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An abstract strategy game is a board or card 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[by whom?] to resemble a series of puzzles the players pose to each other.
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A purist's[who?] definition of an abstract strategy game requires that it cannot have random elements or hidden information. In practice, however, many games which do not strictly meet these criteria are commonly classed as abstract strategy games. Games such as Backgammon, Octiles, Can't Stop, Sequence and Mentalis have all been described[who?] 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.[who?][original research?]
The analysis of a “pure” abstract strategy game tends to fall under combinatorial game theory.[original research?] 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.[original research?]
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.[citation needed]
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 in the vicinity of 10123. This explains largely why computer programs, through "brute force" calculation alone, are now besting human players.[original research?] As for Go, the possible legal game positions range in the magnitude of 10360, partly the reason why, to this day, computer programs can only play below "Dan" level.[original research?] Go players and Chess players alike agree that Chess is a more tactical game as opposed to Go, which is a more strategic game.[citation needed]