More elaborate varieties of Rummy were developed in the 1930s under the influence of Contract Bridge. In Contract Rummy, you're dealt an increasing number of cards in successive deals, and in each deal you can only go out by making a particular combination of melds. For example, from a 10-card hand you may be required to make a run of four and two sets of three. Contract Rummy remains one of the most popular domestic games of the whole family and is very much a folk game - that is, groups of players tend to have their own house rules and, as often as not, their own name for the game.

One of the most developed varieties of Rummy is Canasta. This has the Bridge-inspired distinction of being a four-player partnership game with a very formal code of rules and scores. Canasta dates from the 1940s and gave rise to highly elaborate versions such as Samba and Bolivia. Yet another branch of the Rummy family has the peculiarity that your melds are not private affairs.

Instead, all melds are laid face up on the table and on your turn to play you can add cards to them and re-form them into different melds, provided they all obey the rules of correct formation. This procedure is well known in the proprietary form of the game known as Rummikub, which dates from the 1970s and is played with tiles instead of cards. However, its basic principle goes back to earlier card games such as Carousel, Vatikan, and Czech Rummy.