I'm having some trouble fully understanding composition and aggregation. From what i'm understanding a composition relationship means if one dies the other dies. aggregation means they're formed of that, but not necessarily dependent on that things continued existence.
This is the UML I put together for a game of hearts. Am I grasping this concept correctly?

What is composition and aggregation ?
The composition and aggregation represents a whole/part relationship (UML 2.5, section 11.5.3.1):
A binary Association may represent a composite aggregation (i.e., a
whole/part relationship).
So if you use a diamond, you should first ask yourself if it's really a whole/part relationship, before thinking how objects are created or deleted.
Then composition have additional constraints over a shared aggregation. In a composition relationship (UML 2.5, section 9.5.3):
(...) the composite object has responsibility for the existence and storage
of the composed objects.
Composite aggregation is a strong form of
aggregation that requires a part object be included in at most one
composite object at a time. If a composite object is deleted, all of
its part instances that are objects are deleted with it.
Analysis of your specific diagramm
According to your diagram:
- The players exists only within a game (i.e. temporary identification not accounts existing across several games). The composition could make sense, as players can be seen as parts of the game.
- The hand exist only in relation to a player. That makes sense. But is it really a composition relationship ? Is the hand a part of a player ? Is the player composed of hands ? Wouldn't a player have several hands sequentially but not in the same time ? I really have my doubt about a composition here; I'd represent this with a normal 1 player to many hands association.
- The game aggregates several decks. I don't know your game but I'd expect one deck. If several decks are used, and the decks only exists within a game (similarly to the players), I'd rather see a composition instead of an aggregation. Alternatively you could mean not the deck, but the deck together with its state. In this case, I'd opt for a one to many association and not a composition (the deck+state would not be a component of your game, but define the state of the game).
- A deck is the aggregation of cards that exist independently of the deck. This troubles me a lot, as my world experience has always shown that a card is part of a deck. If I find an isolated card somewhere I always look for it's deck. I'd therefore rather expect a composition between cards and deck.
- Finally a hand is the aggregation of several cards, which seems to make sense. Note that this is not incompatible with a composition between the deck and the card.