Difference between revisions of "Small boards"
m (→Size 9: changed the attribution) |
(→Size 7: add proof tree link from the top of the page) |
||
| Line 21: | Line 21: | ||
=== Size 7 === | === Size 7 === | ||
| − | Size 7 was first solved by [[Ryan Hayward]] using [[domination]]. | + | Size 7 was first solved by [[Ryan Hayward]] using [[domination]]. The proof tree can be found at http://www.cs.ualberta.ca/~hayward/hex7trees/ |
<hex>R7 C7 Q1 Ha1 Hb1 Hc1 Hd1 He1 Hf1 Vg1 Ha2 Hb2 Vc2 Hd2 Ve2 Vf2 Vg2 Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Hg3 Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ha5 Vb5 Vc5 Vd5 Ve5 Vf5 Hg5 Va6 Vb6 Vc6 Hd6 Ve6 Hf6 Hg6 Va7 Hb7 Hc7 Hd7 He7 Hf7 Hg7</hex> | <hex>R7 C7 Q1 Ha1 Hb1 Hc1 Hd1 He1 Hf1 Vg1 Ha2 Hb2 Vc2 Hd2 Ve2 Vf2 Vg2 Ha3 Vb3 Vc3 Vd3 Ve3 Vf3 Hg3 Va4 Vb4 Vc4 Vd4 Ve4 Vf4 Vg4 Ha5 Vb5 Vc5 Vd5 Ve5 Vf5 Hg5 Va6 Vb6 Vc6 Hd6 Ve6 Hf6 Hg6 Va7 Hb7 Hc7 Hd7 He7 Hf7 Hg7</hex> | ||
Revision as of 22:41, 5 October 2017
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. The proof tree can be found at http://www.cs.ualberta.ca/~hayward/hex7trees/
Size 8
The outcomes for size 8 were computer generated by Javerberg. The solution was independently computer generated by Hayward et al. and appeared in IJCAI09.
Size 9
The outcomes for size 9 by Jakub Pawlewicz and Ryan Hayward.
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.
- This article by Jakub Pawlewicz and Ryan Hayward is a reference for size 9x9.
See also
- Board size
- Jing Yang designed a decomposition method to find winning strategy in Hex. Home Page.
- For corresponding information on the game of Y, please visit Where to swap (y).
