Strategy game
A strategy game is a game (e.g. computer, video or board game) in which the players' decision-making skills have a high significance in determining the outcome. Many games include this element to a greater or lesser degree, making demarcation difficult. It is therefore more accurate to describe a particular game as having a certain degree of strategic elements, as in being mainly based around strategic principles.
The crucial factor that separates this type of game from all others is that there is relatively little chance involved. All players have equal degree of knowledge of the elements of the game. There is no physical skill required other than that necessary to interact with the game pieces.
Its benefit is the open interaction with other people. The game partners have similar starting points and evaluate how other humans may react under same conditions. So game strategies evolve with more or less spirit involved to get advantages and/or protect artfully.
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Strategy (and tactics) are usually contrasted with luck, the outcome of luck-based games relying on probability. Games exist on a continuum from pure skill to pure chance, with strategic games usually towards the skill end of the spectrum. The word "strategy" is borrowed from a military jargon. It originally refers to a planning at a very high level and often strategy games deal rather planning in smaller scale for which a word "tactics" is used in military context.
Types
Abstract strategy
In abstract strategy games, the game is only loosely tied to a real-world theme, if at all. The mechanics do not attempt to simulate reality, but rather serve the internal logic of the game. To win, the player must think about the problem, rather than the graphical representation of the situation. Chess, Checkers and Go are excellent examples.
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.
Simulation
This type of game is an attempt to capture the decisions and processes inherent to some real-world situation. Most of the mechanics are chosen to reflect what the real-world consequences would be of each player action and decision. Abstract games cannot be cleanly divided from simulations and so games can be thought of as existing on a continuum of almost pure abstraction (like Abalone) to almost pure simulation (like Strat-o-Matic Baseball).
Wargame
Wargames are simulations of historical or hypothetical military battles, campaigns or entire wars. Players will have to consider situations that are analogous to the situations faced by leaders of historical battles. As such, war games are usually heavy on simulation elements, and while they are all 'strategy games', they can also be 'strategic' or 'tactical' in the military jargon sense.
Traditionally, wargames have been played either with miniatures, using physical models of detailed terrain and miniature representations of people and equipment to depict the game state; or on a board, which commonly uses cardboard counters on a hex map.
Popular miniature wargames include Warhammer 40,000 or its fantasy counterpart Warhammer Fantasy. A popular strategic board wargame would be Axis and Allies, and Diplomacy has been a successful one for decades. Advanced Squad Leader is a successful tactical scale wargame. A successful translation of the traditional genre into a computer game would be SSI's Panzer General series.
Strategy video games
Strategy games instantiated on computers generally take one of four archetypal forms, depending on whether the game is turn-based or real-time and whether the game's focus is upon military strategy or tactics.