Ataxx (7x7) opening moves

There are only five unique opening moves for red in Ataxx (7x7): a2, b2, a1a3, a1b3 and a1c3. The other 11 possible moves (of 16) are symmetric to these 5. With that in mind, which opening move is best? Using the same notation and C++ code I used in analyzing smaller Ataxx boards, I obtained the following results:

Opening move: 1.
 Resulting score at each ply, starting at 1:
 Average score:
 Average in four highest plies:
b2
 0, 1, 0, 1, -1, 3, -2 [67M], 4 [890M], -2
 +0.44
 +0.75
a2
 0, 1, 0, 1, -1, 2, -2 [28M], 3 [893M]
 +0.50
 +0.50
a1c3
 -1, 0, -2, 1, -2, 2, -3 [38M], 3 [1063M]
 -0.25
 0.00
a1b3
 -1, 0, -2, 1, -2, 2, -3 [26M], 3 [1645M]
 -0.25
 0.00
a1a3
 -1, 0, -2, 1, -2, 2, -3 [18M], 2 [572M]
 -0.38
 -0.25
For this table, the numbers in square brackets are counts of leaf nodes searched, where M denotes millions (10^6). Between 250,000 and 600,000 nodes per second are searched on my 1200 MHz AMD Athlon.

There is no strong difference between the five possible opening moves for red. However, in a game where one piece can make the difference, only 1.b2, and perhaps 1.a2 can be justified with the evidence thus far.

With that in mind, how should blue respond to 1.b2? A similar analysis of the eight possible moves (8 symmetries not considered) is below. (Node counts from here onwards are of the sum of leaves and internal nodes.)

Response to 1.b2 - 1...:
 Resulting score at each ply, starting at 1:
 Average score:
 Average in four highest plies:
b6
 1,0,2,-1,3,-2 [14M], 4 [147M], -2 [2533M]
 +0.63
 +0.75
b7
 1,0,1,0,3,-2 [17M], 4 [217M], -2 [2608M]
 +0.63 +0.75
a6
 1,0,2,-1,4,-2 [9.3M], 4 [55M], -2 [2212M]
 +0.75
 +1.00
a7c7
 2,1,3,0,3,-1 [13M], 5 [172M], -1 [2280M]
 +1.50
 +1.50
a7c6
 2,1,3,0,4,-1 [12M], 4 [240M], -1 [2182M]
 +1.50
 +1.50
a7a5
 3,2,3,2,4,2 [1.4M], 5 [54M], 0 [267M]
 +2.63
 +2.75
a7b5
 3,2,3,2,5 [1.4M], 2 [1.6M], 6 [102M], 1 [219M]
 +3.00
 +3.50
a7c5
 3,2,5,1,1005,1005 [3.5M]
 red wins
 red wins

A similar analysis in response to 1.a2, for which no blue move symmetries exist, is:

Response to 1.a2 - 1...:
 Resulting score at each ply, starting at 1:
 Average score:
 Average in four highest plies:
f2
 1,0,1,0,2,-2 [8.5M], 3 [210M]
 +0.71
 +0.75
f1
 1,0,1,0,2,-2 [5.8M], 3 [126M]
 +0.71
 +0.75
g2
 1,0,1,0,2,-1 [3.2M], 3 [277M]
 +0.86
 +1.00
b6
 1,0,2,-1,3,-2 [2.4M], 4 [39M]
 +1.00
 +1.00
a6
 1,0,2,-1,4,-2 [1.3M], 4 [52M]
 +1.14
 +1.25
b7
 1,0,1,0,3,-1 [3.0M], 4 [64M]
 +1.14
 +1.50
a7c6
 2,1,3,0,3,-1 [5.5M], 4 [114M]
 +1.71
 +1.50
a7c7
 2,1,3,0,3,-1 [7.3M], 4 [91M]
 +1.71 +1.50
g1e2 2,1,3,0,4,-2 [11M], 4 [171M]
 +1.71
 +1.50
g1e3
 2,1,3,0,3,-1 [7.4M], 4 [196M]
 +1.71
 +1.50
g1f3
 2,1,3,0,3,-1 [11M], 4 [254M]
 +1.71
 +1.50
g1g3
 2,1,3,0,3,-1 [7.4M], 4 [110M]
 +1.71
 +1.50
g1e1
 2,1,3,0,4,-1 [5.3M], 5 [54M]
 +2.00
 +2.00
a7c5 (bad!)
 3,2,3,1,5,0 [3.5M], 5 [103M]
 +2.71
 +2.75
a7a5 (bad!) 3,2,3,2,4,3 [0.5M], 5 [44M]
 +3.14
 +3.50
a7b5 (bad!) 3,2,3,2,5,2 [0.8M], 6 [104M]
 +3.29
 +3.75

So go figure - the best opening lines is likely 1. b2 b6|b7|a6, followed closely by 1. a2 f2|f1, then 1. a2 g2, 1...b6, 1...a6, and 1...b7. Using a hop move as an opening move as red is interesting, but is likely just a loss of one point.

Last updated at 2004-09(sept.)-06-1605h (UTC/GMT)