There is a family of card games known as climbing games. There are climbing games with many variants throughout the world and known by many names(Choh Dai Di, Chinese Poker, Kings and Asses, Scum, President, Dilbert's Corporate Shuffle, etc.).
Big Two is one popular variant.
Each player starts with a hand of cards and the object is to be the first to get rid of all your cards by playing combinations. The game consists of playing combinations of cards: single cards, pairs, three of a kind, and traditional poker hands (straights, flushes, etc.). When a player plays a combination, only a combination of that type can beat it - you must play a pair to beat a pair for instance. Big Two has a sizable luck element but there is room for skillful play as the players learn how to best manage the cards they are dealt. Best with four players, but still fun with two and three.
