Beginners Endgame Exercise 1 / Miai Value

Black first  

is gote: is sente and White can play it any time

Let's fix the count at 4 here

White first - Black's basic answer  

is sente as it can revive he 4 stones After , White can play sente again with

White gote  

Then -- is gote and the count is 0

Black sente  

turning here is sente because next it would make more in the follow up than it makes here.

Black's follow up  

If is allowed to capture here, then after and at , Black makes another 4 points. If White omits , then Black can destroy at least another 2 points.

Hence this is the eventual count of White going first: 1

White first - Black's tesuji  

After this exchange the count is fixed: a, b and c are all dame and the count is 1.

White first - Charles' move  

Since Black can next answer a with b, this variation too leads to a count of 1

Hence the value tree looks like this

               1 (3)
              /   \
             4 (1) 1
            / \
           5   4

and White is a 3 point sente move, Black being a 3 point reverse sente