In order to form their melds while discarding unwanted cards, players alternately draw from the draw pile and the discard pile. The game goes on until either the draw pile runs out or onyou rummye player successfully melds all of their cards. As you advance in your rummy journey, becoming familiar with these fundamental components will lay a strong foundation for creating increasingly complex strategies. Monitoring Cards for Strategic Understanding. Keeping track of which cards have been discarded and which are still in play is one of the best practice methods.