The game is set as a clash between neighboring dynasties at the dawn of civilization and is named after the rivers Tigris and Euphrates, in the region now called the Middle East.
The rivers together formed natural borders for an area which harboured several grand ancient civilizations, including Sumer, Babylonia, and Assyria.
Luck plays a role, as players draw tiles from a bag, but it is seldom decisive.
There are four types of tiles with corresponding leaders: temples and priests (red), farms and farmers (blue), markets and merchants (green), and settlements and kings (black).
During the game, players collect points in each of the four colors as a result of playing tiles, resolving conflicts and controlling monuments.