When it is a player's turn, they can discard a card from their hand and draw a card from the discard pile. Setting the score for rummy. Therummy rainbow game goes until either no one declares "Rummy" and the draw pile runs out or until one player forms sets, runs with all of their cards, and declares "Rummy.". A player must place their sets and runs on the table so that all other players can see them when they declare rummy.