This pages describes the proof-trees found for all 7x7 Hex opening moves, as described in Solving 7x7 Hex: Virtual Connections and Game-state Reduction, in Advances in Computer Games (2003), Van den Herik/Iida/Heinz eds., 261-278. The above figure shows the value of each possible opening move by the player owning the north and south edges: a blue cell is a winning move, a red cell is a losing move (and the label is a winning responding move).
For the final version of the paper, and to compute the trees described on this webpage, the solver program was compiled with gcc 3.2.3 and run on a 533 MHz Celeron with 128 MB memory running OpenBSD Unix, with the exception of the a4 and g4 openings, which were compiled with gcc 3.2.2 and run on a dual processor 1GHz Pentium 3.
A program which allows viewing of the proof trees listed below is available
here.
The program can be executed under Linux with Qt version 3 or newer.
After
unzipping and expanding the .gtz file, go to directory "Viewer" and run
"qmake" and then "make". Next go to the subdirectory Hex and type "make".
Then download the tree you wish to view into the "Viewer" directory. To
execute the game-tree viewer, type "GTV Hex treefilename.gtf" from within
the viewer directory. Finally, once the program is executing, you can traverse
the tree using the up/down/left/right arrows on your keyboard (you need
to gunzip the downloaded xx.gtf.gz files).
| Position | Countermove | Nodes | Time (Seconds) | Proof File Size (bytes) | Proof Download Link |
|---|---|---|---|---|---|
| a1 | c4 | 80688 | 34148.9 | 578360 | a1.gtf.gz |
| a2 | e3 | 345718 | 154546 | 2515027 | a2.gtf.gz |
| a3 | d4 | 1801214 | 697532 | 13030752 | a3.gtf.gz |
| a4 | -- | 2295743 | -- | 16918344 | a4.gtf.gz |
| a5 | b6 | 275080 | 116193 | 2007327 | a5.gtf.gz |
| a6 | -- | 1268025 | 621174 | 9064629 | a6.gtf.gz |
| a7 | -- | 535309 | 178621 | 3721397 | a7.gtf.gz |
| b1 | c4 | 69626 | 26807.4 | 498708 | b1.gtf.gz |
| b2 | e3 | 203902 | 89382.7 | 1516849 | b2.gtf.gz |
| b3 | -- | 3245 | 3920.56 | 26350 | b3.gtf.gz |
| b4 | -- | 444843 | 179119 | 3331063 | b4.gtf.gz |
| b5 | -- | 39363 | 20896 | 304548 | b5.gtf.gz |
| b6 | -- | 207 | 262.8 | 1978 | b6.gtf.gz |
| b7 | b6 | 1296 | 1123.66 | 9725 | b7.gtf.gz |
| c1 | c4 | 55760 | 20281.9 | 396620 | c1.gtf.gz |
| c2 | -- | 15975 | 7250.06 | 122509 | c2.gtf.gz |
| c3 | -- | 18451 | 7464.03 | 137185 | c3.gtf.gz |
| c4 | -- | 8389 | 6707.37 | 62935 | c4.gtf.gz |
| c5 | -- | 1517 | 1071.13 | 12902 | c5.gtf.gz |
| c6 | -- | 136957 | 33329.3 | 965913 | c6.gtf.gz |
| c7 | b6 | 1262 | 975.2 | 9488 | c7.gtf.gz |
| d1 | b6 | 190 | 228.05 | 1841 | d1.gtf.gz |
| d2 | c5 | 3308 | 1584.1 | 25942 | d2.gtf.gz |
| d3 | -- | 2395 | 1027.41 | 17389 | d3.gtf.gz |
| d4 | -- | 1257 | 1534.97 | 9994 | d4.gtf.gz |
| d5 | -- | 2943 | 1752.71 | 20851 | d5.gtf.gz |
| d6 | e3 | 5132 | 3257.86 | 38857 | d6.gtf.gz |
| d7 | b6 | 1292 | 926.91 | 9632 | d7.gtf.gz |
| e1 | b6 | 154 | 220.06 | 1555 | e1.gtf.gz |
| e2 | -- | 57827 | 16583.8 | 406614 | e2.gtf.gz |
| e3 | -- | 1161 | 938.15 | 9428 | e3.gtf.gz |
| e4 | -- | 6881 | 4973.04 | 52490 | e4.gtf.gz |
| e5 | -- | 19437 | 8030.65 | 146076 | e5.gtf.gz |
| e6 | -- | 14355 | 6888.95 | 107113 | e6.gtf.gz |
| e7 | d3 | 32224 | 13506.5 | 227576 | e7.gtf.gz |
| f1 | b6 | 94 | 172.95 | 1062 | f1.gtf.gz |
| f2 | -- | 99 | 137.23 | 1007 | f2.gtf.gz |
| f3 | -- | 44737 | 21867.3 | 347976 | f3.gtf.gz |
| f4 | -- | 430663 | 207239 | 3252339 | f4.gtf.gz |
| f5 | -- | 2867 | 2961.74 | 22581 | f5.gtf.gz |
| f6 | c5 | 211782 | 116392 | 1570266 | f6.gtf.gz |
| f7 | d3 | 53252 | 22946.1 | 380636 | f7.gtf.gz |
| g1 | -- | 574417 | 249835 | 4042710 | g1.gtf.gz |
| g2 | -- | 1169377 | 555253 | 8469212 | g2.gtf.gz |
| g3 | f2 | 243986 | 96893.2 | 1771454 | g3.gtf.gz |
| g4 | -- | 2762787 | -- | 20410408 | g4.gtf.gz |
| g5 | d4 | 1806650 | 829891 | 13365275 | g5.gtf.gz |
| g6 | c5 | 416868 | 209076 | 2994766 | g6.gtf.gz |
| g7 | d3 | 88954 | 34998.2 | 621834 | g7.gtf.gz |