Hate

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Good vs. Evil Hate
Angel Angels
Archangel Archangels
Devil Devils
Arch Devil Arch Devils
Genie Genies
Master Genie Master Genies
Efreet Efreeti
Efreet Sultan Efreet Sultans
Titan Titans Black Dragon Black Dragons
Effect: +50% Damage
Elemental Hate
Air Elemental Air Elementals
Storm Elemental Storm Elementals
Earth Elemental Earth Elementals
Magma Elemental Magma Elementals
Water Elemental Water Elementals
Ice Elemental Ice Elementals
Fire Elemental Fire Elementals
Energy Elemental Energy Elementals
Effect: +100% Damage

Hate is a special ability of creatures, which causes attacking unit to "burn with anger" and deal 50% more base damage (see damage calculation) to a creature type it hates.

Typically hatred is a symmetric relation that involve both basic and upgraded versions of creatures. For example, Angels and Archangels hate both Devils and Arch Devils and vice versa. However, Giants and Red dragons do not hate each other nor do they hate their upgraded versions Titans and Black Dragons. Additionally, Titans and Black Dragons hate each other.

Hate doesn't affect morale if creatures hating each other are in the same army (Devils/Archdevils will even get +1 morale if they are alongside Angels/Archangels - while there won't be morale bonus for all troops from the same town), and doesn't prevent units from spreading their magic abilities on hated allies (i.e Archangels may resurrect Devils and Archdevils, and Master Genies may cast spells on any type of Efreeti, aside from those ones to which Efreeti are immune). More precisely, hate is just a simple damage modifier applied before the attack, and nothing more.