The Heart of the Cards is a commonly used phrase in the English dub of Yu-Gi-Oh! which reflects a belief and terminology derived from the Japanese manga and anime to varying degrees, and which refers to the seemingly mystical ability of a Duelist to draw the right card(s) at the right time needed for the situation, especially when Dueling for a righteous cause with high stakes rather than for fun. The phrase is also used often by real-life Duelists who presume to be in a tight situation (either as per its original meaning or sarcastically), for instance when they have no hand, or when their opponent has a massive advantage and the outcome of the game rests on the next card drawn (see Top-Decking). A more mundane way to interpret the "Heart of the Cards" is as a reference to the belief and faith a Duelist has in their Deck, as well as trusting in the construction of one's Deck and affirming that every card in a Deck is potentially of use.
A real-life example of Heart of the Cards is as follows. The opponent's field contains many powerful monsters with the weakest having 1900 attack, and nearly full Life Points. The turn player is losing with 200 Life Points, and has only one monster on the field, in this case "Crystal Beast Sapphire Pegasus". On the player's field is "Ancient City - Rainbow Ruins" and three Crystal Beast monsters in the Spell & Trap Zone. The turn player, chancing everything on the Heart of the Cards, attacks their 1900 ATK point monster, losing 100 life points, and putting "Sapphire Pegasus" into the Spell & Trap Card Zone, allowing the player to draw once more during this turn. The Heart of the Cards responds by giving "Crystal Abundance", allowing the player to wipe the field and Special Summon a horde of Crystal Beasts. The opponent, unable to Summon any new monsters or not being able to Summon any powerful enough to combat the Beasts, loses the Duel.
On the surface the concept seems similar to "luck" or "destiny", but it differs in crucial ways from these concepts. For example, Yami Yugi is able to defeat the supernaturally lucky Ryuichi Fuwa in a Shadow Game by turning his own luck against him, demonstrating that trusting in luck or even possessing it in abundance is not the same as being mindful and having respect for the game one is playing. Likewise, Seto Kaiba is able to change destiny in his game against Ishizu Ishtar by choosing to trust his last-minute vision and act against his instincts in favor of his heart, winning the Duel in the process. Knowing when to embrace the unknown, strategizing around one's ability to pull and play the right card, and when to trust the cards one is dealt, may mean the difference between victory and defeat. When a Duelist has a close bond with his or her Deck to the point of knowing it by heart, this may be called the "Heart of the Cards" both in practice and in parlance.
In the Yu-Gi-Oh! story-line, Yugi Muto learned about the Heart of the Cards from his grandfather; he often credits it for helping him to win Duels, or criticizes his opponents for not believing in it, especially when the Duelists see cards as mere tools for victory or power, or when their lack of belief in their cards reflects a lack of belief in, or love for, themselves, others, or both. To Yugi, powerful cards, talent, and cold strategy are not enough to play at one's best in a game, holding that they will even be destructive to the self or others if abused or misused. Yugi's best friend, Joey Wheeler, also strongly believes in the "Heart of the Cards", and Yami Yugi even professes that cards and other objects can have souls, going as far as to taunt Seto Kaiba during their first Duel for his lack of belief that they can.
Unsurprisingly, the belief that objects can have souls is very Egyptian, as the Ancient Egyptians believed that objects could be endowed with "Ba" and a unique character as a result of their interactions with people, akin to how people are influenced by the Ba of others. As a result some objects were regarded as an extension of a person's Ba as a result of a deep and fundamental connection to that person. This belief is exemplified in the manga when the "soul" of Grandpa Muto's Blue-Eyes White Dragon refuses to fight for Seto Kaiba as a result of Kaiba's soul not being in Muto's card.
Although this concept lies within the realm of superstition, it can be assumed that a Duelist who sincerely trusts in their Deck, when thoughtfully crafted by the Duelist or those the Duelist trusts, holding it to be worthy and helpful, will often find that trust reciprocated in a key reversal card drawn at the right time. Yugi Muto places this level of trust in the Deck he inherited from his Grandpa due to knowing how much care went into its construction, and he maintains this same respect for the cards of his friends.
In Yu-Gi-Oh! GX, the concept is referred to during Jaden Yuki's Duel with Dimitri. Winged Kuriboh points out that since Dimitri is not Yugi, the "Heart of the Cards" is not on his side, and although not stated directly, multiple characters remark on Jaden's ability to always draw the right card when he needs it (an example of this is him seemingly always drawing "Elemental Hero Neos" even though Jaden only carries one copy in his Deck). Jaden has stated that the reason he draws what he needs is because he believes in his Deck, and because his Deck also believes in him.
In Yu-Gi-Oh! 5D's, the concept is referred to by Yusei Fudo several times during different Duels. He talks about believing in the cards and how the cards will always answer if you do. Additionally, though he does not explicitly state it, Crow Hogan seems to believe in this concept, as evidenced by his dubbed quote: "Another Blackwing. Not exactly what I was hoping for, but hey, maybe my Deck's trying to tell me something."
In Yu-Gi-Oh! ZEXAL, Astral seems to believe in this concept, as he tells Yuma to tap into his heart and believe in his cards. Some characters, including Yuma, actually have a visible power to draw exactly what they need (see Shining Draw and Chaos Draw). Kite also believes in this concept and uses it in episode 106.
In Yu-Gi-Oh! VRAINS, in episode 30, Ai says "Heart of the Cards, guide me" (referencing Yugi) when drawing a card from Ghost Gal's Deck in which the one who drew the prettiest card would get to choose which way to go; though it failed as he instead drew Fake Trap, giving Ghost Gal the win by default (although every card in said deck was Fake Trap). In episode 45), Ai and Playmaker face Varis with his five Extra Linked monsters. Ai kneels down to pray that Playmaker draws a good card to boost their defenses, to which the latter reminds him of his own words that "AI-s do not pray."
In the original Japanese version, the concept of "Heart of the Cards" is touched on in the first episode, but largely not referred to since. However, it is frequently said that since you put all of your feelings into building your Deck, it can be relied on to help you win.
In the Japanese version of Yu-Gi-Oh! 5D's, there is a concept similar to "Heart of the Cards" known as possessing the soul of a duelist, which also relies on believing in one's cards.
The video game Yu-Gi-Oh! The Duelists of the Roses features a concept known as the Destiny Draw. It could be considered similar to the Heart of the Cards, since the Destiny Draw has a chance of adding a card to the player's Deck that could potentially turn a losing Duel around.
Many of the current video games also involve a similar mechanic to the Heart of the Cards in the form of a "Destiny Draw" feature. Whenever a character is severely losing, they can choose to draw a card that would reverse the tide of the Duel. This feature allows a player to select which card is their "Destiny Draw" so that players can pull a win from behind.