In general real-life terms, an "illusionist" usually refers to sleight-of-hand masters who use their skills to illude audiences and bewilder skeptics. However, when using the term in BZPB, it refers to a mage who strictly specializes in controlling the senses of others to confuse them and gain an edge in battle.
Against an illusionist of high skill, even the most powerful of wills and the keenest of minds will not win the day - A master illusionist easily surpasses the astutia of his opponents, poking and prying in a strategic manner to discover how to break their defenses. Also, there are a wide variety of different illusions - Ranging from the genjutsu used by shinobi to powerful magic used by sorcerors.
Lastly, an illusionist's power is most vividly seen when battling another illusionist. As two combatants limited only by their imagination engage each other in combat, the normal laws of fighting an illusionist are thrown out the window. Akin to a fantasy battling a fantasy, most times, two illusionists are only limited by their abilities to predict, react, and in some cases, how far they're able to bend the laws of perception.
A basic illusion is, ironically, anything but simple. It can range from blocking an opponent's sight to completely manipulating each of their senses at once. While general illusionists are only able to hamper opponents for a quick advantage in battle, the most skilled of illusionists using this technique can overload an opponent's senses with fear or other sensations to render them unconscious.
Trumping the laws of reality, a Real Illusion takes an illusory vision and turns it into a real effect. While something like a simple creature or image is easy enough, creating an effect like, say, a fireball is much more difficult. Additionally, it rapidly drains any user's energy to "realize" truly stupendous effects for more than an instant at any one time. Due to this, users of Real Illusions must always carefully monitor their energy so as to not abruptly run out of steam in the middle of a battle.
In battle with another illusionist, an illusionist is most vulnerable at one instant: When he's assumed that he's won before knowing for sure. With this split-second lapse of concentration, the other illusionist can perform the equivalent of breaking a hold before countering: Dissolving the illusion trapping them before proceeding to capture the foe in an illusion of their own making.
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The indigo Mist Flames, with their abilities of Construction, are perfectly-suited to use by illusionists - Especially in the generation of Real Illusions. However, these Flames are very poor for direct combat due to their low density, and it would be foolhardy to attempt to directly assail strong foes with these Flames.