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Three Approach System

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When games want to give different, distinct ways to play a game, 3 is a dime a dozen. This allows for a decent range of different gameplay styles while staying small in number.
Usually, players will be given a class or character who specialises in one approach. This can give replay value to single-player games, as players can go for a different specialisation on different playthroughs, while multiplayer games benefit from having clearly defined roles, giving a clear idea of what each player needs to do for their group. In more complex games, there may be a range of characters or classes who share one approach but handle them in different ways and/or are capable of dealing with more than one approach but not to the level of someone more specialised.
More rarely, a character may actually be capable of all three approaches with what style they go for up to the player. This is usually found in single-player games where the player only controls one character, as there is less of a need for defined roles.
While this is a gameplay trope, sometimes the approach of a character will affect the story as well. This can range in minor ways, different aftermaths for one-off quests from different methods, to outright Story Branching, with each approach essentially having its own story path.
Three Approach Systems commonly found in games:
Balance, Speed, Strength Trio: A fast but weak character, a strong but slow character, and an all-rounder.
Combat, Diplomacy, Stealth: Three paths commonly available in non-linear games, based on solving problems with either violence, words, or sneaking around them.
Damager, Healer, Tank: A trio mostly found in MMOs linked to damage (dealing it out, healing it, and soaking it up)
Fighter, Mage, Thief: Three classic RPG archetypes focusing on strength, sorcery, and finesse respectively.
Physical, Mystical, Technological: Similar to the above archetype, with hi-tech gadgets replacing finesse though the two tropes can sometimes overlap.
Compare with Three-Stat System, where character attributes follow Rule of Three. See also Balance, Power, Skill, Gimmick, where the three approaches are represented by three different playable characters plus a Jack of All Stats who's moderate in all approaches.
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Chrononauts has three ways to win: create a Close-Enough Timeline and go home, collect the artifacts for your secret mission and get paid a ton of money, or build up your hand size to ten cards (generally from rewards from fixing temporal paradoxes or selling artifacts) and retire in comfort. Any given play may put you closer to one or more of these, or put your opponent further away from theirs (you hope), or it may be a neutral move in hopes that your opponent wastes a countermove on it.
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Knights of the Old Republic starts out allowing the player to have the protagonist's combat-focused Soldier, utility focused Scoundrel and the balanced Scout. Eventually, the protagonist will gain levels in Jedi classes which fall into the Fighter, Mage, Thief trope with the Guardian, Consular and Sentinel filling one of those three roles respectively.
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Mobile rhythm games with a gachapon mechanic for cards typically abide by the system popularized by Love Live! School Idol Festival, where cards are split into three major archetypes: Scorers (increase score gain), Healers (regenerate lost HP), and Perfect Locks (convert notes above a certain judgment to Perfect judgments). How heavily the stick to these archetypes varies on the game; some games introduce a fourth archetype that boosts the activation rate of other cards, some make all cards boost score but give Scorers more raw power as a result, and so forth.
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Sonic Heroes have teams of three, each member fitting the archetype of Speed, Flight or Power. The current leader decides the current approach of the trio, with a Speed character leading allowing fast speeds and homing attacks, a Flight character leading allowing safety and an advantage against aerial enemies, and a Power character leading allowing powerful attacks.
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The late game of any nation in Civilization V is largely dictated by the chosen ideology, which increases the chances of achieving victory in any of the three "buffed" ways.note Bonuses for Cultural Victory are present in all ideologies, but the other two types differ.
Autocracy enhances the strength of units and the amount of strategic resources, allowing to significantly reinforce the existing army, which can be used both for direct territorial conquests and for pressure on scattered city-states in order to attain a Diplomatic Victory.
Freedom makes the economic component and improvements built by Great People even better, also encouraging a more active use of specialists, which helps both in the course of the space race and in the consolidation of city-states across the globe.
Order improves the individual performance of the civilization's cities, placing a particular emphasis on production, which will come in handy both to make spaceship components and to modernize the military and expand the empire's holdings.
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Street Fighter 6 is designed with three different ways to play and enjoy the game: World Tour, a Wide-Open Sandbox Action RPG where players can build a character of their own and interact with the core cast of the game; Battle Hub, a multiplayer hub where players can interact and play with one another; and Fighting Ground, where players can jump straight into fighting through a variety of modes, from arcade ladders to unique "Extreme" battles.
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The first 3 Geneforge games have a unique take with this trope with each class being strong, average, and weak in three areas (later games adding classes with the same logic).
Shapers are strong at making creations, average at spellcasting, and weak in melee combat.
Guardians are strong in melee combat, average at making creations, and weak at spellcasting.
Agents are strong at spellcasting, average at melee combat, and weak at making creations.
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Indiana Jones and the Fate of Atlantis has three separate paths through the game. They all lead to Atlantis eventually but the Fists path is more combat-oriented, the Wits path has more difficult puzzles, and the Team path is based on diplomacy and working together with Sophia.
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Team Fortress 2 divides the nine classes into three class roles.
Scouts, Soldiers, and Pyros are Offensive classes, being the main attack force of their teams.
Demomen, Heavies, and Engineers are Defensive classes, aiming to inhibit enemy access and to hold enemies back from vital points on the map.
Medic, Sniper, and Spy are Support classes, who cannot hold the fight on their own, but their specialised abilities can tip the balance in their team's favour.
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In 7 Wonders Duel, there are three ways to win the game: having the most Victory Points once all three Ages are over, Military Supremacy and Scientific Supremacy. The latter two are Instant-Win Conditions.
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The first Hexen game allows you to choose one of three characters to play the game with.
Baratus the Fighter, a strong, tough and quick warrior who lacks long-ranged weaponry.
Daedolon the Mage, who is slow and fragile but possesses powerful magic to keep enemies at bay.
Parias the Cleric, who has a mix of physical ability and magical power that allows both short-ranged and long-ranged combat to be an option.
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Freedom Planet's three heroines have different ways to tackle the stages:
Lilac the Water Dragon is innately the fastest of the three along with being capable of boost attack that can launch in any direction
Carol the Wild Cat can climb walls and has access to a motorcycle power-up. She can also deliver a flurry of kicks for as long as her energy bar is filled.
Milla Basset has less health than the other two heroines but makes up for it with ranged attacks and a deflector shield.
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