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...it's like TV Tropes, but LINKED DATA!

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The whole is more than the sum of the parts.
Sometimes, several items put together deliver additional benefits more than if you just numerically or synergistically added up the power of all the items. It can apply both to powers and objects.
Most of the time there is no In-Universe explanation offered for why these items have to be together to produce the extra effects. It could be said that the enchantments need to 'overlap' or that the pieces when connected form the circuit of a system that then produces the effects. Most games with this mechanic will also have each item's description "kindly" inform the player of the potential benefits, without any proper explanation of just how the character could know about them. Maybe they were written somewhere on the items themselves.
This trope is absurdly prevalent (though by no means universal) in MMORPGs, but it turns up in other genres as well. It is often used to encourage trading among players, but it has the side effect of making the more obsessed sink extra time and money into a game. If significant enough, this trope should hopefully cut down on Rainbow Pimp Gear. Outside of MMORPGs, stories may have magical accessories, weapons, or magic rings be created as part of a set by powerful mages with this intended effect.
Related to Gotta Catch Them All. Compare Counterpart Artifacts and Signature Device.
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DBTropes
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The eponymous artifacts in Harry Potter and the Deathly Hallows were believed to make the owner of all three Master of Death, granting immortality. The true Master of Death is one who knows Death is inevitable despite the existence of magic and accepts it when it comes.
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Bleach: In the anime filler Gotei 13 Invasion arc, seven lieutenants and the filler heroine, Nozomi, are fighting one reigai captain, but don't have enough power to defeat him. Nozomi uses her shikai to absorb all seven lieutenants' zanpakutou powers to combine it with her own into a single attack. The captain is promptly one-shotted. The anime never offers any explanation for how this fusion magically turned "not enough power" into "more than enough power".
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In one episode of White Collar, a thief was collecting a set of jade elephants that became much more valuable when all of them were sold together. Neal tried to lure her in by offering to team up so they could sell the full set and split the profits.
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This shows up every so often in Heroes. Hiro's time-travelling is greatly helped by hints from Isaac's ability to predict the future. Samuel's ability to control earth (and ink) and Lydia's empath powers combine into a limited form of clairvoyance, which Samuel uses to find other people with abilities.
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Fallout: Equestria: The Ministry Mare statuettes are based off the Vault Boy bobbleheads from Fallout. Littlepip finds herself stronger or smarter every time she collects one; the "level-up" notes at the end of each chapter put it in game terms, where she is gaining a boost to each stat with every statuette. When she gets the last one, their magic increases, and she immediately decides not to separate them again. The end of chapter note says she got a bonus to her Luck Stat for completing the set.
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In Lazer Team, the Champion Suit's full potential can only be realized when all the components (intelligence-boosting helmet, left shield-generating gauntlet, right blaster gauntlet, and Super-Speed boots) are working together.
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In Toriko, each of the ingredients in Acacia's Full Course apparently has amazing effects. Eating all of them together also grants the power to use Gourmet Cells at peak efficiency.
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The "objects" in The Lost Room can be lethal on their own, but when one person has more than one they tend to become obscenely powerful. One particular combination of objects can potentially create a localized rip in space-time.
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The Shen Gong Wu in Xiaolin Showdown tend to have this effect. There's a subset of them that when combined will create the dreaded Mala-Mala Jong.
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Sushi Go! and its Updated Re-release Sushi Go Party! are drafting games that rely heavily on collecting favourable sets of cards:
If you take a wasabi card, the value of your next nigiri will be tripled.
Tempura cards are scored in pairs, sashimi cards are scored in trios, and the green tea ice cream dessert is scored in groups of four. It's all or nothing — leftover cards have no value. Denying someone their third sashimi can be devastating.
A set of 1/2/3/4 different onigiri shapes is worth 1/4/9/16 points. The more onigiri shapes you have, the more valuable each card is on average.
A set of 1/2/3/4/5 dumplings is worth 1/3/6/10/15 points, so the value of each dumpling increases the more of them you take.
Exaggerated with the eel. One card is worth -3 points, but a set of 2 or more gives you 7 points.
Zig-zagged with the tofu. One tofu card is worth 2 points and a pair of them is worth 6, but if you gather 3 or more, they all become worth 0.
Invoked with the tea card, which is worth 1 point for each card in your largest set of cards with the same background colour.
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Azul: During the game, you get bonus points for having set of tiles that connect horizontally or vertically. At the end of the game, you are rewarded for each complete horizontal line, each complete vertical line, and for each colour you have a full set of 5 tiles in.
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Risk provides additional troop bonuses when you occupy an entire continent, as well as when you trade in three cards with matching symbols.
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Kamen Rider Build gets in on the idea with the Full Bottles, which are divided into organic (like Rabbit, Hawk, Pirate, Ninja, etc) and inorganic (Tank, Gatling, Train, Comic, etc), and Build needs to use one of each to transform. Every Bottle has one specific "Best Match", a Bottle of the opposite type with which it has high compatibility (like Rabbit and Tank); transforming with a Best Match makes Build stronger than if he just used random combinations and sometimes gives him access to unique abilities and custom-themed weapons.
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Kamen Rider Ex-Aid inverts this with Drago Knight Hunter Z. This form grants one Rider a big suit of dragon-themed armor, or the Transformation Trinket can be invoked by all four Riders at the same time to hand out one piece to each Rider. The form is based on Co-Op Multiplayer games, so it's the individual pieces that get the power boost, making the complete set an example of Clipped-Wing Angel.
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In Kamen Rider Geats, any Rider can use any Raise Buckle, but certain Raise Buckles have better compatibility with certain Riders' Core IDs.
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In Kamen Rider Saber, the Riders draw their power from magical storybooks. Any Rider can use any storybook, but they get a better effect if they use ones from the set that matches their Elemental Power.
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The point of the Rusty and Co. arc with Prestige Perkins: Prestige suspects that the Illithid Mobs are gathering lesser magical trinkets to create a dangerous weapon, later revealed to be a literal Magic Missile.
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All The Skills - A Deckbuilding LitRPG: Cards are sometimes arranged into sets, and are often much more effective if someone can collect the whole set — to the point where the Crown discourages it, because it's too potent. Even without being in official sets, different cards can have powerful synergies together.
When Arthur obtains cards for extradimensional storage space, perfect memory, and the ability to review memories on a mental bookshelf, they combine into a new set — and the combination gives him the additional ability to mentally visit his storage space as an offshoot of the bookshelf, interacting with stored items and even training skills there, without time passing outside.
Master of Skills also turns out to have excellent synergy with Prince Marion's "Instant Tool and Weapon Competence" card. Master of Skills does nothing for weapons, but for tools, it adds an extra three levels on top of Instance Competence's ten, and makes all thirteen levels permanent even after Instant Competence is removed.
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In Slayers, Lina has four magical amplifiers (that she bought off of Xellos) that work better in tandem than separately.
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The three Orbs in The Wizard, The Witch, and Two Girls from Jersey have their powers magnified when multiple Orbs are possessed by the same person. With two, the Twilight Queen has plunged the land into twilight; with all three she can create eternal night. The Chosen One can defeat her by claiming all three Orbs.
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The Makluan Rings in Iron Man: Armored Adventures that the Mandarin is after.
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Dungeons & Dragons:
Fourth Edition has the Adventurer's Vault 2, which offers a few item sets. Most are the typical matched armor and/or weapon sets that gain additional bonuses when a character has more pieces of the set equipped. There are also a few 'group' sets which have similar bonuses for each member of the adventuring party using them.
3.5 introduced non-artifact set items in the Magic Item Compendium, though the original D&D set items are probably the Regalia of Might, printed in Eldritch Wizardry in 1976. 3 alignment specific sets consisting each of a Rod, an Orb and a Crown. All three were powerful artifacts in their own right, and made stronger when brought together. The Hand and Eye of Vecna probably also count.
Also originating in Eldritch Wizardry, and possibly D&D's Ur-Example, is the Rod of Seven Parts. In its backstory, it was originally the Rod of Law, wielded by the Wind Dukes of Aaqa against the Queen of Chaos, and shattered in the climactic battle of the first war of Law vs Chaos, banishing the Queen's lover Mishka the Wolf-Spider, Prince of Demons and decimating both armies, forcing a stalemate. Each part had a separate power, groups of parts added more and greater powers, and nearly unparalleled abilities were available to a wielder who united all the parts. Since it was impossible to completely repair it, though, using the unified powers carried a chance of re-shattering the Rod and re-scattering its parts (with the side effect of Critical Existence Failure for the overly ambitious invoker). The words used to activate its parts were given as "Ruat," "Caelum," "Fiat," "Justitia," "Ecce," "Lex," and "Rex." The Easter Egg being that, as a Latin phrase, those words translate as "Though heaven fall, let justice be done. Behold! Law is king!"
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Jackie Chan Adventures season 1 has the bad guys looking for 12 magical talismans in order to release the demon Shendu from imprisonment. Each talisman has its own power, and several of them work well together:
Jade is fond of pointing out the Rooster's Levitation and the Rabbit's Super-Speed combine to create flight.
The Horse's Healing and the Dog's Immortality might seem redundant at first, but having only the latter doesn't stop you from feeling pain.
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In ThunderCats (2011), the Thundercats and their Arch-Enemy Mumm-Ra hunt for various Power Crystals, one of which is the Cats' own Amulet of Concentrated Awesome, the Eye of Thundera. If all are placed in a sword and gauntlet, the wielder will be rendered nigh omnipotent.
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In Transformers: Armada, there are three sets of Mini-cons that fuse together to form the Star Saber, the Skyboom Shield, and the Requiem Blaster.
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In The Wonderful Wizard of Oz, simply wearing one of the two Silver Slippers (Ruby in the movie) is enough to give the wearer near complete invulnerability to magical attack and physical harm. Having both gives the wearer wish granting abilities close to a 3 or 4 on the Super Weight scale.
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Kamen Rider:
Kamen Rider OOO's belt is powered by inserting Core Medals into three slots, corresponding to the Head, Body, and Legs of his transformed form. Using three Medals of the same color creates a "Combo" which gives him increased powers and a new ability at the cost of leaving him exhausted when he powers down. The Greeed villains similarly gain increased powers the more Medals they have, along with a special Set Bonus of their own when they have all nine of their respective color. It's most notable with Gamel, whose bonus ability is a Touch of Death that takes him from the least dangerous of the Greeed to a Person of Mass Destruction.
Kamen Rider Ex-Aid inverts this with Drago Knight Hunter Z. This form grants one Rider a big suit of dragon-themed armor, or the Transformation Trinket can be invoked by all four Riders at the same time to hand out one piece to each Rider. The form is based on Co-Op Multiplayer games, so it's the individual pieces that get the power boost, making the complete set an example of Clipped-Wing Angel.
Kamen Rider Build gets in on the idea with the Full Bottles, which are divided into organic (like Rabbit, Hawk, Pirate, Ninja, etc) and inorganic (Tank, Gatling, Train, Comic, etc), and Build needs to use one of each to transform. Every Bottle has one specific "Best Match", a Bottle of the opposite type with which it has high compatibility (like Rabbit and Tank); transforming with a Best Match makes Build stronger than if he just used random combinations and sometimes gives him access to unique abilities and custom-themed weapons.
In Kamen Rider Saber, the Riders draw their power from magical storybooks. Any Rider can use any storybook, but they get a better effect if they use ones from the set that matches their Elemental Power.
In Kamen Rider Geats, any Rider can use any Raise Buckle, but certain Raise Buckles have better compatibility with certain Riders' Core IDs.
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In Gargoyles, the Eye of Odin, the Phoenix Gate, and the Grimoire Acanorum are also known as the Three Keys of Power. Each is already a powerful artifact. Bringing all three together unlocks vast magical power. The spell responsible for the Gargoyles' Magic Pants was cast by a mage who possessed the Three Keys of Power at the behest of Caesar Augustus since he found the nudity of awakening Gargoyles distasteful. In the actual animated series the Archmage's Evil Plan was to obtain the Eye of Odin and the Phoenix Gate (he already had the Grimoire) to gain ultimate power. By the end of the animated series all three are lost forever. The Grimoire (which the Archmage ate to absorb it) destroys itself and the Archmage from within after he could no control its power due to losing the Eye. Odin reclaims his missing Eye. Goliath hurls the Phoenix Gate into the timestream to prevent anyone from using it again. In the comics the Gate is broken and releases the actual Phoenix that was imprisoned inside it.
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In Darken, the Regalia of Evil is comprised of a thorn crown, sword and gauntlet. By themselves, they have relatively minor effects. Get all three, and they fuse with the wielder, who gets exponentially more powerful.
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Kamen Rider OOO's belt is powered by inserting Core Medals into three slots, corresponding to the Head, Body, and Legs of his transformed form. Using three Medals of the same color creates a "Combo" which gives him increased powers and a new ability at the cost of leaving him exhausted when he powers down. The Greeed villains similarly gain increased powers the more Medals they have, along with a special Set Bonus of their own when they have all nine of their respective color. It's most notable with Gamel, whose bonus ability is a Touch of Death that takes him from the least dangerous of the Greeed to a Person of Mass Destruction.
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Digimon Card Game: While technically any Digimon can Digivolve from any other Digimon so long as the color requirements are met, certain Digivolution lines are specifically designed to work better together, whether it's from inherited effects that all have the same trigger, effects that only work if certain other cards are in their Digivolution cards, or outright searching for more cards of the same archetype. This extends to Tamers as well, as many have effects that either follow the same theme as their partners or explicitly mention them. A deck made from a random assortment of red digimon won't fare very well against a deck entirely devoted to the Greymon family.
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In Citadels, having all five types of districts in your city will give you bonus points in the final count.
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The Pokémon board game Master Trainer gives you a bonus if you collect Pokémon from the same evolutionary line. If you have two of them, the highest evolution gets a +3 attack bonus, and if you have 3, the highest gets a +5. The game leaves it up to house rules what to do if you get more of the Eeveelutions than just Eevee and an evolved form, since it's the only set in the game with more than 3 members and no defined "highest" evolutionnote the game was produced in Gen I, and the Eevee family was the only "branched evolution" in the franchise at the time.
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Magic: The Gathering:
The most ubiquitous example is the "Urzatron" lands: Urza's Mine, Urza's Tower, and Urza's Power Plant. They give one mana each normally, but if you control all three, you get a total of seven mana from them.
Visions had Feral Shadow, Breathstealer, and Urborg Panther. Sacrifice all three of them to bring Spirit of the Night into play directly from your deck.
Having Helm, Shield, and Sword of Kaldra all in play (each a strong card in their own right) and you can put a 4/4 legendary token creature (aptly named Kaldra) into play and attach all three of them to it for a much lower cost than attaching individually.
A storyline example appears in the Weatherlight Saga. The Legacy was Urza's ultimate weapon against Yawgmoth. Described as thought given purpose, the Legacy was a collection of artifacts and beings that was constantly changing and evolving, even incorporating artifacts that Urza didn't intend into its design. In card form, the Legacy Weapon is a single artifact card that can remove any permanent from the game. One of the artwork variants displays all of the artifacts that made up the Legacy. Nearly all of the component artifacts have cards of their own, too.
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The Meta-Nanites from Generator Rex, one lets you control temperature, one lets you control energy, one lets you control Gravity, one lets you control Time, and the last one imitates Rex's powerset. Each one is at least a class 3 on the super weight scale but linked through Rex they are at least a class 5 if not class 7.
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In Green Lantern this is the case when anyone wears more than one lantern ring, the wielder gets to essentially dual wield (or multi wield) superpowers. Combining different colored rings can be even more spectacular since they have interesting synergies. Hal Jordan has done this◊ twice with Green and Yellow rings. In Brightest Day, Krona did this with rings of every color!
Particularly notable here is the interaction between the Green and Blue rings, representing Will and Hope respectively, even when they're worn by separate wielders. The Blue rings are near-powerless on their own, but when Hope is bolstered by Will (the presence of a Green ring) it practically becomes capable of miracles. In turn, the power of Hope supercharges the Will of nearby Green rings.
Kyle Rayner learns the benefits and the downsides of using a ring of every color in the New 52. He later learns how to invoke this with a single ring, which leads to becoming a White Lantern.
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The Elements of Harmony from My Little Pony: Friendship Is Magic, individually they are just jewelry but together they can perform feats such as world healing waves.
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7 Wonders:
In the original game, the value of each scientific symbol increases if you gather several copies of one symbol (1/4/9/16/... points for 1/2/3/4... copies) or sets of three different ones (7 points per set).
In the Duel spin-off:
Scientific symbols are useless on their own, but getting a matching pair lets you take a Progress Token, and collecting 6 different ones is an Instant-Win Condition.
In Agora, each pair of 2 blue buildings gives you an additional Senate action whenever you take a Senator. This maxes out at 3 actions.
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In Yu-Gi-Oh!, the (Nameless) Pharaoh, aka Yami Yugi, cannot move on to the afterlife without all seven Millennium Items and knowledge of his true name.
In the card game, you can summon Exodia. He's five level 1 cards: two arms, two legs, and a head. On their own, they're weak as hell. Together? Instant win.
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Quite a few games have a scoring mechanism where a value of a set of cards increases faster than the number of cards. For instance, the point value of a set of Palace Guards in Guillotine or a set of unique artifacts in Stone Age equals the square (1, 4, 9, etc) of the number collected.
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Monopoly:
Owning an entire block of properties doubles the basic rent, and allows the owner to build houses and hotels to increase the rent further.
Railroads and Utilities have similar perks. Each Railroad the player owns doubles the rent. The two Utilities, the Electric Company and the Waterworks, normally charge rent equal to four times the number of the dice roll which landed the player on the Utility. If both Utilities are owned by one player, the multiplier is increased to ten.
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Yu-Gi-Oh!:
The five Exodia cards are worthless on their own. Get all five in your hand, and you automatically win the game. note They have to be in your hand; somehow managing to get all five onto the field, while an impressive feat, does nothing.
If all five Exodia cards are in the graveyard, the player can use "Contract with Exodia" to special summon "Exodia Necross", an invincible zombie that gets stronger every turn. The only way to get rid of it is to remove one of the Exodia cards from the graveyard.
There are dozens of archetypes that entire decks can be built around (Six Samurai, Laval, Ice Barrier, Evol, Archfiends...)
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