The difference between composition and aggregation is not whether a board can exist with zero pawns, but whether pawns can exist without boards, and also whether players and game boards can exist without a game.
In other words, if destroying a game will destroy all the players and boards then you have composition. If players and boards can live outside a game, then you have aggregation.
If destroying a board with destroy the pawns then you have composition. If pawns can live without a board, you have aggregation.
In general, if destroying the container destroys its elements, that's composition. Elements whose existence is not dependent on the container are said to be held by aggregation.
The classic examples of aggregation are:
- Countries within alliances, because countries continue to exist if the alliance is disbanded
- People within organizations, since the people still live when the organization ceases to exist
The classic examples of composition are:
- The schedule(s) of a person, since if the person goes away, the schedule does too.