Variable Player powers is a mechanic that grants different abilities and/or paths to victory to the players. So in a game, each player will control a character, corporation, entity, or faction that are different from one another. It adds more choices and replayability in a game. RPGs were among the first with this mechanic with archetypes like cleric, fighter, wizard, rogue, and more. It makes each game play more unique. Most games, you play the same type of character with the same abilities or actions.
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Usually you find this mechanic in character driven games like One Deck Dungeon, Tiny Epic Defenders, Gloomhaven, Spirit Island, Shadows of Brimstone, and character packs of Hero Realms. But there are games where you are not a character but a faction or corporation like in Scythe, Small World, and Terraforming Mars.
So in a game like Spirit Island which is character driven, you have a variety of Spirits to play and each has strengths and weaknesses. Also each spirit has different innate abilities. For example Lightning's Swift Strike is very good at destroying the enemy towns and cities and can make it its abilities work before the enemy settlers do its turn. But its weakness is that it doesn't start with much energy to power its powers and has no defense against the settlers. Vital Strength of the Earth on the other hand starts with more energy and can gain more energy, but can only play very few cards per turn. He is very good at defense, but doesn't have much offensive abilities against the Settlers.
In Scythe, each faction has the same top and bottom actions, but they are grouped differently for each faction on their player boards. And when you buy a Mech, you unlock different abilities and most are unique to the faction.
Here is a list of games that has the Variable Player powers mechanic. Obviously there are more so please comment on any additional games that this mechanic I may have missed.
Tiny Epic Defenders
Tiny Epic Quest
King of Tokyo