Difference between revisions of "Small boards"
(added reference + javerberg results) |
(→Winner depending on the first move) |
||
| Line 9: | Line 9: | ||
== Winner depending on the first move == | == 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. | 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. | ||
| − | <hex>R2 C2 Vb1 Va2 Ha1 Hb2</hex> | + | <hex>R2 C2 Q1 Vb1 Va2 Ha1 Hb2</hex> |
| − | <hex>R3 C3 Va2 Va3 Hb1 Vb2 Hb3 Vc1 Vc2 Ha1 Hc3</hex> | + | <hex>R3 C3 Q1 Va2 Va3 Hb1 Vb2 Hb3 Vc1 Vc2 Ha1 Hc3</hex> |
| − | <hex>R4 C4 Va4 Vb3 Vc2 Vd1 Ha1 Ha2 Ha3 Hb1 Hb2 Hb4 Hc1 Hc3 Hc4 Hd2 Hd3 Hd4</hex> | + | <hex>R4 C4 Q1 Va4 Vb3 Vc2 Vd1 Ha1 Ha2 Ha3 Hb1 Hb2 Hb4 Hc1 Hc3 Hc4 Hd2 Hd3 Hd4</hex> |
| − | <hex>R5 C5 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Ha3 Hb1 Hc1 Hd1 Hb5 Hc5 Hd5 He5 He4 He3</hex> | + | <hex>R5 C5 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Ha3 Hb1 Hc1 Hd1 Hb5 Hc5 Hd5 He5 He4 He3</hex> |
| − | <hex>R6 C6 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Va3 Hb1 Hc1 Hd1 He1 Vb5 Vc5 Vd5 Ve5 Ve4 Ve3 Vf1 Vf2 Vf3 Vf4 Hf5 Hf6 He6 Hd6 Hc6 Hb6 Va6</hex> | + | <hex>R6 C6 Q1 Ve1 Vb2 Vc2 Vd2 Ve2 Vb3 Vc3 Vd3 Va4 Vb4 Vc4 Vd4 Va5 Ha1 Ha2 Va3 Hb1 Hc1 Hd1 He1 Vb5 Vc5 Vd5 Ve5 Ve4 Ve3 Vf1 Vf2 Vf3 Vf4 Hf5 Hf6 He6 Hd6 Hc6 Hb6 Va6</hex> |
=== Size 7 === | === Size 7 === | ||
| Line 29: | Line 29: | ||
The outcomes for size 8 were computer generated by [[Javerberg]]. | The outcomes for size 8 were computer generated by [[Javerberg]]. | ||
| − | <hex>R8 C8 Q1 | + | <hex> |
| − | Ha1 Hb1 | + | R8 C8 Q1 |
| − | + | Ha1 Hb1 Hc1 Hd1 He1 Hf1 Hg1 Vh1 | |
| − | + | Ha2 Hb2 Hc2 Hd2 He2 Hf2 Vg2 Vh2 | |
| − | + | Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Vg3 Hh3 | |
| − | + | Ha4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Vh4 | |
| − | + | Va5 Vb5 Vc5 Vd5 Ve5 Vf5 Vg5 Hh5 | |
| − | + | Ha6 Vb6 Vc6 Vd6 Ve6 Vf6 Vg6 Hh6 | |
| − | + | Va7 Vb7 Hc7 Hd7 He7 Hf7 Hg7 Hh7 | |
| + | Va8 Hb8 Hc8 Hd8 He8 Hf8 Hg8 Hh8 | ||
</hex> | </hex> | ||
Revision as of 21:50, 5 February 2009
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/
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.
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.
