The Heart of the Cards is a commonly used phrase in the English dub of Yu-Gi-Oh!. It refers to a mystical force that helps a Duelist draw the right card(s) at the right time needed for the situation. The phrase is also used by real-life Duelists who presume to be in a tight situation (either as per its original meaning or sarcastically), often with no hand, or when their opponent has a massive advantage and the outcome of the game resides on the next card drawn (see Top-Decking). The "Heart of the Cards" also means the belief and faith a Duelist has in their Deck, putting hope that every card the Deck gives will be useful.
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 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, loses the Duel.
Yugi Muto also often refers to the "Heart of the Cards" as if it helps him win Duels, as well as criticizing his opponents for not believing in it. His friend Joey Wheeler has also shown belief in the "Heart of the Cards".
Although this concept lies within the realm of superstition, it can be assumed that a Duelist who sincerely trusts in their Deck to help them out will often find that trust reciprocated in a key reversal card being drawn at the right time. As such, Yugi gives the Heart of the Cards a lot of credit for helping him win Duels. Often, it is noted that when a Duelist has a close bond with his Deck to the point of knowing it by heart can result in usage of the term as well.
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, 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).
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.
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.