"And you feel that you have exerted your very best efforts in this matter, do you? That you have exercised all of your considerable ingenuity?" - Albus Dumbledore
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The Magician, one of the opening cards of the Major Arcana, represents an essential, primal force of nature - the masculine power of creation. The self-confidence and determination in this card allow the Magician to harness the energy of the material world with skillful dexterity and diplomacy.
As the Merlin figure of the story, Headmaster Dumbledore appears infalliable in his knowledge, skill, and wit. His wisdom doesn't stem from some arbitrary all-knowing source, however; it is acquired through many years of experience, observation, and contemplation. It is Dumbledore's qualities of open-mindedness and resourcefulness - in essence, his willingness to take notice and make use of the world around him - that allow him to become the most powerful and respected wizard of his time.
The Magician is usually depicted with the four suits (Wand, Sword, Cup, and Pentacle) before him to show his mastery over each element of the world. This is represented here by the four houses in the Hogwarts crest, as well as the presence of the four Hogwarts founders' artifacts, as appropriate for Dumbledore's position of Headmaster - and because they are the minor suits in this deck.