Kōnane

{{Short description|Two-player strategy board game from Hawaii}} {{for|the fictional character|Konane (Arrowverse)}} thumb|250px|Mathematicians playing ''kōnane'' at a combinatorial game theory workshop thumb|Konane gaming table erroneously set up at Puʻuhonua o Hōnaunau NHP, 2017 '''Kōnane''' or rarely {{Lang|haw|'''mū'''}}<ref name=":1">{{Cite book |last=Brigham |first=William Tufts |author-link=William Tufts Brigham |url=https://www.google.com/books/edition/Old_Hawaiian_Carvings_Found_in_a_Cave_on/utkSAAAAYAAJ?hl=en&gbpv=1&dq=konane+papamu&pg=PA180&printsec=frontcover |title=Old Hawaiian Carvings Found in a Cave on the Island of Hawaii |date=1906 |publisher=Bishop Museum Press |pages=16-18 |language=en}}</ref> is a two-player Hawaiian strategy board game invented and played by its native people. 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 or draughts, though both players' pieces mingle in position by default occupying every square of the board unlike the separate sides in checkers; the objective and winning conditions of the game are also completely different.<ref name="selin" /> All moves in ''{{Lang|haw|kōnane}}'' 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.<ref name="dunford" /><ref name="nochance3">{{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}}</ref> The first player unable to capture is the loser.<ref name="dunford">{{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}}</ref><ref name="selin">{{Cite book| last=Selin |first=Helaine |author-link=Helaine Selin |title= Mathematics Across Cultures: The History of Non-Western Mathematics |publisher=Kluwer Academic Publishers |year= 2000 |page=278}}</ref> The word {{Lang|haw|mū}} may had referred the act of capturing people as slaves or sacrifice.<ref name=":1" />

Kōnane has some resemblances to games of the English leap frog, ''fanorona'' in Madagascar and {{Lang|ms|main cuki}} (also spelled ''chuki'' or ''tjuki'') among the Malays and Javanese of Southeast Asia.<ref name=":0" /> 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.<ref name="islandlife">{{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}}</ref> It was recorded in the Kumulipo, it was also noted by James Cook described the game during his only visit to Hawaii on his third and final voyage prior to his death there.<ref name=":2" />

The Bishop Museum organized the first professional tournament of the game in February 2026.<ref>{{Cite web |last=Allen |first=Kevin |date=2026-02-24 |title=Kōnane players perpetuate Hawaiian strategy game at inaugural tournament |url=https://www.hawaiipublicradio.org/the-conversation/2026-02-23/konane-players-perpetuate-hawaiian-strategy-game-at-inaugural-tournament |access-date=2026-04-21 |website=The Conversation |publisher=Hawai'i Public Radio |language=en}}</ref>

== Equipment == thumb|upright|Kōnane played with stones on a wooden board The game is traditionally played on a rectangular board ({{Lang|haw|papa}}, also {{Lang|haw|papa mū}} "capture board" or {{Lang|haw|papamū}}) consisting of an even and odd number of columns and rows, though modern {{Lang|haw|kōnane}} is often played on a square board with an even number of both columns and rows; modern versions use felt boards and marbles as pieces.<ref>{{Cite web |last=Negrin |first=Matt |date=2025-09-20 |title=They Tried to Snuff Out Hawaii's Native Board Game. Meet the Man Keeping It Alive |url=https://www.rollingstone.com/culture/rs-gaming/konane-hawaii-board-game-history-1235428364/ |access-date=2026-04-21 |website=Rolling Stone |language=en-US}}</ref> Pieces are laid out on 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 sometimes with indented ({{Lang|haw|puka}}). Furthermore, the game can be generalized to any size geometrically.<ref name="nochance3"/> In practice, square {{Lang|haw|kōnane}} boards can range from 6×6 to over 14×14.<ref name="thompsondarby">{{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}}</ref> Traditional rectangular board dimensions include 6×7, 8×9, 9×13, 14×17,<ref name=":2">{{Cite book |last=Cook |first=James |url=http://archive.org/details/bim_eighteenth-century_a-voyage-to-the-pacific-_cook-james_1784_2 |title=A Voyage to The Pacific Ocean: Undertaken, by the Command of His Majesty, for making discoveries in the Northern Hemisphere |last2=King |first2=James |author-link2=James King (Royal Navy officer) |date=1784|pages=312}}<br><blockquote>''One of their games resemble our game of Draughts; but, from the number of squares, it seems to be much more intricate. The board is of the length of about two feet, and is divided into two hundred and thrity-eight squares, fourteen in a row.''</blockquote></ref> and 13×20.<ref name="selin"/><ref name="nochance3"/>

== Rules and gameplay == The game begins with all the pieces on the board (or table, ground, etc.) arranged in an alternating pattern.<ref name="selin"/><ref name="nochance3"/><ref name="thompsondarby"/> 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).<ref name="selin"/><ref name="thompsondarby"/> # 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.<ref name="selin"/><ref name="thompsondarby"/> # From here on, players take turns capturing each other's pieces. ''All moves must be capturing moves''.<ref name="dunford"/> 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.<ref name="selin"/><ref name="nochance3"/> 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.<ref name="dunford"/><ref name="thompsondarby"/> The player unable to make a capture is the loser; their opponent is the winner.<ref name="dunford"/><ref name="selin"/><ref name="nochance3"/><ref name="thompsondarby"/> 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.<ref>{{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}}</ref><ref>{{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}}</ref> There have been some positive results for restricted configurations. Ernst<ref name=":0">{{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}}</ref> derives Combinatorial-Game-Theoretic values for several interesting positions. Chan and Tsai<ref>{{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|archive-date=2019-07-28|access-date=2016-07-11|archive-url=https://web.archive.org/web/20190728201107/http://library.msri.org/books/Book42/files/chan.pdf|url-status=dead}}</ref> 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.<ref>{{Cite journal |last=dos Santos |first=Carlos Pereira |last2=Silva |first2=Jorge Nuno |date=2008 |title=Konane has infinite nim-dimension. |url=https://eudml.org/doc/117409 |journal=Integers |volume=8 |issue=1 |pages=Article G02, 6 p., electronic only–Article G02, 6 p., electronic only |issn=1867-0652}}</ref><ref>[https://celebratio.org/Berlekamp_ER/article/843/ Elwyn Berlekamp Autobiography] Mathematical Sciences Publishers: Celebratio Mathematica. 2021</ref>

== 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 - board game played by the Malagasy of Madagascar * Mū tōrere - board game played by the Māori of New Zealand

==References== {{reflist}}

==Further reading== * {{citation |last=Bell |first=R. C. |authorlink=Robert Charles Bell |title=The Boardgame Book |publisher=Exeter Books |year=1983 |chapter=Konane |pages=132–33 |isbn=0-671-06030-9}} * {{cite book |last=Murray |first=H. J. R. |authorlink=H. J. R. Murray |title=A History of Board-Games other than Chess |edition=Reissued |publisher=Hacker Art Books Inc |year=1978 |page=97 |isbn=0-87817-211-4}}

==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}} *[https://www.rollingstone.com/culture/rs-gaming/konane-hawaii-board-game-history-1235428364/ Article about kōnane from ''Rolling Stone''], September 20, 2025

Category:Abstract strategy games Category:Culture of Hawaii