On 15 ene, 12:21, luigi <
luis.9.8...@gmail.com> wrote:
> So we can say for sure that Square Oust is "trivially soft drawless"
> for all bi-dimensional boards.
Actually, for all boards bigger than 1x2, even one-dimensional. More
or less formal proof:
Let's assume, as before, that both players keep playing on their
designated point color till
there is only one white (A) and one black (B) point left. These points
can be adjacent to each other or non-adjacent to each other. Let's say
we're using an even-sized board, so it's Black's turn.
- If A and B are adjacent to each other, Black will always be able to
capture all his opponent's stones on a single turn by making his first
placement at A and following at B.
- If A and B aren't adjacent to each other, Black plays at A and keeps
capturing as long as he can. He then ends his turn by playing at B,
after which White can only make a non-capturing placement. Next, Black
will necessarily capture all enemy stones on a single turn.
Example on a 1x8 board:
x o . o x . x o
x o . . x x x .
x o x . x x x .
x o x o x x x .
x o x . x x x x
x . x x x x x x