The first player - called BoxMaker - tries to pick all elements of a single box.
The box game was first presented by Paul Erdős and Václav Chvátal.
In general, the optimal strategy for BoxBreaker is to break the boxes with the smallest number of remaining elements.
The optimal strategy for BoxMaker is to try to balance the sizes of all boxes.
By simulating these strategies, Hamidoune and Las-Vergnas[2] found a sufficient and necessary condition for each player in the (p:q) box game.