More Games such as Playing Rummy.
With rummy a player needs to be more aware of what cards have been played than other card game. The main reason for this is because you are only using one single deck of cards, meaning that the likelihood of any card that has been discarded coming up again is rather slim. For example if you are chasing the ace of diamonds and it is at the bottom of the pile then you will have a really slim chance of acquiring that card, and this where a change of strategy will need to take place.
A player should also pay attention to what cards their opponent is throwing to the side. Although these cards do not have any significance to the opposition you could use them in an elimination process to tell what it is they are looking for. Gin Rummy is a great game to play.