Kyoya uses a Dragon Ein deck, his Buddy is Demonic Demise Dragon, Azi Dahaka. His special Flag, rather than listing a World for him to use, allows him to use any card from any World as long as it has Dragon on its attributes, in exchange, he starts the game with 4 cards in his hand and 12 Life. Kyoya uses Ancient World spells to increase his smaller opening hand while safely pay their life costs with his higher starting life, Dragon Shield spells for protection and extra advantages, and a wide array of Dragons from various Worlds for combat, including several Move monsters.
Dragon Ein allows Kyoya to cast Dragon Throne, a Set Spell that increases his Size limit to 4 and prevents his item from being destroyed or returned to his hand. With it, he can call Azi Dahaka and wipe out the opponent's entire field at once while still dealing damage. However, his true goal is for Azi Dahaka to be destroyed, when it does, he can equip Demonic Demise Sword, Aqulta Gwaneff.
When he was younger, Kyoya used a Dragon World deck, his Buddy was Thousand Rapier Dragon.
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To unite the ones who dare, I will become the final destroyer! Dark Luminize, Wings of Demise!
Kyoya uses a similar deck in Season 3, but with a focus on the Purgatory Knights so as to take advantage of their ability to perform multiple attacks in tandem with the pressure provided by his powerfulitems.
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In order to undo the curse of Babel, I will become the final destroyer! Dark Luminize, Wings of Demise!
He now uses a Dragon Zwei deck, with Great Demonic End Dragon, Azi Dahaka as his buddy. His strategy focuses on using the skills of Azi Dahaka so he could get his opponent at a disadvantage, while using the effects of Dragon Zwei in the process.
Then before his final two matches in the season, his deck changes, focusing on Azi Dahaka's final form, that has the skill to attack an enemy as many times as he likes by paying 1 life.
Now that his new flag Dragon Drei got completed, he plans on using Daeva's skill to get Dragon Drei easily from his deck so he can be revived with 5 life quicker. Then he added the colossal size 10 Demonic Dragon Deity of the Black Sun, Gaen in which allows him to prevent his opponent from drawing cards. Given that his opponent would have used most of their hand cards against Dragon Zwei, he can maximize his advantage alongside his army and critical of 5 and regain life using Gaen's effect.
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For the sake of my noble ideals, I will guide the old world to its end. Dark Luminize! World of Demise!