Conquian

A rummy-type of card game played with a Spanish/Latino deck or a modified standard 52-card deck (8s, 9s and 10s removed).

A wikipedia entry describes the potential of Conquian as being the oldest or amongst the oldest of rummy-type games.

A version of the game includes dealing 7 or 8 cards to each player in a 4-player game or 9 cards in 3- or 2-player game (or 8 cards for a 2 player game). The object is to win by playing runs of 3 or more, 3 or 4 of a kind, or melds (or watching players having to meld) to your tableau (the winner's tableau must be the amount of the initial hand + 1 more card) and running out of cards in your hand.

The active player may use the the obligatory drawn card to lay down a run or 3+ of a kind. Your tableau may be arranged in to different melds or runs to accommodate new arrangements. When a set or multiple sets are laid a card must be discarded. If a card is passed, then next player clockwise and likewise is able to utilize the card. If during the same turn someone utilizes the discards (thus laying down sets and ending with another discard) then the process repeats. If no one has won, then the next player clockwise from the current active player continues with a draw.

Any cards melded to another player's tableau allow the opposing player to discard a card.