, as you have actually shown.

Let me repeat the graphs without the calculations.

**Code:**

o A o C

/ \ / \

/ \ / \

/ \ / \

/ \ / \

8 o B 4 o D

/ \ / \

/ \ / \

/ \ / \

5 0 3 0

When we play the gote strategy for A in the four copies, we get these four results: 2*8 + 5 + 0 = 21. The sente strategy for Black yields these four result: 4*5 = 20. Black does better with the gote strategy, so we can use those results to find its territorial count: 21/4 = 5¼.

Using the graph we would first find the count of B, which is (5+0)/2 = 2½, and then find the count of A, assuming it to be gote, which is (8+2½)/2 = 5¼. OC, we can see at a glance that the count of A, assuming it to be sente, is 5, which is less than 5¼, so we conclude that A is gote. Using the graph gives us more information, and may be quicker.

When we play the gote strategy for C in the four copies, we get these four results: 2*4 + 3 + 0 = 11. The sente strategy for Black yields these four result: 4*3 = 12. Black does better with the sente strategy, so we can use those results to find its territorial count: 3.

Using the graph we would first find the count of D, which is (3+0)/2 = 1½, and then find the count of C, assuming it to be gote, which is (4+1½)/2 = 2¾. OC, we can see at a glance that the count of C, assuming it to be sente, is 3, which is greater than 2¾, so we conclude that C is White sente. Using the graph gives us more information, and may be quicker.

----

Suppose we wish to find a general rule to find out whether such a position is sente or gote. Let's relabel the graph with letters.

**Code:**

o A

/ \

/ \

/ \

/ \

a o B

/ \

/ \

/ \

b c

The result with the gote strategy is

2*a + b + c

The result with the sente strategy is

4b

Taking gote as the default, we get this rule:

**Code:**

o A

/ \

/ \

/ \

/ \

a o B

/ \

/ \

/ \

b c

A is White sente if and only if 4*b > 2*a + b + c.

Noting that we can subtract b from both sides of the inequality, we get

**Code:**

o A

/ \

/ \

/ \

/ \

a o B

/ \

/ \

/ \

b c

A is White sente if and only if 3*b > 2*a + c.

Now tell that rule to a regular go player.

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As the flight of birds. . . .

A poem should be motionless in time

As the moon climbs. . . .

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