Rummy's scoring system can vary, but in certain iterations, players score points according to the cards that remain in their opponents' hands after one player leaves. Face cards, for example, are worth ten points ewin 101 ludoach, but numbered cards keep their face value. Score and Strategy. Players must balance their own progress toward melding while monitoring the possible moves of their opponents, which adds another level of strategy to this scoring system. Gamers can improve their chances of winning the game by keeping an eye on the cards that have been discarded and using that information to decide which cards to keep and which to discard.