The Sioux is a cavalry based civilization with very powerful and balanced cavalry but mediocre infantry units.
The Sioux economy does not requires Houses for population, so players should focus on gathering Food in order to procure more villagers in the early game. In the late game, the extra resources can be used to build more buildings and military units, enabling an easier Boom strategy.
Sioux troops are weak against enemy Pikemen and Musketeers, so to counter these units the Sioux can train some Wakina Rifles, some Cetan Bows or Rifle Riders are also useful against them. To be successful in attacks, the Sioux should make their attacks short and quick. They also rely on hunting more then other civilazations, due to poor farm cards, so a good deck should include all buffalo cards. A good way the Sioux could attack is to use a large group of cavalry led by a War Chief (boosting speed and attack with a card), the Sioux should also spot weak spots in the enemy civilization's economy and attack and harass the enemy there constantly. Later in the game when the Sioux gets a substantial army of cavalry units they could use the Fire Dance and raid enemy villagers and destroy their buildings.
Defensive capabilities of the Sioux are limited as they cannot build walls, but they do have unique Teepees, which, can only build up to ten (exception when card sent) to provide a little health bonus (and attack to a degree with a card) to nearby friendly units.
The Sioux have a large selection of Cavalry Units to use, some only costing one population. It is best to use the diverse Cavalry when playing as the Sioux. Although it is not heavily advised, a Sioux player can train an all cavalry army and it would still be quite balanced. Ranged infantry can be countered by Axe Riders, Dog Soldiers, and Tashunke Prowlers. Heavy infantry can be beaten with Dog Soldiers and Rifle Riders. Cavalry can be destroyed with Bow Riders and Rifle Riders and artillery can be countered with any unit. Since they don't need to build houses they are great at rushing since the resources and time spent on houses can be diverted to building an army.
The Sioux navy is average since they are the only Native American civilization to lack the Water Dance. However they make up this through the Fire Dance which increases siege damage of units, allowing their canoes to handle other ships with relative ease. Plus they can have a larger navy due to able to send admiralty twice.