2009년 8월 30일 일요일
PJ step 4. value one and one third (1) /baduk/
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?
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.