The Red Hat is a light armor headgear in Final Fantasy IX. It is mid tier hat that everyone but Steiner and Freya can wear. It teaches the passive abilities Cover, which allows Amarant to protect allies from enemies' attacks, and MP Attack, which allows Zidane and Amarant to expend MP to do more damage with Attack. The Red Hat empowers the wearer's Fire damage.
The Red Hat can be bought for 3,000 gil from Esto Gaza after the storyline events in Desert Palace. It is soon after this found in Mount Gulug; from the entrance , the player needs to head left and then down the ladder to a dead end ledge where the Red Hat lies in the corner. After the party has a flying transport, they can also buy the hat in Ipsen's Castle.
The Red Hat provides a measly 1 Defense but 26 Magic Defense, mainly mitigating damage from magic attacks. It boosts the wearer's Fire damage by 50%, being compatible with Vivi's Fire, Fira, Firaga, and normal attack with Flame Staff, as well as Dagger's Ifrit and Eiko's Phoenix.
The Red Hat is mid game gear that is useful for its abilities as well as its Elem-Atk property; the former are good for Zidane and Amarant, whereas the latter trait is useful for the party's mages. The only character who does not benefit anything unique from the hat is Quina, who cannot learn Cover or MP Attack and learns no Fire abilities. Though many enemies in Mount Gulug take half damage from Fire, some enemies there are also weak to Fire, which would stack with the Elem-Atk from the Red Hat: Blue Wraith, Vepal, and the boss Meltigemini. However, Vivi will not partake in the boss battle and Dagger's commands frequently fail during this time.
Cover lets Amarant protect allies, which is a good ability for him as he specializes in counterattacks. MP Attack is good though it can quickly deplete a character's MP. Amarant can replenish his MP with Chakra, and Zidane mainly needs MP of he is using Soul Blade, and otherwise it is reserved for Trance. Zidane and Amarant have no Fire skills to make use of the hat's Elem-Atk; though some of Zidane's Dynes have fiery animations, they are non-elemental.
If the player does not need the abilities from the hat nor is using Fire skills, then they can pass on the Red Hat and wear the Black Hood instead, sold at the same time as the Red Hat in Esto Gaza, which halves damage from numerous elements, or keep using the Mantra Band/Green Beret for their stat boosts.