Abstract strategy game

An abstract strategy game is a board game with perfect information, no chance, and (usually) two players or teams. Many of the world's classic board games, including checkers, chess, go, irensei, and mancala, fit into this category. Play is sometimes said to resemble a series of puzzles the players pose to each other.

What counts as an abstract strategy game?

A purist's definition of an abstract strategy game requires that it cannot have random elements or hidden information. In practice, however, many games are commonly classed as abstract strategy games which do not strictly meet these criteria. Games such as Backgammon, Octiles, Can't Stop, Sequence and Mentalis have all been described as "abstract strategy" at some point or another, despite having a luck or bluffing element. A smaller category of non-perfect abstract strategy games manage to incorporate hidden information without using any random elements. The best known example here is Stratego. The pragmatic definition seems to be that if a game is strategic and is abstract (as opposed to being a simulation), the term "abstract strategy" should be applicable—this definition is unappealing to purists because the broader class of games falls clearly outside the scope of the techniques of theoretical analysis appropriate to “pure” abstract strategy games.

The analysis of a “pure” abstract strategy game tends to fall under 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.

In some abstract strategy games there are multiple starting positions of which it is suggested that one be randomly determined: at the very least, in all conventional abstract strategy games a starting player needs to be chosen by some means extrinsic to the game. Some games, such as Arimaa and DVONN, have the players build the starting position in a separate initial phase which itself conforms strictly to abstract strategy game principles. However, most people would consider that although one is then starting each game from a different position, the game itself still has no luck element. Indeed, Bobby Fischer promoted randomizing the starting position of a game of chess in order to increase the game's dependence on thinking at the board, which is surely the chief object of an abstract strategy design.

Comparison of Abstract Strategy Games

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, except to say that Tic-Tac-Toe is likely at the bottom of the list. 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^[1], whereas chess has in the vicinity of 10¹²³^[2]. This explains largely why computer programs, through "brute force" calculation alone, are now besting human players. As for Go, the possible legal game positions range in the magnitude of 10³⁶⁰^[3], partly the reason why, to this day, computer programs can only play below "Dan" level.

Go players and Chess players alike agree that Chess is a more tactical game as opposed to Go, which is a more strategic game. Emmanuel Lasker, one of the most important game theoreticians, world chess champion from 1894 to 1921 and inventor of the game Lasca, once said that "If there are sentient beings on other planets, then they play Go". His cousin, Edward Lasker clarified this thought later in a book he wrote about Go called The Game of Go:

"While the Baroque rules of chess could only have been created by humans, the rules of go are so elegant, organic, and rigorously logical that if intelligent life forms exist elsewhere in the universe, they almost certainly play go."^[4]...

List of abstract strategy games

Chess and chess-like games

Chaturanga (Indian Chess)
Chess (Western Chess)
Janggi (Korean Chess)
Makruk (Thai Chess)
Shogi (Japanese Chess)
- Shogi variants
Xiangqi (Chinese Chess)
Other Chess-like games

Paper and pencil games

Dots and Boxes
Sprouts
Tic-tac-toe, also known as Noughts and Crosses.

"n-in-a-row" games

Those marked † can conveniently be played as paper and pencil games.

Boku
Check Lines
Connect Four †
Connect6 †
Gomoku †
Hijara †
Mojo!
Morabaraba
Morris - Three, Six and Nine Men's Morris
Neutreeko
Rhumb Line †
Pente, a slight simplification of Ninuki-renju
Score Four
Qubic
Renju †
Teeko
Tic Tac Toe †
Sequence and its variations

Other games