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Mini-GO
by Ted Drange
A couple of years ago, some others and I worked on mini go.  We never published the results.  The table below shows what we came up with.

The following chart shows our area-counting results (worked out mainly during January-July of 1998).  The first column gives Black's margin of victory for ideal (or best = B) play.  The second column gives the result for second-best (S) opening, and the third gives it for third-best (T) opening (with a negative number if White wins).  Parentheses indicate opening with a pass-play.  In the future we may try working it out for territory counting (i.e., the, ugh!, Japanese rules).
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B    S    T               B    S    T               B     S    T
1x2   (0)  -2    -        2x2    1    -    -        3x3    9     3   -9
1x3    3   -3    -        2x3   (0)  -2   -6        3x4    4     3    0
1x4    4   -4    -        2x4    8   -8    -        3x5   15    15    1*
1x5    0    0   (0)       2x5   10   10   -10       3x6   18    18    2
1x6    1   -1   -1        2x6   12   12   -12       3x7    5
1x7    2    2   -2        2x7   14   14   -2        3x8   24
1x8    3    1   -1        2x8   16    0   -2        4x4    2   (-2)  -16
1x9    0    0   -2        2x9   18    2             4x5   20
1x10   1                  2x10   4                  4x6    1
1x11   2                  2x11   4    2   -2        4x7    4
1x12   1                                            5x5   25     3    -1
1x13   2                  6x6    4                  5x6    2     2     0
6x7    6                  5x7    9
*(start at 1-2 pt.)
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The blanks indicate future projects, and that includes, e.g., second-best and third-best for 6x6 and other forms.  For the best opening in 6x6, the following would indicate canonical play:  1-D3, 2-C4, 3-D4, 4-C3, 5-D2, 6-C5, 7-B2, 8-D5, 9-B3, 10-C2, 11-C1, 12-E4, 13-E3, 14-F4, 15-E6, 16-E5, 17-B4, 18-B5, 19-A5, 20-B6, 21-D6, 22-F6, 23-F5x1, 24-C6, 25-F3, 26-F6x3, 27-A4, 28-A6.  Score: Black 20, White 16.

Ted Drange- "Bill Spight pointed out to me that the alleged canonical sequence that I give for 6x6 go (in the "Mini-go" essay on the Mathpuzzle.com page) is defective. By proper play, White could cut Black's win to only 1 point, instead of 4 points, starting at move #20, but Black could thwart that by playing differently at move #15. For an improved (and I think the correct canonical) sequence, please delete the moves beginning with #15 and put the following in place of them:

15-F3, 16-E6, 17-B4, 18-B5, 19-A5, 20-E1, 21-D1, 22-A4, 23-A3x1, 24-B1, 25-A1x1, 26-F2, 27-B1, 28-B6, 29-E2, 30-A6, 31-F1x2, 32-A4x1, 33-F5, 34-E5, 35-B5x1, 36-pass, 37-A4. [37 moves on a 36-point board!] Score: Black 20, White 16. (Note: the moves starting with 15-F3 and the reasons for them were pointed out to me by Bill Spight.)"