What is Konane on 6×6, 10×10 and 12×12?
Konane needs nothing more than a board covered with alternating black and white stones, so it can be played at many sizes. Here you can choose a 6×6, 10×10 or 12×12 board in the table setup instead of the standard 8×8. Every square starts filled, in a checkerboard pattern, and the rules of play stay the same: each move is an orthogonal jump over an opposing stone into an empty square, a stone may keep jumping in the same direction, and the player who cannot jump on their turn loses.
The opening works on every size. Black lifts one black stone from the centre of the board or from a corner, and White lifts a white stone orthogonally next to that gap. On an even board two of the four centre squares and two of the four corners hold black stones, so Black always has the same four choices as on 8×8.
The 6×6 board holds 36 stones and plays out quickly: the edges are close, few jumps are available at any time, and counting the moves each side has left matters from the first jumps. The 10×10 and 12×12 boards hold 100 and 144 stones. There is far more room, long multi-jumps across the board become possible, and the middle game turns into a patient fight over who keeps moves in reserve for the end.
Rule changes
| Rule | Standard Konane | Konane on 6×6, 10×10 and 12×12 |
|---|---|---|
| Board | Standard Konane8×8, 64 squares. | Konane on 6×6, 10×10 and 12×126×6 (36 squares), 10×10 (100 squares) or 12×12 (144 squares), chosen in the table setup. |
| Starting position | Standard KonaneEvery square holds a stone, black and white alternating: 32 of each colour. | Konane on 6×6, 10×10 and 12×12The same checkerboard pattern on the chosen board: 18, 50 or 72 stones of each colour. |
| Opening removals | Standard KonaneBlack lifts a black stone from the centre or a corner, then White lifts a white stone orthogonally next to the gap. | Konane on 6×6, 10×10 and 12×12The same on every size: the centre and corner squares of the chosen board, with the same four choices for Black. |
| Jumps | Standard KonaneJump orthogonally over an opposing stone into an empty square. You may keep jumping in the same direction, and stop after any jump. | Konane on 6×6, 10×10 and 12×12The same. On 10×10 and 12×12 a single move can chain more jumps along a longer row or column. |
| End of the game | Standard KonaneThe first player who cannot jump on their turn loses. There are no draws and no passing. | Konane on 6×6, 10×10 and 12×12The same on every size. |
History
Kōnane is a traditional Hawaiian game. It was played on a board called a papamū, often a large carved stone that served as both board and table, and such a stone board can still be seen at Puʻuhonua o Hōnaunau National Historical Park. The game is named in the Kumulipo, the Hawaiian creation chant, and James Cook described it during his visit to Hawaii on his third voyage, in the account published in 1784.
Traditional boards came in many sizes and were often rectangular rather than square, with dimensions such as 6×7, 8×9, 9×13 and 14×17. Modern sets are usually square with an even number of rows, and square boards range from 6×6 to more than 14×14. The rules of play do not depend on the size, which is why 6×6, 10×10 and 12×12 boards play exactly like 8×8.
Konane has also been studied by mathematicians. Michael Ernst worked out the combinatorial game values of several Konane positions in a 1995 article in The UMAP Journal, and Robert Hearn later proved that Konane generalised to boards of any size is PSPACE-complete, a sign that finding the best move on a large board is very hard in general.