RE: computer-go: perfect play

[sdossey@xxxxxxxx]

> On a related matter that has come up.  I am no worse than 192 stones worse
> than GoDevil or GoGod, if I am allowed to place my stones myself.  My
> strategy is to place my handicap stones in a grid (waffle) pattern to fill
> rows 2,5,8,11,14 and 17, and the columns of the same numbers.  Then I will
> pass unless my big group is put into atari, at which point I will capture
> some enemy stones and continue as before.  At the end of the game I will
> have a very comfortable win.

First, this is not quite a conventional bound.  I'd like to see you take a
handicap of 360 stones and win against GoGod.  (I'll let you count Chinese)

If the opponent or a preset handicap pattern dictates where the handicap
stones are placed, it'd be possible to beat someone with a 355 stone
handicap (IE--rabbity-six shape is the only open space).  Heck, the bounds
for "losing from having too many handicap stones placed the way the opponent
likes to place them" could be lower given special properties of the corner.

Now, throwing aside that abnormality.....if you can place the handicap
stones anywhere you'd like 120-360 stones is definitely a mathematically
provable guaranteed win area.  

In fact, if you get a 120 stone handicap, you can pass the entire rest of
the game, and still take the entire board.

http://www.goban.demon.co.uk/go/bestiary/brain_hurts.html
See item #14.

Interestingly enough... for NxN sized boards greater than 1x1 where N is odd
it seems always possible to create such a position with (N*N)/3 stones
(rounded down).  This would be interesting to prove one way or another.  It
would also be
interesting to prove that it is not possible to create such a position with
fewer stones.

Here are examples for a 3x3 and 5x5 board:

3x3 = 9 area 9/3 rounded down = 3 stones.

  A B C
3 . . . 3
2 X X X 2 
1 . . . 1
  A B C

 5x5 = 25 area 25/3 rounded down = 8 stones.

  A B C D E
5 . X . . . 5
4 X . X . . 4
3 . X . X . 3
2 . X X X . 2
1 . . . . . 1
  A B C D E  

Any mathematicians want to prove or disprove this hypothesis?

At any rate.  It's fairly easy to get the upper bound down from here.
William Harold Newman certainly shows convincing evidence that the bound for
maximum number of handicap stones needed to guarantee a win against Go-god
is 23 or perhaps a few less (as long as the right person plays and gets to
place 23 stones wherever he'd like.  

-Scott Dossey