'''Basic Trope''': A character who is incredibly smart, [[InsufferableGenius irritatingly aware of it]], and driven to go beyond himself, which often leads to spectacular failures.
* '''Straight''': Princess Velvet is a bright, canny young woman with a knack for diplomacy and a [[AnIcePerson magical prodigy]]. Her greatest weakness by far is her {{Pride}}, as she tends to overestimate just what she's capable of...
* '''Exaggerated''':
** Princess Velvet is one of the brightest minds of TheGoodKingdom--as she's quick to inform anyone curious about her studies. Cunning and ambitious, she intends to solve all the great conflicts facing their land herself--including dealing with [[EvilOverlord Emperor Evulz]]. In fact, she's completely convinced that she has [[TheStrategist the skills necessary to engineer his defeat]]... but is unaware that she's setting up [[BreakTheHaughty her own wake-up call]].
** Princess Velvet creates a brand new field of science or/[[{{Magitek}} and magic]] from scratch. Said field of science [[GoneHorriblyRight does exactly as Princess Velvet wanted, but too well]], and brings upon countless bloodshed.
* '''Downplayed''': Velvet's very proud of her intelligence, but isn't particularly boastful about it; mostly she just has a way of [[SmugSmiler smiling]] as she lays out her plans and watches them succeed. When one of them doesn't work the way she intended, and she has to watch others scramble to recover on the fly, she becomes very, very quiet.
* '''Justified''': Velvet ''has'' to excel just to be allowed onto the same playing field as her (mostly male) peers; this also feeds her arrogance as she considers herself superior to the more misogynistic members of the lot, and her drive to push the limits and ''prove'' her superiority.
* '''Inverted''':
** Princess Velvet's plans, whether running on cleverness or [[CrazyEnoughToWork hopeful desperation]], are always inevitably foiled by [[TheBrute Clay, the left handed and comically]] ViolentGlaswegian, the boy [[TooDumbToFool so utterly ignorant he comes back around to efficiently clever]] (when [[AchievementsInIgnorance he is not outright bending reality and giving physics, chemistry, biology, calculus, trigonometry, algebra, geometry, applied mathematics, pure mathematics, and basically every field of science known to man the biggest middle finger possible with his stupidity]])
** Princess Velvet is TooDumbToLive (whether or not she is [[MistakenForProfound mistaken for being clever]] is a different question).
* '''Subverted''':
** Velvet appeared to make a mistake, but she made a mistake intentionally to trap Evulz.
** Velvet really ''is'' just as good as she claims to be, and displays intelligence equal to what she believe she had.
* '''Double Subverted''': However, Evulz managed to turn her fake mistake into a real one.
* '''Parodied''': Velvet is essentially [[WesternAnimation/FoghornLeghorn Egghead Jr.]], but her plans tend to explode in her face a lot. Whenever they do, Velvet takes one look at her calculations and angrily [[CarryTheOne begins to erase and rewrite them.]]
* '''Zig Zagged''':
** Sure, Velvet's smart--smart enough to know her limits. But then Emperor Evulz makes it personal and provokes her into making a serious mistake... that turns out to have been a feint on her part, making it ''look'' like she was making a grave error in judgement. However, her success at turning the tables gives her quite the reputation, and while she claims not to care, she ''does'' start growing increasingly smugger and more self-assured...
** The cleverness of Velvet's schemes and what ruins them changes from episode to episode. Sometimes it's the little thing she overlooked that snowballs into mayhem, sometimes it's Bob being TooDumbToFool (even when she figured out he would be and [[StatingTheSimpleSolution simply not drag him into the mess]]), [[WhamEpisode sometimes]] it's Thelonious, her even more clever ArchEnemy, [[TheAnticipator figuring out every single one of her moves to the square root and inch.]]
* '''Averted''': All characters know the limits to their smarts.
* '''Enforced''': As a Princess ''doubling'' as TheSmartGuy, the writers decide Velvet needs some major character flaws to avoid Mary Sue-dom (maybe a ParodySue, at best); thus, her smug arrogance and massive failures that lead to her CharacterDevelopment.
* '''Lampshaded''': ???
* '''Invoked''':
** King Sable drives his daughter to excel simply to earn the right to ''continue'' her studies, as he fears that she'll make herself a target, yet is too wishy-washy to put his foot down so long as it's clear she really ''does'' benefit from it.
** Queen Satine encourages her daughter's superiority complex because she enjoys having an ''unparalleled genius'' as her child.
* '''Exploited''': King Sable sets up a scenario for Velvet to become overconfident and fall into his trap, so he may prove a point and do exposition on where she succeeds and fails.
* '''Defied''':
** King Sale and Queen Satine teach Velvet ''not'' to lord her intellect over others, as it's not good for a future ruler to alienate others.
** Velvet is the first to admit she is not all-knowing.
* '''Discussed''': ???
* '''Conversed''': ???
* '''Deconstructed''': Velvet's arrogance further isolates her from her peers, including those who would ''gladly'' befriend her given the chance, and makes her a target. After she fails spectacularly, her enemies use it to completely ruin her reputation. Velvet is also shaken by her failure, and [[OnceDoneNeverForgotten never manages to escape the specter of]] [[MyGreatestFailure her biggest mistake]].
* '''Reconstructed''': While she learns from her mistakes, the rejection of her peers keep Velvet from entirely shedding her arrogant demeanor; she retains it as a defensive mechanism, only [[DefrostingIceQueen gradually learning to let down her guard around her]] [[TrueCompanions most trusted friends]].
* '''Played For Drama''': Princess Velvet decides to prove her cleverness by engineering Emperor Evulz' downfall, and recruits the heroes as her agents, sending them on various covert missions. However, her pride and overconfidence lead to her severely underestimating the evil overlord, as he [[BatmanGambit feeds her more than enough rope to metaphorically hang herself]] before exposing her deeds--and [[FalseFlagOperation framing her for a tragedy in his own lands]], giving him ample excuse to attack her kingdom.
* '''Played For Horror''':
** Velvet's failures lead to her undergoing SanitySlippage.
** The atrocities Evulz performs to rub in Velvet's face that she is not all-knowing, invincible, and definitely unable to predict him are single-handedly responsible for the work's "X" rating.
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%% Optional items, added after Conversed, at your discretion:
%%* '''Implied''': ???
%%* '''Plotted A Good Waste''': ???
%%* '''Played For Laughs''': ???