By definition, 4X is the abbreviation of eXploration, eXpansion, eXploitation, and eXtermination, a term originally coined by Alan Emrich. In terms of use and practice, 4X is some what more complex and may have expanded from its original definition.

Traditionally 4X was first popularly used to identify strategy games such as Sid Meier's Civilization and Master of Orion, although 4X games by its characteristics may have existed far earlier than the aforementioned games.

A 4X game must fulfill ALL the following requirements:

Strategic gameplay - the player usually plays the role of a leader or adviser to a race, faction, country, civilization, nation, or any bunch of blokes in a large scale population against opposing forces. The game genre is usually limited to the strategy gameplay. No other genres have been identified under 4X.
eXploration - the purpose of exploring surrounding territories, which may signify the use of a map. Exploration is conducted by sending out units to unexplored regions, where newly discovered locations become and remain revealed, depending on the variations of an implemented fog of war effect.
eXpansion - the objective to expand territory or area of control, usually (optional) after eXploration campaigns have been successfully carried out. The strategy of eXpansion requires a balance between the player's ability to expand as well as the player's ability to defend and hold conquered or areas under the player's control. Existing or new areas/territories (towns, planets, etc.), may then be developed with structural buildings or other enhancements.
eXploitation - the objective to control resources, where resources may or may not be limited. The eXploitation category goes hand-in-hand with the eXpansion category: the more territory the player controls, the less the opponent does, thus the more resources the player has to his/her disposal.
eXtermination - the result of continuous expansion. Conflict is inevitable and when push comes to shove, extermination of the opponent is eminent. Extermination requires the total elimination of an opponent or to subdue the opponent under the player's direct or indirect control (i.e. vassal, puppet, etc.) via armed conflict or diplomatic devices.
Randomly generated environments - See the Games with randomly generated environments game group for further information.
Structural building - no 4X game has been identified to do without a structural building or similar devices. Anything from a latrine to a planetary doomsday weapon station may be used to further advance the player's purpose.
Technological advancement - traditionally, 4X games have identified the use of technology advancements (or popularly known as a technology tree). These advancements are usually identified with the requirement to use resources, time to research, upgrade an idea or object, or other steps/factors needed before a certain (new or upgraded) technological benefit, unit, building, or similar devices be available to the player.
Diplomacy - the concept of not being alone in this existence refers to other beings(s) that may have different goals or priorities than the player. Diplomacy is the bridge to those differences of 4X. Diplomacy is used to make allies or enemies, trade resources and information, or even as a channel for espionage. Most 4X games prefer complex uses of diplomacy rather than the standard friend or foe commonly found in non-4X strategy war games.

Limitations

For purposes of this game group, games where primary gameplay focuses only on eXtermination without any other possible victory conditions are excluded from this game group.

This means games such as Age of Empires, Command & Conquer, Heroes of Might and Magic, or WarCraft should not go here.

Additional note

Some hybrid games do not follow the traditional identification of 4X games, disabling one or more of its common features, yet may officially identify itself under the same genre. Whether or not these games should be included remain open for debate.

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