In the beginning of the series, Yuma's Deck was very basic containing a random assortment of monsters with no central strategy tying them together. However, as he gathers the "Numbers," Yuma's Deck slowly matures, especially after he receives cards from the Duel Sanctuary.
Yuma's primary strategy is the Summoning of his ace card, "Number 39: Utopia", which has a number of upgraded forms as well. He powers up this monster in a variety of ways, such as with "Double or Nothing!" or "Emperor's Armor". Yuma occasionally uses other "Numbers", but "Utopia" remains his ace card throughout the series. His Spell Cards tend to focus on augmenting the ATK and effects of his monsters, while his Trap Cards like "Half Unbreak" and "Damage Diet" are usually more defensive in nature. As his opponents use Xyz Monsters themselves, Yuma plays a number of cards to specifically counter this as well, such as "Rainbow Kuriboh" and "Overlay Owl".
When Yuma's opponent is not wielding a "Number" or "Chaos Xyz" card themselves, Yuma often refrains from using his "Numbers". but is willing to Summon "Utopia" if the opponent demands it. In such situations, the "Djinn" Xyz Monsters or "Heroic Champion - Excalibur" are often his go-to choices.
Yuma originally uses a Number/Syllable Deck. It is supported with a lot of ATK increasing cards such as "Wonder Wand" and Trap Cards which protect his monsters from destruction such as "Bye Bye Damage". It contains some support for his "Gagaga" monsters later on.
This Deck was later replaced by a new version after Yuma received a large amount of new cards from Roku when he defeated Kaze and protected the Duel Sanctuary.
In the finals of the World Duel Carnival, Yuma debuts more non-"Number" Xyz Monsters, "One-Eyed Skill Gainer" and "Gagaga Cowboy". His WDC profile lists his Deck's name as "Xyz One Turn Kill" as he heavily focuses on using Xyz Monsters and normally wipes out of his opponent's remaining Life Points in the final turn. In addition, as Yuma dealt with more dangerous opponents, he relies heavily on augmenting his "Number C39: Utopia Ray" with abilities of his "ZW -" monsters through the power of ZEXAL than he did before.
Yuma debuts more support for his Xyz Monsters and procures "Rank-Down-Magic Numeron Fall" which he can use to downgrade "Number 39: Utopia" into "Number 39: Utopia Roots". During his Duel with Mr. Heartland, Yuma gained the ability to create "ZS -" monsters. Unlike "ZW -" monsters, these monsters do not function as Equip Cards
After defeating Nash, Astral obtained all 100 "Numbers." As he and Yuma were Dueling over the fate of Barian World, Astral naturally decided to keep the "Numbers" to himself during their Duel. Thus, Yuma modified his Deck before the Duel. The Deck focuses on "Gagaga" monsters and support. During the Duel he would later get a new Ace Monster called Number F0: Future King Hope.
In the Aim For Number 1 in the World! non-canon episode, his Deck appears similar to his usual anime Deck, including "Number" monsters. He also Dueled Astral in an explanation Duel at the beginning of the special.