Rummy games
Rummy games are about sorting. You draw, you discard, and you try to arrange your hand into tidy groups before anybody else finishes theirs.
Every game in this family is built from two shapes. A set is three or four cards of the same rank. A run is three or more consecutive cards in one suit. Both are called melds, and your hand is a work-in-progress attempt to turn twelve unrelated cards into them.
The turn structure barely varies: draw one card from the stock or the discard pile, optionally put melds down, then discard one. What varies enormously is when the round ends and what the leftovers cost you. In basic Rummy you shed everything and the winner scores what the losers are still holding. Gin Rummy lets you end the round by knocking with a small amount of unmatched deadwood, and scores the difference — which turns it into a duel of judgement about when to stop improving and start finishing.
Canasta takes the same parts and inflates them: two decks, wild cards, a minimum value before your first meld counts, and a requirement to build a seven-card meld before you are allowed to go out at all. It plays much longer and much more cooperatively, since you and your partner are building a shared board.
Kings in the Corner is the odd one out and included because it belongs here in feel rather than lineage: no sets or runs, just a cross of piles you build down in alternating colours, with kings opening new space. It is the gentlest game in this group and the best one to teach a child.
The family is credited to Mexican or Chinese ancestry depending on which historian you read — the Chinese game Khanhoo and the Mexican Conquian are both cited as forerunners — and it reached its greatest popularity in the United States in the 1940s, when Canasta briefly outsold every other card game in the country.