computer-go: Handicap patterns against perfect players

[Roland <goprog@xxxxxxx>]

Hello computer-go,

still on the subject of how many handicap we need to win against a
perfect player, how about this: the idea is to build territory with
the 3.line as border. If we manage to control the whole border region,
we would have 38*2 + 30*2 = 136 territory, whereas white
in the center would have at most 11*11 = 121, that if we don't invade
the center which we can easily accomplish.

The first idea would be to place stones at the 3.line leaving a gap
between two consecutive stones: for this configuration we would need
28 stones. The question is if the border is really secured or can
the opponent invade it?

     A B C D E F G H J K L M N O P Q R S T
  19 . . . . . . . . . . . . . . . . . . . 19
  18 . . . . . . . . . . . . . . . . . . . 18
  17 . . X . X . X . X . X . X . X . X . . 17
  16 . . . . . . . . . . . . . . . . . . . 16
  15 . . X . . . . . . . . . . . . . X . . 15
  14 . . . . . . . . . . . . . . . . . . . 14
  13 . . X . . . . . . . . . . . . . X . . 13
  12 . . . . . . . . . . . . . . . . . . . 12
  11 . . X . . . . . . . . . . . . . X . . 11
  10 . . . . . . . . . . . . . . . . . . . 10
   9 . . X . . . . . . . . . . . . . X . . 9
   8 . . . . . . . . . . . . . . . . . . . 8
   7 . . X . . . . . . . . . . . . . X . . 7
   6 . . . . . . . . . . . . . . . . . . . 6
   5 . . X . . . . . . . . . . . . . X . . 5
   4 . . . . . . . . . . . . . . . . . . . 4
   3 . . X . X . X . X . X . X . X . X . . 3
   2 . . . . . . . . . . . . . . . . . . . 2
   1 . . . . . . . . . . . . . . . . . . . 1
     A B C D E F G H J K L M N O P Q R S T  


One weakness of the above are the corners, because if white plays at
the 4-4 points he has a double threat to invade, so maybe we should
add 4 more stones to make the corners secure. This would give us the
following configuration with 32 stones:

     A B C D E F G H J K L M N O P Q R S T
  19 . . . . . . . . . . . . . . . . . . . 19
  18 . . . . . . . . . . . . . . . . . . . 18
  17 . . X X X . X . X . X . X . X . X . . 17
  16 . . . . . . . . . . . . . . . . X . . 16
  15 . . X . . . . . . . . . . . . . X . . 15
  14 . . . . . . . . . . . . . . . . . . . 14
  13 . . X . . . . . . . . . . . . . X . . 13
  12 . . . . . . . . . . . . . . . . . . . 12
  11 . . X . . . . . . . . . . . . . X . . 11
  10 . . . . . . . . . . . . . . . . . . . 10
   9 . . X . . . . . . . . . . . . . X . . 9
   8 . . . . . . . . . . . . . . . . . . . 8
   7 . . X . . . . . . . . . . . . . X . . 7
   6 . . . . . . . . . . . . . . . . . . . 6
   5 . . X . . . . . . . . . . . . . X . . 5
   4 . . X . . . . . . . . . . . . . . . . 4
   3 . . X . X . X . X . X . X . X X X . . 3
   2 . . . . . . . . . . . . . . . . . . . 2
   1 . . . . . . . . . . . . . . . . . . . 1
     A B C D E F G H J K L M N O P Q R S T

If you still think the above is not secure we might add more stones to
reduce the number of gaps, so how about we add 12 more stones and
arrive at the following with a total of 44 stones:

     A B C D E F G H J K L M N O P Q R S T
  19 . . . . . . . . . . . . . . . . . . . 19
  18 . . . . . . . . . . . . . . . . . . . 18
  17 . . X X X . X X X . X X X . X X X . . 17
  16 . . X . . . . . . . . . . . . . X . . 16
  15 . . X . . . . . . . . . . . . . X . . 15
  14 . . . . . . . . . . . . . . . . . . . 14
  13 . . X . . . . . . . . . . . . . X . . 13
  12 . . X . . . . . . . . . . . . . X . . 12
  11 . . X . . . . . . . . . . . . . X . . 11
  10 . . . . . . . . . . . . . . . . . . . 10
   9 . . X . . . . . . . . . . . . . X . . 9
   8 . . X . . . . . . . . . . . . . X . . 8
   7 . . X . . . . . . . . . . . . . X . . 7
   6 . . . . . . . . . . . . . . . . . . . 6
   5 . . X . . . . . . . . . . . . . X . . 5
   4 . . X . . . . . . . . . . . . . X . . 4
   3 . . X X X . X X X . X X X . X X X . . 3
   2 . . . . . . . . . . . . . . . . . . . 2
   1 . . . . . . . . . . . . . . . . . . . 1
     A B C D E F G H J K L M N O P Q R S T

Looks secure enough doesn't it? Well if you are really paranoid you
can still close the final gaps adding between 4 and 12 stones. If you
add 12 stones you would achieve a full wall needing 56 handicap
stones.

How about the following needing 33 handicap stones:

     A B C D E F G H J K L M N O P Q R S T
  19 . . . . . . . . . . . . . . . . . . . 19
  18 . . . . . . . . . . . . . . . . . . . 18
  17 . . . . . . . . . . . . . . . . . . . 17
  16 . . . . . . . . . . . . . . . . . . . 16
  15 . . . . . . . . . . . . . . . . . . . 15
  14 . . . . . . . . . . . . . . . . . . . 14
  13 . . . . . . . . . . . . . . . . . . . 13
  12 . . . . . . . . . . . . . . . . . . . 12
  11 . . . . . . . . . . . . . . . . . . . 11
  10 X X X . . . . . . . . . . . . . X X X 10
   9 . . X . . . . . . . . . . . . . X . . 9
   8 . . X . . . . . . . . . . . . . X . . 8
   7 . . X . . . . . . . . . . . . . X . . 7
   6 . . X . . . . . . . . . . . . . X . . 6
   5 . . X . . . . . . . . . . . . . X . . 5
   4 . . X . . . . . . . . . . . . . X . . 4
   3 . . X X X X X X X X X X X X X X X . . 3
   2 . . . . . . . . . . . . . . . . . . . 2
   1 . . . . . . . . . . . . . . . . . . . 1
     A B C D E F G H J K L M N O P Q R S T

Black seems to have secured at least 38 + 2*14 = 66 territory(the
bottom border region). But it also can take big chunks of whites territory
away and control a large part of the bottom center region?
So I also think it's an easy win for black...

-- 
Best regards,
 Roland                          mailto:goprog@xxxxxxxxxxxxxxxxx