An abstract strategy game is a strategy game in which the theme is not important to the experience of playing. Many of the world's classic board games, including chess, Go, checkers and draughts, xiangqi (Chinese chess), shogi (Japanese chess), Reversi (marketed as "Othello"), nine men's morris, and most mancala variants, fit into this category. 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:
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 .
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.
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.
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 1031 possible positions, whereas chess has approximately 10123. This suggests that computer programs, through brute force calculation alone, should often be able to surpass human players' abilities. 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 restricting the competition to players' five best events, and was renamed to the Modern Abstract Games World Championship. It was again won by David Pearce.
- 2008: David M. Pearce (England)
- 2009: David M. Pearce (England)
- 2010: David M. Pearce (England)
- 2011: David M. Pearce (England)
- 2012: Andres Kuusk (Estonia)
- 2013: 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
- Thompson, J. Mark (July 2000). "Defining the Abstract". The Games Journal. Retrieved July 27, 2017.
- "Abstract strategy games and other genres out of scope of IAGO". International Abstract Games Organisation. Archived from the original on August 18, 2011.
- "List of abstract strategy games". BoardGameGeek. Retrieved July 27, 2017.
- "The IAGO Hall of Fame". International Abstract Games Organisation. Archived from the original on May 7, 2010.
- "Abstract Games". Mind Sports Olympiad. Archived from the original on March 25, 2012. Retrieved July 27, 2017.
- van Reem, Eric (May 31, 2001). "The birth of Fischer Random Chess". The Chess Variant Pages. Retrieved July 27, 2017.
- "MSO XV Pentamind". Mind Sports Olympiad. August 28, 2011. Archived from the original on July 22, 2012.