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A hero's mana is equal to the level of the hero at 0:00 UTC each day. (For example, a hero leveled at 2:00 am from level 2-3 will have 2 mana until 0:00 UTC where it will increase to 3 mana and remain at that amount of mana until the hero is leveled again.)
Mana is the number of times a hero can be entered into a dungeon, either as a single hero or part of a Hero Team to take on a Medium or Large Dungeon. (For example, a hero with 3 Mana could enter a Small Dungeon 3 Times or join a party and attempt to take down a Medium or Large Dungeon 3 Times, or any combination of the above.)
In short, each and every time a hero enters a dungeon their available mana is reduced by 1.
Once the Hero's mana is reduced to 0 they become exhausted and must wait until 0:00 UTC where their mana will be fully recovered and ready to join the next dungeon Adventure.