Dummy Rummy: Game Rules, Variations, How To PlayGetMegaWe have covered the shanghai rummy hands in the section below. Shanghai Rummy Scoring . Shanghai rummy rules 7 rounds are followed below along with the progressive rummy rules and scoring. Value Of The Shanghai Rummy Cards. 3 to 9: 5 points each; 10 to King: 10 points each; Ace: 15 points; 2: 25 points; Joker: 50 points; The player going out