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Kōnane is a two-player
strategy Strategy (from Greek στρατηγία ''stratēgia'', "troop leadership; office of general, command, generalship") is a general plan to achieve one or more long-term or overall goals under conditions of uncertainty. In the sense of the " a ...
board game A board game is a type of tabletop game that involves small objects () that are placed and moved in particular ways on a specially designed patterned game board, potentially including other components, e.g. dice. The earliest known uses of the ...
from
Hawaii Hawaii ( ; ) is an island U.S. state, state of the United States, in the Pacific Ocean about southwest of the U.S. mainland. One of the two Non-contiguous United States, non-contiguous U.S. states (along with Alaska), it is the only sta ...
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 Checkers (American English), also known as draughts (; English in the Commonwealth of Nations, Commonwealth English), is a group of Abstract strategy game, strategy board games for two players which involve forward movements of uniform game ...
. The first player unable to capture is the loser. 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. While the game of Kōnane has been compared to
draughts Checkers (American English), also known as draughts (; Commonwealth English), is a group of strategy board games for two players which involve forward movements of uniform game pieces and mandatory captures by jumping over opponent pieces. ...
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 In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...
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. Kōnane has some resemblances to the games of
Leap Frog Leapfrog is a children's game of physical movement of the body in which players vault over each other's stooped backs. History Games of this sort have been called by this name since at least the late sixteenth century.Fanorona Fanorona () is a Abstract strategy game, strategy board game for two players. The game is indigenous to Madagascar. Rules Fanorona has three standard versions: Fanoron-Telo, Fanoron-Dimy, and Fanoron-Sivy. The difference between these variants i ...
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

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. 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 In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (PSPACE, polynomial space) and if every other problem that can be solved in polynomial sp ...
with respect to the dimensions of the board, by a reduction from
nondeterministic constraint logic In theoretical computer science, nondeterministic constraint logic is a combinatorial system in which an orientation is given to the edges of a weighted undirected graph, subject to certain constraints. One can change this orientation by steps i ...
. There have been some positive results for restricted configurations. Ernst derives Combinatorial-Game-Theoretic values for several interesting positions. Chan and Tsai 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", Carlos Pereira dos Santos and Jorge Nuna Silva showed that Kōnane contains all other combinatorial games.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.


See also

*
Fanorona Fanorona () is a Abstract strategy game, strategy board game for two players. The game is indigenous to Madagascar. Rules Fanorona has three standard versions: Fanoron-Telo, Fanoron-Dimy, and Fanoron-Sivy. The difference between these variants i ...


References


Further reading

* *


External links


Konane: Hawaiian Checker game
Gail Kaapuni, Waiakeawaena and Kalanianaole Elementary Schools, Hawaii *{{bgg, 8122, Konane Abstract strategy games Hawaii culture