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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!,
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.)
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.)"
Any comments or questions you may have about this would be welcome. Send Email to tmdrange at earthlink.net (Ed - You'll have to put Ted's address together)
Each of the forms listed in the chart is a puzzle. For example:
consider 3x4 go. What is the ideal sequence? What is Black's
second-best opening, and what is the ideal sequence proceeding from that?
What is Black's third-best opening, and what is the ideal sequence leading
from that? These puzzles regarding 3x4 go are indeed quite formidable.
Try them and see!