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Terrain (地形) is a staple game mechanic of the Fire Emblem series. Terrain is basically the different types of spaces that a character can have their units stand on.
Different aspects of Terrain have different effects, some give attacking and defending bonuses to the unit standing on the space while others impair unit movement, and some pieces of Terrain are completely impassable.
Most pieces of Terrain occupy a single space on a map, although sometimes a large formation (like a mountain) will cover several spaces, each space being individually classified as a mountain (or in some games 'peak').
Plain: The most common terrain, included in all games. A Plain provides zero bonuses to both Avoid and Defense and does not affect movement.
Forest: A common form of Terrain found in Fire Emblem maps that are outside, the Forest provides a +1 bonus to Defense and +20 bonus to Avoid, allowing the unit under cover to take less damage and also help with the ability to avoid enemy attacks. It is noteworthy that entering or passing through a Forest requires two remaining move tiles, meaning the Terrain also reduces movement.
Floor: The indoor counterpart of the Plain terrain, but is found indoors instead of outdoors.
Pillar: The indoor counterpart of the Forest terrain, the Pillar terrain has the same bonuses and restrictions, but is found indoors instead of outdoors.
Mountain: Another outdoor Terrain version, the mountain is restricted only to units that are not mounted (with the exception of pegasi and wyvern riders), but gives a greater bonus than the Forest, providing +2 Defence and +30 to Avoid. In the later 3-D Fire Emblem games, spaces with the Terrain type 'Mountain' were impassible by all except Bersekers (and pegasi/wyvern riders).
Peak: Another outdoor Terrain version, the Peak provides a +2 to Defense and +40 to Avoid, its con being its restriction to the Brigand class. It is commonly placed among mountains.
Gate/Throne: Terrain that appears in most games, the Gate and Throne provide the same bonuses as the peak, +2 to Defense and +40 to Avoid, the same as the Peak, but its bonuses are available to all classes except the Pegasus and Wyvern riders, which do not gain the bonuses from Terrain. It also gives you a Health boost like a Fort.
Sea: One of the lesser used terrains, it can only be used by Pirates, Berserkers and flying units. It only gives +10 to Avoid.
Desert: More of a hindrance than a help, the Desert terrain requires the sacrifice of 2 move tiles to go through one tile of desert terrain (although this doesn't affect magic units or flying units), and for mounted units it lowers their move down to 1 or 2 tiles. It still provides a +5 bonus to Avoid, however.