Promotions

§ It's well known that in war battle-tested veterans are more successful than green troops. They are better at staying alive, and better at seeing that the enemy doesn't stay alive. In Civilization IV, experienced troops earn "promotions" which give them special bonuses on offense, defense, healing, movement, and other martial-related skills.
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Experience Points

§ Units gain promotions by acquiring "experience points" (or XPs) representing their training and practical battlefield experience. Only land and naval units get experience points; air units do not.
§ Training Experience Points
§ Training XPs come from several sources. A land unit built in a city with a Barracks automatically receives 4 XPs. Drydocks do the same for naval units. Various other Buildings and Wonders provide training XPs too. The civic Vassalage gives all new units 2 XPs, and the Theocracy civic also grants 2 XPs for units built in cities with your state religion. Finally, certain civilization Leader Traits give bonuses also.
§ Combat Experience Points
§ Units gain combat experience points by destroying an enemy unit in battle. It doesn't matter if the unit attacked or defended; as long as its enemy is destroyed, it gets an XP. Units DO NOT gain XPs for Bombarding fortifications, nor do they get them if the enemy unit Withdraws from combat (or if they themselves withdraw!).
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Getting Promotions

§ Promotions occur on a sliding scale of experience points. A unit gets its first promotion upon achieving 2 XPs. The second promotion requires 3 additional XPs (for a total of 5), the third 4 more XP (10 total), etc.
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Promotion Choice

§ Not all promotions are available to all units, and some promotions require that a unit have already gotten a specific previous promotion. When the unit is due for a promotion, the available promotions are displayed in the unit's "action box."
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Promotions List

§ Look at the Promotions List page to see all the promotions available in the game. Click on a promotion to discover which units can get it, its requirements, and its effects.