PJ step 7. 1 n one third (4) /baduk/

White sequence, there is nothing.

Black sequence, there is 1 ( A ) and one third ( B ) black cross.

Two sequences made 1 and one third, so each one sequence earns two thirds.
At the second Dia, white earns two thirds, but there is nothing, so there already exists two thirds black cross.
Each side has the right, so the value is 1 and one third.

Conclusion : exist two thirds / value is 1 n one third.

to be continued.

PJ step 6. 1 n one third (3) /baduk/

White 1 sequence A, there is nothing.
Black 1 sequence A, there is 1 and one third black cross.
Two sequences make 1 and one third, the value of each 1 sequence is as well, and 1 sequence makes two thirds.
White 1 sequence A, white earns two thirds, but there is nothing, so there is already two thirds black at first.

Conclusion : Exist two thirds black. / Value is 1 n one third.

White crosses are 12.
Black crosses : decided area 10 + non-decided area two thirds = 10 and two thirds.
So, white has strong 1 advantage.

to be continued

PJ step 5. value 1 n one third (2) /baduk/

At this post, more detailed explanations, so more dia.

White 1 sequence, there is nothing. (W)

Black 1 sequence. If black places A, there are 3 black crosses.
So, if there is not ending game bigger than this*, white must respond.
( *2 n one third I think. It's almost unusual anyway. )

Now white responded.
Can black go other side?
If black goes other side, white will do ponuki and you ought to remember second dia - there is noting. But here, white do ponuki. - So, black can't go other side.

So, this is a set of black 1 sequence. (X)

If black 1 sequence more, there are 2 black crosses include of 1 dead stone. (Y)
3 sequences ( W, X, Y ) make 2 crosses, so each 1 sequence makes two thirds.
Now, black 2 sequences ( X, Y ) make 1 and one third, but there are 2 crosses, so at first, there already exists two thirds black cross.
Got it? It may be difficult.

Conclusion 1 : Exist two thirds black cross in first dia.

White 1 sequence, there is two thirds black cross because of 1 minus one third. ( remember dead stone ) (Z)
Because W, X, Y are the same, and there is two thirds black cross, so Z is as well.

And, as you know, black and white has same right. ( so, two thirds multiple 2 )

Conclusion 2 : W, X, Y, Z has value of 1 n one third.

Not yet, to be continued.

PJ step 4. value one and one third (1) /baduk/

Two groups are same.
If black places A, there is nothing.
If white places A and B, there is 2 whte territories because of dead stone.
Total 3 sequences make 2 terrotories, so, one sequence makes two thirds.
Now, black places A, makes two thirds, but there is nothing!
Therefore, there exists already two thirds white territory.
And each side has chance to make two thirds, multiply 2 by two thirds, it's value is one and one third.

Suppose that white places A, and rightly black places B.
First white has two thirds, and white earns two thirds, and black earns two thirds.
Then, white must have two thirds, right?

Remember one black dead stone.
There is one third black cross on the board, and one black dead stone off the board.
So, one minus one third is two thirds.
I proved it.

Conclusion : Exists two thirds. / Value is one and one third.

It's not end of it yet.