Kōnane

File:Puʻuhonua o Hōnaunau National Historical Park kanone game.jpg

Kōnane is a two-player strategy board game from Hawaii which was invented by the ancient Hawaiian Polynesians. The game is played on a rectangular board and begins with black and white counters filling the board in an alternating pattern. Players then hop over one another's pieces, capturing them similar to checkers. The first player unable to capture is the loser.{{cite book

| last1 = Dunford | first1 = Betty

| last2 = Andrews | first2 = Lilinoe

| last3 = Ayau | first3 = Mikiʻala

| last4 = Honda | first4 = Liana I.

| last5 = Williams | first5 = Julie Stewart

| page = 174

| publisher = The Bess Press, Inc.

| title = The Hawaiians of Old

| year = 2002}}{{Cite book| last=Selin |first=Helaine |title= Mathematics Across Cultures: The History of Non-Western Mathematics |publisher=Kluwer Academic Publishers |year= 2000 |page=278}}

Before contact with Europeans, the game was played using small pieces of white coral and black lava on a large carved rock which functioned as both the board and a table. The Puʻuhonua o Hōnaunau National Historical Park has one of these stone gameboards on its premises.{{cite news |last=Scheid |first=Debbi |url=http://westhawaiitoday.com/news/local-features/island-life-7-7-14 |title=Island Life |date=2014-07-07 |newspaper=West Hawaii Today |accessdate=2014-10-18}}

While the game of Kōnane has been compared to draughts since the time of Captain James Cook, the similarity begins and ends with how the pieces move and capture, the objective and winning condition of the game are completely different, and is best understood independently from draughts. In draughts, one player's pieces are initially set up on one side of the board opposite the other player's pieces. In Kōnane, both players' pieces are intermixed in a checkered pattern of black and white occupying every square of the board. Furthermore, in Kōnane, all moves are capturing moves, captures are made in an orthogonal direction (not diagonally) by "jumping" over the opposite color piece into an empty space, and in a multiple-capture move, the capturing piece may not change direction.{{cite book| last=Hearn |first=Robert|author-link=Bob Hearn |url=http://www.msri.org/people/staff/levy/files/Book56/31hearn.pdf |title=Games of No Chance 3 |publisher=MSRI Publications |year=2009 |volume=56 |pages=287–299}}

Kōnane has some resemblances to the games of Leap Frog, Fanorona and Main Chuki or Tjuki. In both Kōnane and Leap Frog, every square of the board is occupied by a playing piece in the beginning of the game, and the only legal moves (after the first turn) are orthogonal captures by the short leap method. However, there are significant differences in Kōnane and Leap Frog.

Equipment

File:USMC-14131.jpg

The game is traditionally played on a rectangular board consisting of an even and odd number of columns and rows, though modern Kōnane is often played on a square board with an even number of both columns and rows. Pieces are laid out in the beginning of the game in an alternating checkerboard pattern of two colors on top of a table, on the ground, or on any flat surface. Furthermore, the game can be generalized to any size geometrically. In practice, square Kōnane boards can range from 6×6 to over 14×14.{{Cite thesis |last=Thompson |first=Darby |title=Teaching a Neural Network to Play Kōnane |url=http://cs.brynmawr.edu/Theses/Thompson.pdf |year= 2005 |accessdate=2014-10-12 |pages=2–3}} Traditional rectangular board dimensions include 6×7, 8×9, 9×13, 14×17, and 13×20.

Rules and gameplay

The game begins with all the pieces on the board (or table, ground, etc.) arranged in an alternating pattern. Players decide which colors to play (black or white).

Black traditionally starts first and must remove one of their pieces either from the middle of the board, where there are 2 black and 2 white pieces that are diagonally opposite each other or remove a black piece from one of the four corners of the board (which will also consist of 2 black and 2 white pieces diagonally opposite from each other).
White then removes one of their pieces orthogonally adjacent to the empty space created by Black. There are now two orthogonally adjacent empty spaces on the board.
From here on, players take turns capturing each other's pieces. All moves must be capturing moves. A player captures an enemy piece by hopping over it with their own piece similar to draughts; however, unlike draughts, captures can be done only orthogonally and not diagonally. The player's piece hops over the orthogonally adjacent enemy piece and lands on a vacant space immediately beyond. The player's piece can continue to hop over enemy pieces, but only in the same orthogonal direction. The player can stop hopping over enemy pieces at any time, but must at least capture one enemy piece in a turn. After the piece has stopped hopping, the player's turn ends. Only one piece may be used in a turn to capture enemy pieces.

The player unable to make a capture is the loser; their opponent is the winner. It is impossible to draw in Kōnane, because one player eventually cannot perform a capture.

Mathematical analysis

Bob Hearn proved that Kōnane is PSPACE-complete with respect to the dimensions of the board, by a reduction from nondeterministic constraint logic.{{cite thesis | first1=Robert | last1=Hearn|author1-link=Bob Hearn | url=https://groups.csail.mit.edu/mac/users/bob/hearn-thesis-final.pdf | title=Games, Puzzles, and Computation, PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts | date=May 2006}}{{cite journal|last1=Hearn|first1=Robert|author1-link=Bob Hearn|title=Amazons, Konane, and Cross Purposes are PSPACE-complete|journal=Games of No Chance 3|date=2008|pages=287–306|url=http://www.msri.org/people/staff/levy/files/Book56/31hearn.pdf}} There have been some positive results for restricted configurations. Ernst{{cite journal |last1=Ernst |first1=Michael |date=Spring 1995 |title=Playing Konane mathematically: A combinatorial game-theoretic analysis |url=https://homes.cs.washington.edu/~mernst/pubs/konane-tr9524.pdf |journal=UMAP Journal |volume=16 |issue=2 |pages=95–121}} derives Combinatorial-Game-Theoretic values for several interesting positions. Chan and Tsai{{cite journal|last1=Chan|first1=Alice|last2=Tsai|first2=Alice|title=1×n Konane: A Summary of Results|journal=More Games of No Chance|date=2002|pages=331–339|url=http://library.msri.org/books/Book42/files/chan.pdf}} analyze the 1 × n game, but even this version of the game is not yet solved. In the 2008 paper "Konane has infinite nim-dimension",[https://www.kurims.kyoto-u.ac.jp/EMIS/journals/INTEGERS/papers/ig2/ig2.pdf Electronic Journal of Combinatorial Number Theory, January 2008] Carlos Pereira dos Santos and Jorge Nuna Silva showed that Kōnane contains all other combinatorial games.[https://celebratio.org/Berlekamp_ER/article/843/ Elwyn Berlekamp Autobiography] Mathematical Sciences Publishers: Celebratio Mathematica. 2021

Other conversions

Brainvita, also called Peg Solitaire, is a game for one person, in which the rules of Kōnane are used to move clockwise in turns. The procedure and aim of the game are identical to the original.

References

External links

[https://web.archive.org/web/20090325101718/http://www.k12.hi.us/~gkaapuni/konane.htm Konane: Hawaiian Checker game] Gail Kaapuni, Waiakeawaena and Kalanianaole Elementary Schools, Hawaii
{{bgg|8122|Konane}}

Category:Abstract strategy games

Category:Hawaii culture