Various historical abstract strategy games on display in Spanish Renaissance fair
Abstract strategy games are games like Chess, Draughts and Go. They are typically strategy games with minimal or no narrative theme, an outcome determined mostly by player choice (with minimal or no randomness), and in which there is little to no hidden information. Many abstracts are also perfect information games.[1][2] Pure abstract strategy games are typically deterministic, fully observable, and governed by simple, explicit rules whose strategic depth arises from combinatorial complexity rather than chance. Abstract strategy games are also games of analytical skill, which grows over time as players develop experience and a greater understanding of the game. Experienced players with greater ability to analyze multiple moves in advance will almost always beat beginners.
There are numerous types of abstract strategy games, from pure strategy to mixed strategy games that may have elements of random or hidden information. Go, Pente and checkers are "pure" abstract perfect information games since they perfectly fulfill all three criteria; Chess games, Tafl games and Hive feature recognizable themes (though they are highly stylized or minimalistic); Stratego is a borderline or exception case, since it is deterministic, loosely based on Napoleonic warfare, and features some concealed information. Furthermore, some games with elements of chance, like backgammon and pachisi, may also be considered abstract strategy games, though there is disagreement on this issue among ludologists. However, since they contain an element of luck and randomness, they are not "pure" abstract strategy games.
Several traditional abstract strategy games like Chess and Go have a long history and are culturally significant products that have been played for generations in various regions of the world. Beyond entertainment, abstract strategy games have served as educational tools to teach logic, patience and foresight. They have also served as status symbols for the intelligentsia and elite classes, and as competitive mind sports. For example, during the Cold War, Chess matches were seen as intellectual battles between East and West.
The term abstract refers to a game’s formal detachment from representational content and theme, not difficulty or artistic style. While pieces may have conventional names (e.g., “king,” “stone,” “pawn”), these labels do not imply a simulation of historical, physical, or fictional realities, and in cases that the piece design resembles a theme, it is purely for aesthetic reasons, remaining unimportant to the game play.[3] A related element of an abstract game is simplicity. Most abstract games have a simpler rules and mechanics in comparison to more complicated games like war games and other simulation games. Similarly, even if an abstract game has a theme, it is often simple and minimalistic, and has no necessary logical connection to the game mechanics (unlike most modern Eurogames). Thus, an abstract game's play is instead centered on spatial and geometric relations, move rules, and logical consequences within a closed system.
The term strategy meanwhile indicates that game outcomes depend primarily on players’ decisions over extended sequences of choices and moves, rather than on reflexes, dexterity, bluffing, guessing, collecting, negotiation, or probabilistic events. Another element of abstract strategy games is that the game elements are all self-contained in the game pieces, parts and rules. Playing the game does not rely on anything external to the game, like physical skill and dexterity, knowledge of language (word games), or any other kind of specific knowledge (trivia games).
The formal definition of an "abstract strategy" game is often debated, but several key elements are shared by most games in this family:[4][3]
Close to perfect Information: Little to nothing is hidden from all players, and all players can see the entire state of the board, pieces and all other game elements at all times.
Little to no randomness: There are usually no dice rolls, shuffled decks, or random events. The "input randomness" is close to zero, and the game's complexity arises from the players' moves and position.
Minimal theme and narrative: While some games have minimal "themes" (e.g., Chess represents a stylized medieval court or battle), the mechanics do not rely on this or on any narrative element. The game would function identically if the pieces were replaced with simple geometric shapes.
Discrete turn structure: Game play proceeds in alternating turns, with clearly defined legal moves.
Many abstract strategy games that closely follow the above principles also happen to be pure strategy games also known as "combinatorial" games in which there is no hidden information, and no random elements, no simultaneous or hidden movement or setup. Many of these are also two player games where two players or teams take a finite number of alternating turns until a win condition is met. According to Combinatorial Game Theory (2013) by Aaron Siegel, "combinatorial" games have no randomness, no any hidden information, or any simultaneous moves.[5] Winning at these "pure" abstract strategy games relies on pure skill in logic, spatial thinking, and calculation.
Nevertheless, some abstract games like Azuldo have elements of chance, and these may still classified as abstract strategy games.[4][5] However, these games are not "pure" strategy, but "mixed" strategy games. This issue is debated among game designers and ludologists, depending on how strict their definition of "abstract strategy" is, and whether it must be purely combinatorial. Thus, the term abstract strategy game can refer to a superset of pure strategy games which also includes games that do not perfectly fit the definition of combinatorial games but are still very close.[5] Thus, according to Cesco Reale, this broader definition of abstract strategy includes mixed abstract strategy games like "Backgammon (which has chance), Chinese Checkers with more than 2 players (which has possible alliances), 55stones (which has simultaneous moves), or Stratego (which has hidden information).[5]
According to J. Mark Thompson, abstract play is sometimes said to resemble a series of puzzles the players pose to each other:[6][7]
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 games which are abstract in nature historically might have developed from thematic games, such as representation of military tactics.[8] 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. Nevertheless, the theme is aesthetic, and does not affect the actual game play.
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.[9]
Typology
At the core of abstract game typology are pure strategy games like Chess and Go, where a player or computer can, in theory, analyze a "tree" of all possible moves to find an optimal play. These games are deterministic, meaning they have no hidden elements or luck. Within this category, scholars further distinguish between "impartial" games (where available moves depend only on the state of the board, like Nim) and "partisan" games (where players have different pieces or move sets, like Chess).[5] If one includes other types of games, the category of abstract strategy may then expands into a broader class of games that are less than pure strategy. This category encompasses games with hidden information, elements of luck (Backgammon), or simultaneous moves.[5]
Another critical dimension is finiteness and information. Games can be finite, cyclic (allowing for repetitions like "ko" in Go), or transfinite. Transfinite games involve infinite states, such as "Continuous Go" played on a coordinate-free plane or "Tamsk," which uses time-based movement. Furthermore, one can distinguish between "perfect information" (fully knowing the board state) and "complete information" (knowing the opponents' goals and preferences). Incomplete information arises when a player’s motivations or "utility functions" are unknown to others.[5]
Number of players is yet another element. Most games are two players, but there are also numerous games for three, four or more players. These multiplayer abstracts also open up the possibility of the "kingmaker" effect, which happens when one losing player makes a choice that improves the chances of the eventual winner.
Thus the following basic game typology emerges:[5]
Game Category
Key Characteristics
Examples
Pureabstract strategy (Combinatorial)
Deterministic, no hidden info, sequential moves. Typically 2 players.
Apart from the basic binary distinction between combinatorial or "pure abstracts" and those which contain some element of chance or hidden information, there are other ways to classify abstract games. One common approach distinguishes games according to their primary objective. Abstract strategy games can be categorized by their primary objective or mechanical "win condition" which include:[5][4]
Category
Description
Examples
Territory Control
Players compete to occupy or surround the most space on the board.
While some abstracts like chess and checkers begin with a determined starting position, others like Go and Hive begin with an empty board or field, which is filled placing the game pieces or tiles one by one in each turn. 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.[10]
Pieces and boards
Hive is played with different hexagonal tiles and no board
In some abstract games, pieces do not move once placed, while in others they may move according to specific rules. Another important axis of classification concerns the nature of game pieces. In some games, pieces possess fixed identities and differentiated movement rules, producing a hierarchy of roles and values. In others, all pieces are functionally identical, and strategic complexity arises entirely from spatial relations and accumulation rather than from intrinsic piece power. This distinction has significant implications for how players conceptualize material advantage, exchange, and sacrifice.
The rules governing the interaction of the pieces is also another key element differentiating abstract games. For example, capture based games can be based on various means of capture, such as displacement capture (e.g. chess), jumping over a piece (checkers), and surrounding a piece (tafl).
Board structure and design provides a further basis for typology. Many abstract strategy games are played on regular grids that constrain movement orthogonally or diagonally, while others rely on graph-based boards in which movement follows predefined connections between nodes. Grid based boards vary in the basic geometric shape used, with squares (chess), and hexagons (Hex) being the most common. While most are two dimensional, some are 3D, like those in the various types of Three-dimensional chess. In many grid based boards, all grids are the same, but in certain games, certain spaces might have unique features or properties that affect play (Xiangqi). In certain games like Trax and Hive, the effective structure of the "board" emerges through play itself, as the accumulation of pieces transforms the strategic landscape over time.
Symmetry is yet another element. While many abstract games begin from perfectly symmetrical positions, others like tafl games introduce asymmetry in roles, objectives, or initial placement. Such asymmetry often serves to balance first-move advantage or to explore strategic dynamics unavailable in symmetric systems.
The earliest known board games were abstract. Senet (c. 3100 BCE) from Ancient Egypt and the Royal Game of Ur (c. 2600 BCE) contained elements of luck but they paved the way for pure strategy. A board resembling a Draughts board was found in Ur dating from 3000 BC, found by British archaeologist Sir Leonard Woolley in the 1920s.[11][12] 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.[13][14]Plato mentioned a game, πεττεία or Petteia[el], as being of Egyptian origin,[14] and Homer also mentions it.[14] A similar type of strategy game was played in the Roman Empire under the name ludus latrunculorum.[15]
Go (Ch: Weiqi), originating in China over 2,500 years ago, remains the oldest abstract game still played in its original form. It 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[16][17] (c. 4th century BC).[18]
The family of games known today as Mancala dates back to at least the third century in the Middle East, and possibly much earlier. Mancala variants spread across Africa, the Middle East, and Asia during the medieval period.[19]
Chess is believed to have originated in northwest India, in the Gupta Empire (c. 280–550),[20][21][22][23] where its early form in the 6th century was known as chaturaṅga (Sanskrit: 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.[24]
Modern chess developed from the Middle Eastern Shatranj, a medieval descendant of the Indian game. Numerous different regional versions of this game developed, like Xiangqi, Makruk and Sittuyin. The Japanese Shogi was the earliest chess type game to allow captured pieces to be returned to the board by the capturing player.[25] 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.[26]
Other popular medieval abstract strategy games include the "Tafl" family of games (like Hnefatafl or "Viking chess"), popular in Northern Europe, which featured asymmetrical gameplay.
Modern developments
The end of a game of Hex on a standard 11×11 board. Here, White wins the game by connecting the left and right sides of the board.
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.[11]
Englishmen Lewis Waterman[27] 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.[28] The game's first reliable mention is on 21 August 1886 edition of The Saturday Review.[citation needed] A variant named Othello, patented in Japan in 1971, has gained worldwide popularity.[29]
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.
The late 20th and early 21st centuries saw the rise of "designer abstracts" like Hex (Piet Hein, John Nash) and Havannah. Modern abstract games often use innovative materials (like Bakelite or 3D-printed plastic) and focus on elegant, minimalist rule sets that produce deep complexity.
The modern era also saw the rise in the use of computers to analyze abstract games and to play them (with other humans over the internet, or against bots of various strengths).
Cultural and competitive contexts
Abstract strategy games have historically been embedded within broader cultural, educational, and philosophical frameworks. In East Asia, games such as go and shogi were traditionally associated with moral cultivation, disciplined thinking, and elite education. In Europe, chess became a central symbol of rationality, and intellectual refinement. Across cultures, abstract games have served as vehicles for social interaction, competition, and the transmission of strategic knowledge.
Modern competitive play has further institutionalized abstract strategy games through ranking systems, organized tournaments, and extensive bodies of literature. Formalized competition has also encouraged the development of standardized rule sets and notational systems, facilitating the preservation and study of exemplary games by elite players, some of whom have become celebrities.
Study and theory
Analysis of "pure" abstract strategy games is the subject of combinatorial game theory. This branch of mathematics studies games with perfect information. It analyzes "game states" to determine if a position is a win, loss, or draw. The complexity of a game is often measured by its state-space complexity (total number of legal positions) and game-tree complexity (total number of possible paths the game can take).
Abstract strategy games with hidden information, bluffing, or simultaneous move elements are better served by Von Neumann–Morgensterngame 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.
Regarding practical gameplay considerations, a number of strategic concepts recur across many abstract games. The notion of tempo captures the value of forcing moves and strategic initiative. Some capture based abstracts emphasize gaining a material advantage over the opponent by eliminating their pieces and protecting yours. The balance between local tactics and global strategy is especially prominent in games with large boards, where players must decide when to concentrate forces and when to shift attention elsewhere (called tenuki in Go). Sacrifice, exchange, and positional compensation further illustrate how abstract games generate strategic meaning through relational rather than representational structures.
Abstract strategy games have long been used in AI research. Because the rules are rigid and the information is perfect, they provide an ideal environment for testing algorithms. Perhaps the most famous example is Deep Blue (1997), the first computer to beat a reigning World Chess Champion (Garry Kasparov) using brute-force calculation. AlphaGo (2016), developed by Google's DeepMind lab used neural networks and reinforcement learning to defeat world-class Go players. This was a key landmark because Go has more possible positions than there are atoms in the observable universe, making brute force next to impossible.
Design principles and aesthetics
The design and evaluation of new abstract strategy games often emphasize conceptual elegance and simplicity. Modern designers frequently aim to achieve maximal strategic depth with minimal rules, allowing complexity to emerge naturally from player interaction rather than from elaborate mechanics. Game balance is a central concern for modern game designers, particularly with respect to concepts like first-move advantage. Many abstract games incorporate compensatory mechanisms or refined rule adjustments to address this issue.
Another recurring consideration is the relationship between learnability and mastery. Successful abstract games tend to offer straightforward rules that can be understood quickly, while simultaneously supporting a deep and prolonged learning curve as well as extensive replay value. This combination has contributed to the longevity of classical abstract games, which remain strategically relevant centuries after their inception. The goal of many modern game designers is captured in the saying "easy to learn, lifetime to master", which is considered to be a feature of the great classics like Go and Chess.
Abstract games which have depth of play are suitable for elite tournament, often developing a body of theory and literature.
According to J. Mark Thompson, a good abstract must possess four key qualities: depth, clarity, drama, and decisiveness.[3] Depth refers to the capacity of a game to support many distinct levels of skill, such that optimal play remains uncertain in most positions and improvement remains possible over long periods. A deep game resists complete calculation and instead demands refined judgment, allowing measurable stratification among players of different strengths. Clarity, by contrast, concerns intelligibility. In games that are clear, players should generally be able to recognize strong moves, especially decisive ones, and develop reliable heuristics even without exhaustive study. A game that lacks such intelligibility becomes opaque, leaving players without strategic intuition. The challenge for designers lies in ensuring that complexity does not collapse into inscrutability, particularly in newly invented games where it may be difficult to distinguish temporary obscurity from permanent unintelligibility.[3]
Drama requires that a player in an inferior position retain meaningful chances to recover, sustaining suspense and engagement across the whole game rather than allowing early mistakes to render later play pointless. Decisiveness, however, demands that sustained superiority can ultimately be converted into an unavoidable win, rather than being indefinitely neutralized by defensive tactics. Games that fail in this respect risk degenerating into endless draws or futile struggles. Thompson writes that these four qualities exist in tension. Increasing clarity can undermine depth, excessive comeback potential can erode decisiveness, and easily secured wins can drain drama. Only a small number of exceptional games manage to attain a balance between these opposing demands. Such games reward play and serve as profound vehicles for expressing human character and intellect, meriting recognition alongside other liberal arts.[3]
Abstract Games World Championship
The Mind Sports Olympiad first held the Abstract Games World Championship in 2008 to try to find the best abstract strategy games all-rounder.[9] The MSO event saw a change in format in 2011[30] restricting the competition to players' five best events, and was renamed the Modern Abstract Games World Championship.
↑Bodlaender, Hans L.; Duniho, Fergus (1996-09-09). "Shogi: Japanese Chess". The Chess Variant Pages. Archived from the original on 2019-03-24. Retrieved 2012-03-08.
↑Hodges, George, ed. (1980). "Shogi history & the variants". Shogi. No.27. pp.9–13.
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