:Abstract strategy game

File:Stratego.jpg]]

Combinatorial games have no randomizers such as dice, no simultaneous movement, nor hidden information. Some games that do have these elements are sometimes classified as abstract strategy games. (Games such as Continuo, Octiles, Can't Stop, and Sequence, could be considered abstract strategy games, despite having a luck or bluffing element.) A smaller category of abstract strategy games manages to incorporate hidden information without using any random elements; the best known example is Stratego.

Traditional abstract strategy games are often treated as a separate game category, hence the term 'abstract games' is often used for competitions that exclude them and can be thought of as referring to modern abstract strategy games. Two examples are the IAGO World Tour (2007–2010) and the Abstract Games World Championship held annually since 2008 as part of the Mind Sports Olympiad.{{cite web|publisher=Mind Sports Olympiad|title=Abstract Games|access-date=July 27, 2017|url=http://www.boardability.com/game.php?id=abstract_games|archive-url=https://web.archive.org/web/20120325221027/http://www.boardability.com/game.php?id=abstract_games|archive-date=March 25, 2012|url-status=dead|df=mdy-all}}

Some abstract strategy games have multiple starting positions of which it is required that one be randomly determined. For a game to be one of skill, a starting position needs to be chosen by impartial means. Some games, such as Arimaa and DVONN, have the players build the starting position in a separate initial phase which itself conforms strictly to combinatorial game principles. Most players, however, would consider that although one is then starting each game from a different position, the game itself contains no luck element. Indeed, Bobby Fischer promoted randomization of the starting position in chess in order to increase player dependence on thinking at the board.{{cite web|url=http://www.chessvariants.com/diffsetup.dir/fischerh.html|title=The birth of Fischer Random Chess|first=Eric|last=van Reem|website=The Chess Variant Pages|access-date=July 27, 2017|date=May 31, 2001}}

As J. Mark Thompson wrote in his article "Defining the Abstract", play is sometimes said to resemble a series of puzzles the players pose to each other:{{cite web|last=Thompson|first=J. Mark|date=July 2000|title=Defining the Abstract|publisher=The Games Journal|access-date=July 27, 2017|url=http://www.thegamesjournal.com/articles/DefiningtheAbstract.shtml|archive-url=https://web.archive.org/web/20001018073731/http://www.thegamesjournal.com/articles/DefiningtheAbstract.shtml|url-status=usurped|archive-date=October 18, 2000}}{{cite web|publisher=International Abstract Games Organisation|title=Abstract strategy games and other genres out of scope of IAGO|url=http://iagoweb.com/wiki/game-genres |url-status=dead |archive-url=https://web.archive.org/web/20110818060137/http://iagoweb.com/wiki/game-genres |archive-date=August 18, 2011}}

There is an intimate relationship between such games and puzzles: every board position presents the player with the puzzle, What is the best move?, which in theory could be solved by logic alone. A good abstract game can therefore be thought of as a "family" of potentially interesting logic puzzles, and the play consists of each player posing such a puzzle to the other. Good players are the ones who find the most difficult puzzles to present to their opponents.

Many abstract strategy games also happen to be "combinatorial"; i.e., there is no hidden information, no non-deterministic elements (such as shuffled cards or dice rolls), no simultaneous or hidden movement or setup, and (usually) two players or teams take a finite number of alternating {{boardgloss|turns}}.

Many games which are abstract in nature historically might have developed from thematic games, such as representation of military tactics.{{Cite web |title=SFE: Board Game |url=https://sf-encyclopedia.com/entry/board_game |access-date=2022-08-21 |website=sf-encyclopedia.com}} In turn, it is common to see thematic version of such games; for example, chess is considered an abstract game, but many thematic versions, such as Star Wars-themed chess, exist.

There are also many abstract video games, which include open ended solutions to problems, one example is Shapez,{{Cite web |title=Save 65% on shapez on Steam |url=https://store.steampowered.com/app/1318690/shapez/ |access-date=2024-05-23 |website=store.steampowered.com |language=en}} a game which you must deliver a set amount of shapes, but it is entirely up to you how to do so.

File:Akhilleus Aias Staatliche Antikensammlungen 1417.jpg and Ajax playing a board game.]]

A board resembling a Draughts board was found in Ur dating from 3000 BC, found by British archaeologist Sir Leonard Woolley in the 1920s.{{cite book|last=Oxland|first=Kevin|url=https://books.google.com/books?id=l05TkZFbS24C|title=Gameplay and design|publisher=Pearson Education|year=2004|isbn=978-0-321-20467-7|edition=Illustrated|pages=333}} In the British Museum are specimens of ancient Egyptian checkerboards, found with their pieces in burial chambers, and the game was played by Queen Hatasu.{{cite book|last=Strutt|first=Joseph|url=https://books.google.com/books?id=eJwSAAAAYAAJ&pg=PA255|title=The sports and pastimes of the people of England|year=1801|location=London|pages=255}}{{cite news|date=17 February 1916|title=Lure of checkers|pages=1|work=The Ellensburgh Capital|url=https://news.google.com/newspapers?id=yo0KAAAAIBAJ&pg=1525%2C2429787|access-date=2009-04-16}} Plato mentioned a game, πεττεία or {{Interlanguage link|Petteia|lt=Petteia|el|Πέττεια|WD=}}, as being of Egyptian origin, and Homer also mentions it. The game was later imported into the Roman Empire under the name ludus latrunculorum.{{Cite journal |last=Tilley |first=Arthur |date=November 1892 |title=Ludus Latrunculorum |url=https://www.cambridge.org/core/product/identifier/S0009840X00186433/type/journal_article |journal=The Classical Review |language=en |volume=6 |issue=8 |pages=335–336 |doi=10.1017/S0009840X00186433 |s2cid=246880710 |issn=0009-840X|url-access=subscription }}

Go was considered one of the four essential arts of the cultured aristocratic Chinese scholars in antiquity and remains popular today. The earliest written reference to the game is generally recognized as the historical annal Zuo Zhuan{{cite book|last=Burton|first=Watson|title=The Tso Chuan|date=April 15, 1992|publisher=Columbia University Press |isbn=978-0-231-06715-7}}{{Cite web |last=Fairbairn |first=John |year=1995 |title=Go In Ancient China |url=https://www.pandanet.co.jp/English/essay/goancientchina.html |url-status=live |archive-url=https://web.archive.org/web/20230329075559/https://www.pandanet.co.jp/English/essay/goancientchina.html |archive-date=2023-03-29 |access-date=2007-11-02 |language=en}} (c. 4th century BC).{{cite web|title=Warring States Project Chronology #2|publisher=University of Massachusetts Amherst|url=http://www.umass.edu/wsp/project/introductions/chronology2.html|access-date=2007-11-30|url-status=dead|archive-url=https://web.archive.org/web/20071219225436/http://www.umass.edu/wsp/project/introductions/chronology2.html|archive-date=2007-12-19}}

The family of games known today as Mancala dates back to at least the third century in the Middle East, and possibly much earlier.{{cite journal |last1=Natsoulas |title=The Game of Mancala with Reference to Commonalities among the Peoples of Ethiopia and in Comparison to Other African Peoples: Rules and Strategies |journal=Northeast African Studies |date=1995 |volume=2 |issue=2 |pages=7–24 |doi=10.1353/nas.1995.0018 |jstor=41931202 |url=https://www.jstor.org/stable/41931202 |access-date=3 May 2023|url-access=subscription }}

Chess is believed to have originated in northwest India, in the Gupta Empire ({{circa}} 280–550),Leibs (2004), p. 92Robinson & Estes (1996), p. 34Murray (1913)Bird (1893), p. 63 where its early form in the 6th century was known as chaturaṅga ({{Langx|sa|चतुरङ्ग}}), literally four divisions [of the military] – infantry, cavalry, elephants, and chariotry, represented by the pieces that would evolve into the modern pawn, knight, bishop, and rook, respectively. Chaturanga was played on an 8×8 uncheckered board, called ashtāpada.{{cite web|date=2005-07-25|title=Ashtapada|url=http://history.chess.free.fr/ashtapada.htm|access-date=2013-07-16|publisher=Jean-Louis Cazaux}} Shogi was the earliest chess variant to allow captured pieces to be returned to the board by the capturing player.{{cite web |last=Bodlaender |first=Hans L. |last2=Duniho |first2=Fergus |date=1996-09-09 |title=Shogi: Japanese Chess |url=https://www.chessvariants.com/shogi.html |url-status=live |archive-url=https://web.archive.org/web/20190324160420/https://www.chessvariants.com/shogi.html |archive-date=2019-03-24 |access-date=2012-03-08 |work=The Chess Variant Pages |language=en}} This drop rule is speculated to have been invented in the 15th century and possibly connected to the practice of 15th century mercenaries switching loyalties when captured instead of being killed.{{cite magazine | date=1980 | title=Shogi history & the variants | magazine=Shogi | issue=27 | pages=9–13 | editor1-last=Hodges | editor1-first=George }}

As civilization advanced and societies evolved, so too did strategy board games. New inventions such as printing technology in the 15th century allowed for mass production of game sets, making them more accessible to people from various social classes. Games like backgammon and mancala became popular during this time, showcasing different styles of strategic gameplay.{{Cite web |last=Richardson |first=Teresa |date=2023-08-21 |title=History of Strategy Board Games |url=https://www.thegamersguides.com/history-of-strategy-board-games/ |access-date=2024-05-25 |website=The Gamers Guides |language=en-US}}

Englishmen Lewis WatermanNote: He was not the Lewis Waterman who patented the Waterman fountain pen in 1884. {{citation needed|date=March 2016}} and John W. Mollett both claim to have invented the game of Reversi in 1883, each denouncing the other as a fraud. The game gained considerable popularity in England at the end of the nineteenth century.{{cite web|url = http://www.beppi.it/public/OthelloMuseum/pages/history.php|title = Brief history of Othello|publisher = Beppi.it|access-date = 4 January 2015|website = Othello Museum|archive-date = 16 May 2009|archive-url = https://web.archive.org/web/20090516010447/http://www.beppi.it/public/OthelloMuseum/pages/history.php|url-status = dead}} The game's first reliable mention is on 21 August 1886 edition of The Saturday Review.{{Citation needed|date=January 2024}} A variant named Othello, patented in Japan in 1971, has gained worldwide popularity.{{Cite magazine |date=11 November 1976 |title=Modern Living: Japanese Othello |url=http://content.time.com/time/magazine/article/0,9171,914702,00.html |magazine=Time |access-date=28 May 2016}}

After the end of World War 2, these games became more complex. Risk (game) and Diplomacy (game) were released in the 1950s. Risk saw the player try to conquer the world from other players after claiming land at the start of the game, while Diplomacy saw the player go back to Europe during the time just before The Great War, to build alliances with other players, as to secure his safety and victory.

Analysis of "pure" abstract strategy games is the subject of combinatorial game theory. Abstract strategy games with hidden information, bluffing, or simultaneous move elements are better served by Von Neumann–Morgenstern game theory, while those with a component of luck may require probability theory incorporated into either of the above.

As for the qualitative aspects, ranking abstract strategy games according to their interest, complexity, or strategy levels is a daunting task and subject to extreme subjectivity. In terms of measuring how finite a mathematical field each of the three top contenders represents, it is estimated that checkers has a game-tree complexity of 10⁴⁰ possible games, whereas chess has approximately 10¹²³. As for Go, the possible legal game positions range in the magnitude of 10¹⁷⁰.

The Mind Sports Olympiad first held the Abstract Games World Championship in 2008 to try to find the best abstract strategy games all-rounder. The MSO event saw a change in format in 2011{{cite web|url=http://www.boardability.com/article.php?id=10|archive-url=https://web.archive.org/web/20120722015047/http://www.boardability.com/article.php?id=10|archive-date=July 22, 2012|url-status=dead|title=MSO XV Pentamind|date=August 28, 2011|publisher=Mind Sports Olympiad}} restricting the competition to players' five best events, and was renamed the Modern Abstract Games World Championship.

• 2008: {{flagicon|England}} David M. Pearce (England)
• 2009: {{flagicon|England}} David M. Pearce (England)
• 2010: {{flagicon|England}} David M. Pearce (England)
• 2011: {{flagicon|England}} David M. Pearce (England)
• 2012: {{flagicon|Estonia}} Andres Kuusk (Estonia)
• 2013: {{flagicon|Estonia}} Andres Kuusk (Estonia)

• Connection games
• Game complexity
• List of abstract strategy games
• List of world championships in mind sports
• Mind Sports Olympiad
• World Mind Sports Games

{{reflist}}

• [http://www.cs.ualberta.ca/~games The University of Alberta Games Group]
• [http://www.ics.uci.edu/~eppstein/cgt David Eppstein's CGT page]
• [https://www.youtube.com/watch?app=desktop&v=X1kYiBuvEy8 Talk "Redefining the abstract", by Cesco Reale at Board Games Studies 2022]

{{Tabletop games by type}}

{{DEFAULTSORT:Abstract Strategy Game}}

Category:Games of mental skill