The Shanghai Rummy scoring system may seem a little complex at first, but there are a number of ways to shed cards and win the game. It’s important to watch the cards closely and you may need to take a temporary drawback to secure victory. This may seem simple it is pretty easy to grasp the basics, but there are subtleties to master if you want to master this game. Players attempt to shed cards from their hand and the player that gets rid of all their cards first is declared the winner. Shanghai Rummy is an interesting version of a standard rummy game. We may earn a commission through products purchased using links on this page.