Difference between revisions of "Small boards"

Revision as of 02:51, 14 December 2022

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 interesting 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. The board sizes 7 to 9 have been solved with computer programs, too.

Here are the winning first moves on the small boards. Red is vertical and plays first. The cells shaded red are winning moves for red, while those shaded blue are losing.

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

• 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
• Yang, Liao, and Pawlak designed a decomposition method to find a winning strategy for Hex on small boards.
• For corresponding information on the game of Y, please visit Where to swap (y).