Difference between revisions of "Small boards"
(→Winner depending on the first move) |
(→Winner depending on the first move: size 9) |
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=== Size 8 === | === Size 8 === | ||
| − | The outcomes for size 8 were computer generated by [[Javerberg]]. | + | The outcomes for size 8 were computer generated by [[Javerberg]]. The solution was independantly computer generated by Hayward et al. and appeared in [[INJCAI|IJCAI09]]. |
<hex> | <hex> | ||
| Line 39: | Line 39: | ||
Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7 | Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7 | ||
Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8 | Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8 | ||
| + | </hex> | ||
| + | |||
| + | === Size 9 === | ||
| + | |||
| + | The outcomes for size 9 are computer generated by [[University of Alberta]]'s Hex group. | ||
| + | |||
| + | <hex> | ||
| + | R9 C9 Q1 | ||
| + | Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Hh1 Pi1 | ||
| + | Pa2 Pb2 Pc2 Hd2 He2 Hf2 Hg2 Vh2 Pi2 | ||
| + | Pa3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Ph3 Pi3 | ||
| + | Pa4 Pb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ph4 Pi4 | ||
| + | Pa5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Vh5 Pi5 | ||
| + | Pa6 Pb6 Vc6 Vd6 Ve6 Vf6 Vg6 Ph6 Pi6 | ||
| + | Pa7 Pb7 Vc7 Vd7 Ve7 Vf7 Vg7 Vh7 Pi7 | ||
| + | Pa8 Vb8 Hc8 Hd8 He8 Hf8 Pg8 Ph8 Pi8 | ||
| + | Pa9 Hb9 Hc9 Hd9 He9 Hf9 Hg9 Hh9 Hi9 | ||
</hex> | </hex> | ||
Revision as of 10:59, 21 April 2010
Playing Hex on boards of size smaller than 10 × 10 is not very interesting, since many players will be able to play almost perfectly. However it may still be intersting for theoretical studies, and for making problems.
The boards of size up to five can be solved by hand. Hex on 6 × 6 has been solved by Queenbee.
Here are the winning first moves on the small boards. Red is vertical and plays first. The cells containing a red stone are winning moves for red, while those containing a blue stone are losing. For more details, visit Queenbee's own opening page.
Update: The 7 × 7 board has been solved by R. Hayward, et.al. For more details, visit http://www.cs.ualberta.ca/~hayward/hex7trees/
Contents
Winner depending on the first move
The following boards can help you decide where you should swap when playing on small boards, and it might give you ideas of patterns for bigger boards.
Size 7
Size 7 was first solved by Ryan Hayward using domination.
Size 8
The outcomes for size 8 were computer generated by Javerberg. The solution was independantly computer generated by Hayward et al. and appeared in IJCAI09.
Size 9
The outcomes for size 9 are computer generated by University of Alberta's Hex group.
Reference
- Queenbee's opening page is a reference for sizes under 6x6.
- This article by Ryan Hayward et al. is a reference for 7x7.
- This Little Golem's forum thread is a reference for size 8x8.
See also
- Board size
- Jing Yang designed a decomposition method to find winning strategy in Hex. Home Page.
