Kōnane is a two-player strategyboard game from Hawaii. It was invented by the ancient Hawaiian Polynesians. The game is played on a rectangular board. It 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; their opponent is the winner.[1][2]
Mathematicians playing Kōnane at a combinatorial game theory workshop
Before contact with Europeans, the game was played using small pieces of white coral and black lava on a large carved rock which doubled as both board and table. The Puʻuhonua o Hōnaunau National Historical Park has one of these stone gameboards on its premises.[3]
The game is somewhat similar to draughts. Pieces hop over one another when capturing; however, the similarities end there. 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.[2] Furthermore, in Kōnane all moves are capturing moves, captures are made in an orthogonal direction (not diagonally), and in a multiple-capture move the capturing piece may not change direction.[1][4]
Kōnane has some resemblances to the games of Leap Frog, Fanorona and Main Chuki or Tjuki.[5] 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.
The game is played on a rectangular or square board. Pieces can be 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.[4] In practice, square Kōnane boards can range from 6×6 to over 14×14.[6] Traditional rectangular board dimensions include 9×13, 14×17, and 13×20.[2][4]
Goaledit
The first player unable to capture an enemy piece is the loser, and the other player is the winner.[1][2][4][6]
Rules and gameplayedit
The game begins with all the pieces on the board (or table, ground, etc.) arranged in an alternating pattern.[2][4][6] 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).[2][6]
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.[2][6]
From here on, players take turns capturing each other's pieces. All moves must be capturing moves.[1] 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.[2][4] The player's piece can continue to hop over enemy pieces but only in the same orthogonal direction. The player can stop hopping 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.[1][6]
The player unable to make a capture is the loser; their opponent is the winner.[1][2][4][6] It is impossible to draw in Kōnane, because one player eventually cannot perform a capture.
Mathematical analysisedit
Hearn proved that Kōnane is PSPACE-complete with respect to the dimensions of the board, by a reduction from Constraint Logic.[7][8] There have been some positive results for restricted configurations. Ernst[5] derives Combinatorial-Game-Theoretic values for several interesting positions. Chan and Tsai[9] 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",[10] Carlos Pereira dos Santos and Jorge Nuna Silva showed that Kōnane contains all other combinatorial games.[11]
Other conversionsedit
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.
^ abcdefDunford, Betty; Andrews, Lilinoe; Ayau, Mikiʻala; Honda, Liana I.; Williams, Julie Stewart (2002). The Hawaiians of Old. The Bess Press, Inc. p. 174.
^ abcdefghiSelin, Helaine (2000). Mathematics Across Cultures: The History of Non-Western Mathematics. Kluwer Academic Publishers. p. 278.
^Scheid, Debbi (2014-07-07). "Island Life". West Hawaii Today. Retrieved 2014-10-18.
^ abcdefgHearn, Robert (2009). Games of No Chance 3(PDF). Vol. 56. MSRI Publications. pp. 287–299.
^ abErnst, Michael (Spring 1995). "Playing Konane mathematically: A combinatorial game-theoretic analysis" (PDF). UMAP Journal. 16 (2): 95–121.
^ abcdefgThompson, Darby (2005). Teaching a Neural Network to Play Kōnane(PDF) (Thesis). pp. 2–3. Retrieved 2014-10-12.
^Hearn, Robert (May 2006). Games, Puzzles, and Computation, PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts(PDF) (Thesis).
^Hearn, Robert (2008). "Amazons, Konane, and Cross Purposes are PSPACE-complete" (PDF). Games of No Chance 3: 287–306.
^Chan, Alice; Tsai, Alice (2002). "1×n Konane: A Summary of Results" (PDF). More Games of No Chance: 331–339.
^Electronic Journal of Combinatorial Number Theory, January 2008
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For the fictional character see Konane Arrowverse Kōnane is a two player strategy board game from Hawaii It was invented by the ancient Hawaiian Polynesians The game is played on a rectangular board It 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 their opponent is the winner 1 2 Mathematicians playing Kōnane at a combinatorial game theory workshopBefore contact with Europeans the game was played using small pieces of white coral and black lava on a large carved rock which doubled as both board and table The Puʻuhonua o Hōnaunau National Historical Park has one of these stone gameboards on its premises 3 The game is somewhat similar to draughts Pieces hop over one another when capturing however the similarities end there 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 2 Furthermore in Kōnane all moves are capturing moves captures are made in an orthogonal direction not diagonally and in a multiple capture move the capturing piece may not change direction 1 4 Kōnane has some resemblances to the games of Leap Frog Fanorona and Main Chuki or Tjuki 5 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 Contents 1 Equipment 2 Goal 3 Rules and gameplay 4 Mathematical analysis 5 Other conversions 6 See also 7 References 8 Further reading 9 External linksEquipment edit nbsp Kōnane played with stones on a wooden boardThe game is played on a rectangular or square board Pieces can be 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 4 In practice square Kōnane boards can range from 6 6 to over 14 14 6 Traditional rectangular board dimensions include 9 13 14 17 and 13 20 2 4 Goal editThe first player unable to capture an enemy piece is the loser and the other player is the winner 1 2 4 6 Rules and gameplay editThe game begins with all the pieces on the board or table ground etc arranged in an alternating pattern 2 4 6 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 2 6 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 2 6 From here on players take turns capturing each other s pieces All moves must be capturing moves 1 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 2 4 The player s piece can continue to hop over enemy pieces but only in the same orthogonal direction The player can stop hopping 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 1 6 The player unable to make a capture is the loser their opponent is the winner 1 2 4 6 It is impossible to draw in Kōnane because one player eventually cannot perform a capture Mathematical analysis editHearn proved that Kōnane is PSPACE complete with respect to the dimensions of the board by a reduction from Constraint Logic 7 8 There have been some positive results for restricted configurations Ernst 5 derives Combinatorial Game Theoretic values for several interesting positions Chan and Tsai 9 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 10 Carlos Pereira dos Santos and Jorge Nuna Silva showed that Kōnane contains all other combinatorial games 11 Other conversions editBrainvita 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 editFanoronaReferences edit a b c d e f Dunford Betty Andrews Lilinoe Ayau Mikiʻala Honda Liana I Williams Julie Stewart 2002 The Hawaiians of Old The Bess Press Inc p 174 a b c d e f g h i Selin Helaine 2000 Mathematics Across Cultures The History of Non Western Mathematics Kluwer Academic Publishers p 278 Scheid Debbi 2014 07 07 Island Life West Hawaii Today Retrieved 2014 10 18 a b c d e f g Hearn Robert 2009 Games of No Chance 3 PDF Vol 56 MSRI Publications pp 287 299 a b Ernst Michael Spring 1995 Playing Konane mathematically A combinatorial game theoretic analysis PDF UMAP Journal 16 2 95 121 a b c d e f g Thompson Darby 2005 Teaching a Neural Network to Play Kōnane PDF Thesis pp 2 3 Retrieved 2014 10 12 Hearn Robert May 2006 Games Puzzles and Computation PhD thesis Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts PDF Thesis Hearn Robert 2008 Amazons Konane and Cross Purposes are PSPACE complete PDF Games of No Chance 3 287 306 Chan Alice Tsai Alice 2002 1 n Konane A Summary of Results PDF More Games of No Chance 331 339 Electronic Journal of Combinatorial Number Theory January 2008 Elwyn Berlekamp Autobiography Mathematical Sciences Publishers Celebratio Mathematica 2021Further reading editBell R C 1983 Konane The Boardgame Book Exeter Books pp 132 33 ISBN 0 671 06030 9 Murray H J R 1978 A History of Board Games other than Chess Reissued ed Hacker Art Books Inc p 97 ISBN 0 87817 211 4 External links editKonane Hawaiian Checker game Gail Kaapuni Waiakeawaena and Kalanianaole Elementary Schools Hawaii Konane at BoardGameGeek Retrieved from https en wikipedia org w index php title Kōnane amp oldid 1212029808, wikipedia, wiki, book, books, library,
