The Magic Poker Equation / Yu-Gi-Oh!

In Yu-Gi-Oh!, skilled players tend to be luckier with their draws, drawing better starting hands and being more likely to draw the card they need in the current situation. In the franchise, it's implied drawing the right card is a combination of skill and faith, particularly in the English dub by 4Kids Entertainment. Frequently, duelists will get starting hands that allow them to bring out their most powerful monster on the opening turn, in order to have it brought down by The Worf Effect to show how powerful the opposing duelist is.

• Detailed in the manga is the 'spirit of the cards', which serves as a Karma Meter mechanic for the game. Play nobly, treat your cards well, don't sacrifice willy-nilly, be cool and your luck increases. Be a jerk, cheat, try to cheat, your luck goes spiraling downwards.
• Many cards that characters use tend to be situational, a trend increasing from 5D's onwards. These cards rarely reappear, and more general cards tend to be used as The Worf Barrage to show the opponent's skill. Duels tend to come down to a battle between the two duelists' ace monsters, and they often use cards that would not see play in real-life competitions.
• They've even turned it into a game mechanic in the Tag Force series; called "Destiny Draw", it can be assigned to up to 5 cards, and it only kicks in when you're about to lose. The Destiny Draw visual cue also shows in the anime: if the draw has a white streak following it, Power Echoes, or both, The Hero just got what he needed. Destiny Draw also appears as a Skill in Yu-Gi-Oh! Duel Links exclusive to Yami Yugi, which allows him to draw any card of his choice once per Duel after losing 2000 Life Points, emulating his ability to draw the exact perfect card to mount a comeback.

Yu-Gi-Oh! examples

• Jonouchi's luck is improbable. He has a lot of luck-based cards in his deck (Graceful Dice, Skull Dice, Time Wizard, Roulette Spider, Gamble, Arduous Decision) he almost always rolls/flips/spins right. On the flipside, he also has a lot of bad draws. For example, during his duel with Yami Marik, he kept praying to draw Giant Trunade so he could blow Marik's Trap Cards off the field, but he never draws it. Time Wizard in particular only failed once against "Ghost" Kotsuzuka/Bonz (despite being statistically a coin flip), so its effect on other monsters (weakening some, strengthening others) can be shown. One of his luckiest draws was in his duel with Valon, where on the final turn, he plays Take One Chance, which requires him to draw a random card from his graveyard and activate or summon it immediately. At the time, he had 18 cards in his graveyard and Valon is in utter disbelief when he draws The Claw of Hermos, exactly what he needed.
• This was invoked in Jonouchi's duel with Keith Howard. Keith has a giant Slot Machine robot thing which can be powered up by a card called "7 Completed". 7 Completed, consequentially, can only be used with the Slot Machine, and Keith has three of these 7 Completed cards in his deck. After using one, he declares that he will use the others to power up his Slot Machine and beat Jonouchi, to which Jonouchi replies that just because he has them in his deck doesn't mean he will draw them. However, this line is dub-only. In this instance, though, Keith cheats by pulling cards out of his sleeve. Similarly, when Keith is brainwashed by Marik and duels Yugi, he plays Graceful Charity to draw three cards, boasting that he will draw Zera the Mant and Zera Ritual and use them to finish Yugi off. Yugi retorts that the odds of drawing specific cards are slim, but Keith again cheats by pulling cards out of his sleeve.
• Entertainingly turned on its head in a scene in the manga and in the original dub where Kaiba needs to draw a card to throw at a gunman, and prays he'll get a common card since throwing cards risks damaging them. He's disgusted to see it's one of his prized Blue-Eyes White Dragons.
• Noah had a lot of this going on. His deck was a theme mishmash based on the ages of the world, and he drew the cards he needed to create his narrative in perfect sequence — he draws Greco-Roman cards and earthquake cards on his first turns, then plays Giant Flood, then Giant Rex, then Ice Age Panic, then Dark Hole followed by Gradius and its support cards. Given that the arc takes place in a virtual world and Noah is its administrator, it's understandable to assume some foul play being involved.
• In the climax of the above duel, Yugi pulls off one of the biggest comebacks thus far with the help of this trope. He starts with 100 LP versus Noah's 10,000, has no cards on his field or in his hand. He topdecks Card of Sanctity which effectively lets him draw cards until he has six, and those six cards form just the right combo that allows him to win the Duel on the spot.
  • In Yami Yugi's Battle City duel against Kaiba, he uses Spell Textbook, which makes him discard his hand and draw one card, and if it is a Spell, he can use it immediately. He gets Card of Sanctity, which greatly helps out his Slifer the Sky Dragon since it gains 1000 ATK for each card in his hand. In the final duel between Yami and Yugi, Yugi uses Spell Textbook and gets Card of Sanctity.
• In his duel against Yami Marik, Yami Yugi draws a card and sets it without even looking at it. The referee declares a violation of the rules because if it was a Monster, it is in the wrong slot, but Kaiba thinks it is interesting and lets the duel continue. The card turns out to be the Spell Fiend's Sanctuary, exactly the card he needed to turn the situation around.
• Rafael uses a Guardian deck, where most of the monsters require specific Equip Spells on the field to be summoned. He uses Guardian Treasure, which forces him to discard 5 cards to draw 2, then lets him draw 2 cards each turn instead of 1. In both of his duels, he gets really good draws and is always able to summon his monsters or draw the right Spells and Traps to protect them.
• When Yami Yugi plays the spell card Berserker Soul in his duel against Haga during the Orichalcos arc, it allows him to attack again for each monster card he draws, and he then draws a lucky streak of 8 monster cards in a row, allowing him to attack Haga even after his Life Points have fallen to zero and the duel is technically over.
• In Yami Yugi's Heroic Rematch with Rafael, at one point, he uses Kuribandit's effect to draw five cards and discard any monsters he draws. Rafael asks what the point of that was and reminds him that his ace monster, Guardian Eatos, increases her strength by the strength of the monsters in his opponent's graveyard, so that move just pumped her up to 7000 ATK. However, Yami Yugi reveals that one of the monsters he discarded was Electromagnetic Turtle, which can end the Battle Phase when it goes to the graveyard. Rafael's monsters were already too strong, so drawing and discarding the turtle was the only move that could have saved him.
• Zigfried's first duel puts him against Haga and Ryuzaki. His opponents have just summoned a reasonably strong monster on their first turn. When Zigfried takes his turn, he wipes them both out using a Ride of the Valkyries. When the details of this card is finally explained, it turns out to be a 5-card combo and he had the perfect mixture of Valkyries in his opening hand to do the job. In a somewhat funnier aversion of this, in his next onscreen duel, he mostly bricks, and so does his opponent, and he has to spend the next few turns stalling out and refreshing his hand until he gets the cards he needs.
• In Kaiba's duel with Zigfried, he ends up with no cards in his hand and on the field, while Zigfried has a card called Magical Alms, which allows both players to declare how many Spells they will play per turn and gain 500 LP times the declaration, but if they play a different number of Spells from what they declared, they will take 1000 damage times the declaration. As soon as Kaiba topdecks his card, he declares he will play four Spells. Zigfried asks if he's lost his mind because he only has one card in his hand, but he plays his drawn card, Card of Demise, to draw five cards. The next three Spells he plays ensure his victory. However, attentive viewers will notice this is actually slightly Subverted. The main Spell he used for his combo was Dimension Fusion, a card that requires 2000 LP as a cost to activate it. Kaiba didn't actually need to play 4 spells, what he actually needed was to draw a way to get Dimension Fusion and enough life points to use it.
• In the final duel of the series, Yami Yugi is able to control what card he draws by altering fate.

Yu-Gi-Oh! GX examples

• Judai/Jaden runs a deck using improbable combos based off of specific and situational cards, meaning he also tends to use up all the cards in his hand and on the field to win a duel. His deck also runs off of Fusion Summoning, meaning he also luckily draws into Polymerization in order to be able to do so. One time during his duel with Ryusei Gin/Lorenzo, Judai plays Climax Hour, which makes it so he can automatically summon a monster if he draws one on his third turn after playing Climax Hour. When it is about to be his third turn, Judai uses Hero Call to put Elemental Hero Neos on top of his deck. Gin counters by using Stage Select to shuffle Judai's deck. However, Gin is shocked when Judai draws Elemental Hero Neos anyway and defeats him with it.
• Played with where Misawa (for part of the series, anyway) has actually calculated the Magic Poker Equation, but doesn't rely on it at all, preferring quick thinking to luck.
• Dr. Allbert Zweinstein had calculated the Magic Poker Equation similar to Misawa and concluded that science is superior to luck. He duels Judai with a deck that that concentrates on manipulating the players' cards to always give him what he needs while preventing Judai from drawing what he needs. He gives Judai one of his toughest duels, but Judai eventually gets a lucky draw and manages to win.
• Kaiser, who, throughout the first season, and as lampshaded in flashbacks to his training dojo days, always pulls out Cyber End Dragon within his first 3 turns.
• Edo's second duel with Judai involved using Elemental Heroes, but he switches midway to using Destiny Heroes. Both archetypes had little to no common support at the time, and it looks like he's switched decks completely mid-duel. Also, Edo always gets a Spell card when he uses Destiny Hero Diamondguy's effect. (Reveal the top card of your deck. If it is a Spell, send it to the Graveyard and activate it during your next Standby Phase. If it is not a Spell, put it on the bottom of your deck.)
• Manjoume switches decks and archetypes a lot, but by the Society of Light arc he begins mashing his played archetypes together in a single deck. He's played Ojamas alongside Armed Dragons and VWXYZ, and neither of the three archetypes have common support barring a few singular situational cards, yet he never ends up in a situation where he can't use any of the cards he's drawn.
• Johan uses a deck consisting of the seven Gem Beasts, of which there are only one of each. This means that Johan has only seven monsters in his entire 40-card deck (and Rainbow Dragon, but that has a special summoning condition, and he doesn't have it for a good chunk of the series). Despite this, he never has a problem drawing at least two Gem Beasts in his opening hand. This would almost be justifiable if his other cards let him search for his Monsters, or recycle them when they leave the field, but most of the time, this is not the case.
• Ikkaku Tachibana relies on Slash Draw, which discards cards from his deck equal to the number of cards on the field, then lets him draw a card, and if it's another Slash Draw, he destroys every card on the field and inflicts 1000 damage to his opponent for each one. He never fails, though it's revealed that he achieves this with a Deal with the Devil with a Grim Reaper entity. Toward the end of his duel with Judai, he rejects the entity, and it says he can never succeed with Slash Draw without its help before leaving. He plays Slash Draw and succeeds anyway, but Judai manages to survive and defeat him on his next turn.
• Taizan relies on Miracle Draw, which inflicts 1000 damage to his opponent each time he correctly guesses what card he will draw, and 1000 damage to himself if he guesses wrong. He trained to "draw better" by dropping out of school and pulling cards out of a waterfall, enabling him to use Miracle Draw effectively. However, during his duel with Judai, Taizan still slips up in his drawing skills, as he makes a mistake by calling out that he would draw Shield Crush when he did not. Judai points out he shouldn't rely on perfect draws, as he would eventually make mistakes, but instead go with his instincts and enjoy all the possibilities of a draw, hoping for the best. Judai then draws Elemental Hero Avian, the card he needed to win the duel. Taizan's drawing skills also help him pull the golden eggwich out of a random assortment of sandwiches every time he tries, something Judai is also good at doing.
• Daitokuji's deck is a lesson on a lengthy alchemical process. He needs specific spell cards representing the alchemy tools used to summon specific Alchemy Beast monsters in a specific order. After the process is complete, he draws the card needed to summon a Golden Homunculus. After that's defeated, his strategy changes to use Helios cards representing the sun and planetary alignments.
• Amon Garam has a Spell called Wonder Cloud, which forces him to Banish all the cards in his hand and on his side of the field, then he draws one card for each card his opponent controls, then he Banishes all the cards in his deck. The one time he plays it, the onlookers comment on how suicidal this card is, since if he doesn't draw what he needs, he'll lose by deck-out on his next turn. Naturally, he draws what he needs to win.
• Austin O'Brien does Training from Hell by suspending himself upside down over a cliff by a wire and having a device slowly cut the wire. He doesn't try to escape until he can draw the card he wants. He of course succeeds every time.
• When Johan is possessed by Yubel and duels Amon, he plays Nightmare Shuffle. When playing this, he is not allowed to look at the cards in his graveyard. He picks a card in his graveyard at random and sets it, then during his Standby Phase, he must swap it with another card. He can send Nightmare Shuffle to the graveyard to activate the set card at any time, but if it wasn't a spell or trap or if the activation requirements are not met, he has to send all the cards in his hand and field to the graveyard. When he played it, he had 13 cards in his graveyard. He had to active the set card almost immediately, and it turned out to be Hand Destruction, exactly what he needed to save himself from losing.
• When Sho is practicing with Ryo’s deck in season 4, he notes that his inability to pull out the cards he needs (initially getting out a Cyberdark Monster only to brick himself when his next draw is a support card for the original Cyberdragon series instead) is a sign that he's not yet in tune with his brothers deck yet.

Yu-Gi-Oh! 5Ds examples

• Yusei is often depicted as seeing the winning path depicted as a line of electricity linking the cards in the chain that will pull it out for him. The winning path is determined after the draw and is in part due to Yusei's ability to read what cards his opponents have and determine the best course of action. However since in the world of Yu-Gi-Oh! every deck seems to run only 1 of each card, Yusei still has to guess at what cards out of a staggeringly huge large card pool and still drawing the necessary cards to play around/against/counter against said opponents. In the final duel of the series, Jack Atlas uses his 6000 ATK Scar-Red Nova Dragon to attack Yusei's 3300 ATK Shooting Star Dragon. Yusei uses the card High and Low, which lets him send cards from the top of his deck to the graveyard up to three times and power up his monster by the ATK of any discarded monsters, but if his monster's ATK exceeds his opponent's, his monster will be destroyed. He uses the effect twice and discards the 1000 ATK Sonic Warrior and 900 ATK Speed Warrior, pumping Shooting Star Dragon up to 5200 ATK. Everyone expects Yusei not to use the effect again because of the high risk of Shooting Star Dragon being destroyed and allowing Jack to attack directly, but Yusei does use the effect a third time and discards the 800 ATK Quillbolt Hedgehog, pumping Shooting Star Dragon up to 6000 ATK and letting both monsters destroy each other in a double KO.
• Played a bit with Shooting Star Dragon. Every single time Yusei activates its "attack for all the Tuners on top of your Deck" effect, he gets at least three out of five cards. Normally this wouldn't be too hard - his deck has an abnormally large amount of Tuners he regularly uses - and at one point he even misses out on a clean finisher because he fell one Tuner short of a lethal attack. Though two times he did draw five Tuners in a row, but this is explicitly because the Crimson Dragon was channeling the power of all the Signers into him.
• The Three Emperors of Yliaster always manage to pull their Core monsters on their first turn, as well as the trap cards they need to trigger its effect and summon their Machine Emperor monster by the next turn.
• Subverted with Aporia as a Hope Spot. Aporia has the card After Glow, which shuffles itself into the deck and inflicts 4000 damage to the opponent when it is drawn again (and because 4000 is the starting LP in the anime, it's almost always a One-Hit Kill). To maximize his chances of success, he sends all the cards in his deck to the graveyard so that After Glow will be the only card and he will be sure to draw it. Z-One counters this tactic by using Temporal Machine God Razion to shuffle Aporia's graveyard back into his deck and then explaining that Razion will burn away the rest of Aporia's LP during his Standby Phase, meaning that Aporia's victory depends on whether he draws After Glow the next turn. Z-one declares that with a 1/34 chance, there is no way Aporia can do it. Aporia declares he can do it and draws... Machine Emperor Granel Infinity, and he loses. To rub salt in the wound, Granel was the same monster that was responsible for the "great despairs" of Aporia's life, meaning that Aporia drew the worst (or at least the most insulting) possible card that he could have at that moment.

Yu-Gi-Oh! ZEXAL examples

• There is an early episode of Yu-Gi-Oh! ZEXAL where the opponents in a tag duel are drawing exactly the cards they need to pull off unlikely combos - and the heroes notice their hands are too good. Turns out the opponents were cheaters stacking their decks, but seriously, with the way people draw on this show, how could you tell?
• A great example is Shark's Xyz Dimension Splash, a Trap with a very difficult-to-activate condition (it has to be banished while facedown; banishing a random Set card is something few opponents would do) that supports the summon of Rank 8 Xyz monsters (of which Shark has none). Coincidentally, the Duel he used this in was a Tag Duel with Kaito (who does use Rank 8s) against an opponent whose monster had an indiscriminate banishing effect.
• ZEXAL turns this into a superpower of sorts with the Shining Draw ability, which can let Yuma create a new card to draw, but he can only do so under specific circumstances (it's basically this trope justified by magic). Yuma later faces Eliphas, who can do a Shining Draw whenever he feels like it, unlike Yuma, who can usually only do it once or twice a duel and usually needs to do a Fusion Dance with Astral first.

Yu-Gi-Oh! ARC-V examples

• Yuya has the tendency to draw his three main Pendulum Monsters (Stargazer Magician, Timegazer Magician, and Odd-Eyes Pendulum Dragon) in his first turn or only a few turns later. Though in episode 22, he starts with a dead hand, having six high-level monsters that cannot be Pendulum Summoned because his highest scale would be too low to summon any of them. He draws his Timegazer Magician in his third turn and then summons five monsters at once, but he is still followed with terrible luck in the very same turn. As of later episodes, Yuya's starting to get less lucky with his draws, forcing him to use the cards he has and sometimes not even drawing one of his Magicians.
• Reiji Akaba's DD deck first averts this trope, since he uses cards that allow him to add specific cards from his deck to his hand, until he draws multiple cards at once, which turn out to be his three copies of his DDD Cruel End King Hell Armageddon.
• Tokumatsu is famous in-universe for doing this. It's been hinted through his chanting and poses before drawing the card he needs that this might be a supernatural ability similar to the Shining Draw, but this is unconfirmed.
• Kurosaki gets an opening hand with three copies of Raidraptor - Vanishing Lanius with disturbing frequency.
• Once Yuya gets his hands on Smile World, a mediocre card that slightly boosts the ATK of every monster on the field, he somehow keeps finding situations and combos that make it relevant.
• Surprisingly enough, there is actually some aversion to this trope when looking at the deck types used in the series. Hokuto and Yaiba, who use the Constellar and X-Saber archetypes respectively, make pretty standard plays in respect to how the real Yu-Gi-Oh! card game is played. With those Archetypes, getting out one or two monsters with 2500+ ATK on the first turn is pretty normal, especially when it's shown that characters carry multiple copies of cards.
• Dennis unveiling his alliance with the Fusion Dimension involves him suddenly using a Fusion card when he's spent most of his screentime playing the Xyz-centric Performages. This is downplayed as this maneuver primarily uses cards from his Extra Deck, which are only accessed when needed, and the few Spell Cards involved are one-offs that don't infringe too heavily on the rest of his archetype.

Yu-Gi-Oh! VRAINS examples

• Storm Access is a skill that creates a random card from the Data Storm while its user is on low LP. Theoretically, its randomness should give out results that aren't useful for the situation, but each time it's used, the card its user gain is perfect to get out of the predicament.
  
  Interestingly, the New Powers as the Plot Demands part is actually acknowledged in-universe, as the general reaction to someone using Storm Access is Oh, Crap!. Despite characters stating that Storm Access adds a random card, almost everyone aware of it seems to know it actually means "Card perfectly suited to the current situation", and several characters begin including specific combos (Such as those that cause both players to gain LP) to avoid Storm Access' conditions.
• Zig-zagged in one episode — Naoki/Brave Max is facing off against a Knight of Hanoi, and they both start off with terrible hands. However, the Knight of Hanoi manages to pull a Discard and Draw for their hands, and eventually summons a powerful monster. On the next turn, Brave Max draws a card that he had gotten earlier in the episode, which can exploit the monster's Glass Cannon status, and quickly wins the duel.
• Soulburner has his own skill that acts like this: Burning Draw. While it has the caveat of lowering his life points to 100 and it doesn't give him new cards, he always draws the cards he needs to win. Lampshaded in his final fight with Revolver, the card he drew is also called Burning Draw which gave him enough cards to win the duel.

Yu-Gi-Oh! SEVENS examples

• It's pretty much invoked by Yuga, who specifically wrote the Rush Duel rules to enable massive comebacks at any time (you can draw up to five cards in one turn if your hand is empty, and that's just the base rule) because he believes it's more fun that way. Even so, his own trademark combo errs maybe too much on the side of Awesome, but Impractical even for his new rules, and he's been known to fall short of victory range quite a few times.
• Nail Saionji's deck is an aversion of this, as it uses an incredibly broken monster effect combo to effectively allow Nail to dig through his entire deck for the three pieces of his Maximum Monster "Yggdrago The Heavenly Emperor Dragon Tree". Although even then, his draw combo requires a bunch of specific cards in a specific sequence, and he never fails to get them in the required order.
  • Other Maximum monsters tend to play this straight, though - you require three specific cards to Maximum Summon a monster. In the real life game this trended towards them being somewhat unwieldy to use; in the anime, duelists more often than not will get a full set of three all at once with minimal setup.

Yu-Gi-Oh! GO RUSH!! examples

• Subverted in the first duel of Yu-Gi-Oh! GO RUSH!! - both duelists have rather poor starting hands, with Yuhi only drawing one monster card and Yudias only having level 4 and lower monster cards.
• The duel taking place over episodes 75-77 feature a few notable instances of this coming into play:
  • The first is the Trap Card, "Interstellar Change", which can be activated if an attack is declared and both players have empty hands. Both players then draw five cards, and if *all ten* of the cards drawn are monsters, then the Battle Phase is forcibly ended, and the owner of the card has to allow another player to take over for them. The card is activated twice, and the condition is successfully met both times.
  • While "Interstellar Change" has someone else take over for the owner of the card, the Deck remains the same - but both characters who take over have one of their cards incorporated into the Deck already, and just so happen to draw it when they take over. Played with - while the first instance is played straight, the second instance was added to the Deck by an outside force while the Duel was going on.