Difference between revisions of "Small boards"

Revision as of 10:47, 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/

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 independently 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.
• 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.