Cloud Strife: I couldn't finish 'em. Looks like this's gonna get complicated.
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There is one piece of Lufenian equipment for each of the weapon and armor types, allowing every character to equip a full set. Each piece has the same stats as the other "ultimate" weapon in that type (e.g. the Lufenia's Edge greatsword has the same stats as the Ragnarok), but has a combination attached to it rather than any other special effects.
In Dissidia, Lufenian equipment pieces come with the combination "Wisdom of Lufenia". Activating when three pieces are equipped at once, the combination grants +15% EX Gauge Depletion, causing the user to deplete a significant portion of the opponent's EX Gauge when they land an HP attack. In Dissidia 012, there are two Lufenian abilities: Seal of Lufenia, and Judgment of Lufenia. Seal of Lufenia grants +5% EX Gauge Depletion, while Judgment of Lufenia grants +15% Assist Gauge Depletion.
Pieces of the Lufenian equipment can be won from the Blackjack course of the Duel Colosseum in Dissidia. Red chests in various gateways in Confessions of the Creator in Dissidia 012 reward the player with a piece of Lufenian equipment, but only after they defeat a powerful enemy. In Dissidia the Lufenian equipment is level 99 or level 100, and it is level 100 in Dissidia 012.