Difference between revisions of "Small boards"
(→Winner depending on the first move: size 9) |
(→Size 9: added the remaining opening moves) |
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| Line 47: | Line 47: | ||
<hex> | <hex> | ||
R9 C9 Q1 | R9 C9 Q1 | ||
| − | Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Hh1 | + | Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Hh1 Vi1 |
| − | + | Va2 Vb2 Vc2 Hd2 He2 Hf2 Hg2 Vh2 Vi2 | |
| − | + | Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Vh3 Hi3 | |
| − | + | Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4 Vi4 | |
| − | + | Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Vh5 Vi5 | |
| − | + | Va6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Vh6 Vi6 | |
| − | + | Ha7 Vb7 Vc7 Vd7 Ve7 Vf7 Vg7 Vh7 Hi7 | |
| − | + | Va8 Vb8 Hc8 Hd8 He8 Hf8 Vg8 Vh8 Vi8 | |
| − | + | Va9 Hb9 Hc9 Hd9 He9 Hf9 Hg9 Hh9 Hi9 | |
</hex> | </hex> | ||
Revision as of 05:40, 4 April 2016
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.
