Rummy and melding games
Draw, discard, and lay down sets until somebody goes out. The argument is never about who won the hand; it is about what everyone else was still holding.
Where to start
These three are the ones most tables already half-know — and the ones the rest of this list makes sense from.
All 13 rummy and melding games
By player count
Of these 13, 13 work with two players and 12 with four. The links below cover the whole catalogue at each count, not just this page.